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Mental
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March 29th, 2024 at 9:42:40 AM permalink
Quote: aceside

I quickly looked into this part of your results, quoting “

9,12,47,50,,6c,Qc,...,,3c,9c,2c,5c,8c,Jc,Ac,4c,7c,Ts,Ks
4,10,4,11,-0.099893,-0.116284,0.016391,0,1,2,3,5,6,7,8,9,12,50,,6c,Qc,...,,3c,9c,2c,5c,8c,Jc,Ac,4c,7c,Tc,Ks
4,10,4,11,-0.160931,-0.147615,-0.013317,0,1,2,3,5,6,7,8,9,11,12,,6c,Qc,...,,3c,9c,2c,5c,8c,Jc,Ac,4c,7c,Tc,Kc
4,10,4,0,-0.006074,-0.028120,0.022046,,6c,Qc,,
11,0.301115,13,19600,CSV

For the player hand, Q6, of suited clubs, player needs to see about eight exposed cards all the same suit of clubs to switch the strategy decision from basic Raise to Check, so the consideration of suitedness is unnecessary?

I think what Gordon says is reasonable, quoting “
Note that reducing the possibilty of large bonus payouts on straight and royal flushes will change the values of EV(Raise4) and EV(Check) but will not change the value of ΔEV because the bonus payouts depend upon the size of the bonus bet and will be unaffected by whether the ante bet has been raised or not.“
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Read what I said about this being a little tricky to interpret. You were able to peak at 11 exposed cards and none of them were matching your hole cards. Your hand is much stronger because of that. It takes a lot of flush penalties to counteract that. Suited exposed cards do matter. You just need to start from a fair baseline.
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gordonm888
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March 29th, 2024 at 10:34:37 AM permalink
Notice that all the EV and ΔEV values continue to decline even when the progression goes from 2 suited cards remaining in the deck to zero suited cards left. This continued reduction cannot be due to declining chances that player will make a flush - because with only two or fewer suited cards left there is already zero chance of making a flush.

So why do the EV values continue to decline?

Because you are increasing the probability that dealer will have a flush. By the time Mental has reached the cases where all 13 cards of one suit are seen (or in the players hand) he basically has a dealer drawing a 7 card hand from a 39 card deck with only three suits. Dealer will be getting fewer pairs but a much higher probability of getting straights or flushes. My quick calc is an over 16% chance of getting a 5-card (or longer) flush and over a 17% of getting a straight. Admittedly, this simple calc double counts 7 card hands that have both a straight and a flush (or a straight flush). But even with no suited cards seen, the Dealer has at least a 17.7% chance of having a straight when you see all 13 ranks (In your own hand plus in other hands) and you see no pairs.

So I think this choice of a highly correlated set of '11 cards seen by player' takes us down the rabbit hole into a wonderland where the dealer has atypical hand distributions. I suspect the most valuable information may be the values of the incremental changes in EV and ΔEV as additional "suitedness" occurs. Similar to EOR coefficients.
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Mental
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March 29th, 2024 at 1:41:10 PM permalink
Quote: gordonm888

Notice that all the EV and ΔEV values continue to decline even when the progression goes from 2 suited cards remaining in the deck to zero suited cards left. This continued reduction cannot be due to declining chances that player will make a flush - because with only two or fewer suited cards left there is already zero chance of making a flush.

So why do the EV values continue to decline?

Because you are increasing the probability that dealer will have a flush. By the time Mental has reached the cases where all 13 cards of one suit are seen (or in the players hand) he basically has a dealer drawing a 7 card hand from a 39 card deck with only three suits. Dealer will be getting fewer pairs but a much higher probability of getting straights or flushes. My quick calc is an over 16% chance of getting a 5-card (or longer) flush and over a 17% of getting a straight. Admittedly, this simple calc double counts 7 card hands that have both a straight and a flush (or a straight flush). But even with no suited cards seen, the Dealer has at least a 17.7% chance of having a straight when you see all 13 ranks (In your own hand plus in other hands) and you see no pairs.

So I think this choice of a highly correlated set of '11 cards seen by player' takes us down the rabbit hole into a wonderland where the dealer has atypical hand distributions. I suspect the most valuable information may be the values of the incremental changes in EV and ΔEV as additional "suitedness" occurs. Similar to EOR coefficients.
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Nice insight and explanation! I had noticed delta flush was not zero even when the player was drawing dead, but did not think of a reason. I am really busy and I am glad you clearly understood the format of my results without further explanation.

There are a lot of competing effects in the calculations the way I set them up. It was just easier for me to do it this way. The important thing is calculating the average delta from seeing an exposed card suited to your hole cards and then adjusting your strategy based on card ranks.

If you only see one exposed card, that cards was presumed to be 11/50ths suited to your hole cards before you saw it. Now, it is either 100% suited or 0% suited. If you see five cards, then you would expect one card to be suited. One suited card is neutral to the EV. You can apply a full delta if the number is different than one suited exposed card.
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aceside
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March 30th, 2024 at 5:42:47 AM permalink
The above argument is really convoluted! I only understand some part. Based on the results so far, I judge that exposed card suits are not important for pre-flop Raise/Check decisions. However, based on my experience, I think card suits should be important for post-flop strategic decisions, especially with flush-draw boards and hand situations.

Let me restore back to what I proposed earlier. We consider only these seven borderline player hands, all with the same suit of clubs:

K2, K3, K4, Q6, Q7, J8, J9.

In this calculation, we choose two exposed cards all the way, all with the same suit of clubs. Therefore, there are 7x55 such calculations.

Please help do this calculation if you have time. With the results, I’d like to extrapolate to other unknown situations. Thank you!
Last edited by: aceside on Mar 30, 2024
Mental
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March 30th, 2024 at 6:00:08 PM permalink
Quote: aceside

The above argument is really convoluted! I only understand some part. Based on the results so far, I judge that exposed card suits are not important for pre-flop Raise/Check decisions. However, based on my experience, I think card suits should be important for post-flop strategic decisions, especially with flush-draw boards and hand situations.

Let me restore back to what I proposed earlier. We consider only these seven borderline player hands, all with the same suit of clubs:

K2, K3, K4, Q6, Q7, J8, J9.

In this calculation, we choose two exposed cards all the way, all with the same suit of clubs. Therefore, there are 7x55 such calculations.

Please help do this calculation if you have time. With the results, I’d like to extrapolate to other unknown situations. Thank you!
link to original post



The fundamental issue is that you make your suited hand much stronger by taking flush cards out of the deck. This may seen like a paradox. However, any card in your suit is card that does not match the rank of either of your cards. Matching cards are worse penalties than flush cards. That is why I did the calculations the way I did.

I can do your calculation, but all it will show you is the relatively weak effects of SF and RF penalty cards.
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March 30th, 2024 at 9:56:37 PM permalink
Quote: Mental

Quote: aceside

The above argument is really convoluted! I only understand some part. Based on the results so far, I judge that exposed card suits are not important for pre-flop Raise/Check decisions. However, based on my experience, I think card suits should be important for post-flop strategic decisions, especially with flush-draw boards and hand situations.

Let me restore back to what I proposed earlier. We consider only these seven borderline player hands, all with the same suit of clubs:

K2, K3, K4, Q6, Q7, J8, J9.

In this calculation, we choose two exposed cards all the way, all with the same suit of clubs. Therefore, there are 7x55 such calculations.

Please help do this calculation if you have time. With the results, I’d like to extrapolate to other unknown situations. Thank you!
link to original post



The fundamental issue is that you make your suited hand much stronger by taking flush cards out of the deck. This may seen like a paradox. However, any card in your suit is card that does not match the rank of either of your cards. Matching cards are worse penalties than flush cards. That is why I did the calculations the way I did.

I can do your calculation, but all it will show you is the relatively weak effects of SF and RF penalty cards.
link to original post



I would suggest one case to show whether this is true or not.

Player: J8s No cards seen; Raise4 EV= ? Check EV = ? ΔEV = ??
Player: J8s Neighbor: T7s; Raise4 EV= ? Check EV = ? ΔEV = ??
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March 31st, 2024 at 7:02:54 AM permalink
Quote: gordonm888


link to original post

I would suggest one case to show whether this is true or not.

Player: J8s No cards seen; Raise4 EV= ? Check EV = ? ΔEV = ??
Player: J8s Neighbor: T7s; Raise4 EV= ? Check EV = ? ΔEV = ??
link to original post

I have to take back what I wrote. There are two competing effects that work in the opposite direction. But, I substantially overstated the effect of not having a matching rank. From the results below, you can see that the effect of knowing that two cards don't match your ranks is quite large (about 0.06 for raising and 0.45 for checking). Of course, this tilts you towards raising by 0.015.

But seeing that two SF cards are missing really kills the hand. The EV of raising drops by 0.27 versus 0.18 for checking and checking is strongly favored. The effect is half as large if the suited cards do not connect to your suited hand, for example Jc8c with 2c3c exposed.
Jc8c with no cards exposed
R: 0.107386 C: 0.096318 D: 0.011068
J8s with 7cTc exposed
R: -0.162852 C: -0.087866 D: -0.074986
J8s with 7dTd exposed
R: 0.166568 C: 0.140703 D: 0.025865
J8s with 2c3c exposed
R: -0.034039 C: 0.007935 D: -0.041974

6,9,4,0,0.107386,0.096318,0.011068,,8c,Jc,,,,
6,9,4,2,-0.162852,-0.087866,-0.074986,,8c,Jc,,,7c,Tc
6,9,4,2,0.166568,0.140703,0.025865,,8c,Jc,,,7d,Td
6,9,4,2,-0.034039,0.007935,-0.041974,,8c,Jc,,,2c,3c
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aceside
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March 31st, 2024 at 9:11:46 AM permalink
Excellent! About 0.06 for raising and 0.05 for checking.
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March 31st, 2024 at 9:40:58 AM permalink
Quote: Mental

Quote: gordonm888


link to original post

I would suggest one case to show whether this is true or not.

Player: J8s No cards seen; Raise4 EV= ? Check EV = ? ΔEV = ??
Player: J8s Neighbor: T7s; Raise4 EV= ? Check EV = ? ΔEV = ??
link to original post

I have to take back what I wrote. There are two competing effects that work in the opposite direction. But, I substantially overstated the effect of not having a matching rank. From the results below, you can see that the effect of knowing that two cards don't match your ranks is quite large (about 0.06 for raising and 0.45 for checking). Of course, this tilts you towards raising by 0.015.

But seeing that two SF cards are missing really kills the hand. The EV of raising drops by 0.27 versus 0.18 for checking and checking is strongly favored. The effect is half as large if the suited cards do not connect to your suited hand, for example Jc8c with 2c3c exposed.
Jc8c with no cards exposed
R: 0.107386 C: 0.096318 D: 0.011068
J8s with 7cTc exposed
R: -0.162852 C: -0.087866 D: -0.074986
J8s with 7dTd exposed
R: 0.166568 C: 0.140703 D: 0.025865
J8s with 2c3c exposed
R: -0.034039 C: 0.007935 D: -0.041974

6,9,4,0,0.107386,0.096318,0.011068,,8c,Jc,,,,
6,9,4,2,-0.162852,-0.087866,-0.074986,,8c,Jc,,,7c,Tc
6,9,4,2,0.166568,0.140703,0.025865,,8c,Jc,,,7d,Td
6,9,4,2,-0.034039,0.007935,-0.041974,,8c,Jc,,,2c,3c

link to original post



Brilliant. This is the post that we needed for suited hands. If this topic is game analyst porn, this post was the money shot.

To complete our grand tour through Effect of Removal (EOR) on ΔEV for 8Js if you would kindly calculate:
8cJc,,,2d3d
8cJc,,,KcAc
8cJc,,,KdAd
I expect these will all show that Raise4 is optimum, but it is the EOR coefficients that we need to complete our understanding of the relative importance of suited and unsuited Overs, Mediums and Unders to ΔEV of 8Js.
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Mental
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April 1st, 2024 at 12:03:31 PM permalink
I ran a number of close cases against a single exposed suited or unsuited card. I show a cart for Q6s below. The group on the left is for all of the possible suited exposed cards. On the extreme right is Q6s with no exposed cards. The rest are Q6s with an off-suit exposed card. The negative spikes are for 6 and Q, obviously. You can see all of the overcard, undercard, SF, and RF effects in a graph like this.



You can also compare the delta for different starting hands.
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aceside
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April 1st, 2024 at 1:04:49 PM permalink
From these graphs, I read this discovery, removing one suited under-card is enough to switch the strategic decision from Raise 4X to Check for player's suited hand Q6. In other words, if a player holds Qc6c, he will check this hand whenever seeing an exposed 2c, 3c, 4c, or 5c.
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April 1st, 2024 at 1:19:17 PM permalink
Quote: aceside

From these graphs, I read this discovery, removing one suited under-card is enough to switch the strategic decision from Raise 4X to Check for player's suited hand Q6. In other words, if a player holds Qc6c, he will check this hand whenever seeing an exposed 2c, 3c, 4c, or 5c.
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Yes, you are reading it right. But a suited 7 through J is as also a very marginal check since the delta is slightly negative. Q7s and Q8s never flip except for an off-suit matching rank. Even then, a Q or 8 is not enough to flip Q8s.
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aceside
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April 1st, 2024 at 1:47:29 PM permalink
The effect of middle card suits is secondary. Let me just speculate. Removing two suited under-cards should warrant a strategy switch from Raise 4X to Check for player's suited hand Q7. In other words, if a player holds Qc7c, he will check this hand whenever seeing two exposed 2c, 3c, 4c, 5c, or 6c.
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April 1st, 2024 at 3:23:13 PM permalink
Quote: aceside

The effect of middle card suits is secondary. Let me just speculate. Removing two suited under-cards should warrant a strategy switch from Raise 4X to Check for player's suited hand Q7. In other words, if a player holds Qc7c, he will check this hand whenever seeing two exposed 2c, 3c, 4c, 5c, or 6c.
link to original post

I was hoping you would have an equation that predicts the check and raise EVs based on the the singled exposed card. Then you would be quite confidant in your speculation.

You just need to make a linear equation and optimize the coefficients to match the known values for two exposed cards.
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April 1st, 2024 at 4:59:47 PM permalink
There is a tendency, I suspect, to overlook T9s which is normally checked. But it is a very close call

T9s
Raise4 EV = 0.185169
Check EV = 0.205485
ΔEV = -0.020316

To flip the decision, you need to see cards that improve the strength of T9s. The most powerful cards that improve T9s are offsuit J,Q,K,A. Note that a neighbor's hand with two offsuit overcards, particularly AoKo, is a monster: It increases your chances of pairing Tens or 9s, increases your flush chances, decreases the probability of Dealer making overpairs and even slightly increases your chances of making a straight.

In fact, I seem to remember that almost any two observed cards that are offsuit and not a rank match (i.e., not a T or 9) are usually sufficient to flip the decision. Certainly, I think a hand like (J-A)o, (2-5)o would be sufficient to flip. The small offsuit cards don't block a dealer overpair, but they also don't block a T9s from making a potential straight. I seem to remember that Ts9s get flipped with high frequency.

Doing an Effect of Removal Chart on 9sTs is fun -its an easy hand to understand and you see the effect of 6,7,8,J,Q,K on the potential for 9sTs making a straight. (hint, hint)
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Mental
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April 2nd, 2024 at 4:49:35 AM permalink
Quote: gordonm888

There is a tendency, I suspect, to overlook T9s which is normally checked. But it is a very close call

T9s
Raise4 EV = 0.185169
Check EV = 0.205485
ΔEV = -0.020316

To flip the decision, you need to see cards that improve the strength of T9s. The most powerful cards that improve T9s are offsuit J,Q,K,A. Note that a neighbor's hand with two offsuit overcards, particularly AoKo, is a monster: It increases your chances of pairing Tens or 9s, increases your flush chances, decreases the probability of Dealer making overpairs and even slightly increases your chances of making a straight.

In fact, I seem to remember that almost any two observed cards that are offsuit and not a rank match (i.e., not a T or 9) are usually sufficient to flip the decision. Certainly, I think a hand like (J-A)o, (2-5)o would be sufficient to flip. The small offsuit cards don't block a dealer overpair, but they also don't block a T9s from making a potential straight. I seem to remember that Ts9s get flipped with high frequency.

Doing an Effect of Removal Chart on 9sTs is fun -its an easy hand to understand and you see the effect of 6,7,8,J,Q,K on the potential for 9sTs making a straight. (hint, hint)
link to original post

Yes,T9s has very strong straight penalty effects plus minor SF effect and a very tiny RF effect. So suited Ace removal makes the hand stronger due to an overcard and the flush/RF penalty is not enough to keep it a check.

Seeing one unsuited 6,7,8,9, or T flips it to a raise.
,,,,Raise,Check,Delta,,,,,,
7,8,4,1,0.124096,0.170953,-0.046856,,9c,Tc,,,2c
7,8,4,1,0.130518,0.17258,-0.042062,,9c,Tc,,,3c
7,8,4,1,0.135353,0.173173,-0.037819,,9c,Tc,,,4c
7,8,4,1,0.141449,0.17605,-0.034601,,9c,Tc,,,5c
7,8,4,1,0.081796,0.134632,-0.052836,,9c,Tc,,,6c
7,8,4,1,0.022597,0.09288,-0.070283,,9c,Tc,,,7c
7,8,4,1,-0.035793,0.051102,-0.086895,,9c,Tc,,,8c
7,8,4,1,0.051674,0.086766,-0.035092,,9c,Tc,,,Jc
7,8,4,1,0.103621,0.126661,-0.023041,,9c,Tc,,,Qc
7,8,4,1,0.154299,0.166763,-0.012464,,9c,Tc,,,Kc
7,8,4,1,0.21012,0.209422,0.000698,,9c,Tc,,,Ac
,,,,,,,,,,,,
,,,,,,,,,,,,
,,,,,,,,,,,,
7,8,4,1,0.266402,0.254706,0.011696,,9c,Tc,,,2d
7,8,4,1,0.273266,0.256353,0.016913,,9c,Tc,,,3d
7,8,4,1,0.278695,0.256968,0.021727,,9c,Tc,,,4d
7,8,4,1,0.285406,0.260044,0.025362,,9c,Tc,,,5d
7,8,4,1,0.243811,0.240631,0.003179,,9c,Tc,,,6d
7,8,4,1,0.203229,0.221156,-0.017926,,9c,Tc,,,7d
7,8,4,1,0.163819,0.201754,-0.037935,,9c,Tc,,,8d
7,8,4,1,-0.117079,0.061441,-0.17852,,9c,Tc,,,9d
7,8,4,1,-0.100017,0.070766,-0.170783,,9c,Tc,,,Td
7,8,4,1,0.254551,0.245949,0.008602,,9c,Tc,,,Jd
7,8,4,1,0.287214,0.263442,0.023773,,9c,Tc,,,Qd
7,8,4,1,0.318409,0.281323,0.037086,,9c,Tc,,,Kd
7,8,4,1,0.3552,0.301651,0.053549,,9c,Tc,,,Ad
,,,,,,,,,,,,
7,8,4,0,0.185169,0.205485,-0.020316,,9c,Tc,,,
1,0.195409,25,19600,CSV,,,,,,,,

What is your guess about 98s? Can we just subtract off the base EV to get the answer?
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aceside
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April 2nd, 2024 at 8:41:06 AM permalink
I'm a little confused here. "Seeing one unsuited 6,7,8,9, or T flips it to a raise."
Should be seeing one unsuited 2, 3, 4, 5, or 6 flips it to a raise?
Another thing, before you consider this hand 98s, there is another hand T8s relatively more important to consider.

I think this work is a Nature Magazine material.
Last edited by: aceside on Apr 2, 2024
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April 2nd, 2024 at 9:23:26 AM permalink
Quote: aceside

I'm a little confused here. "Seeing one unsuited 6,7,8,9, or T flips it to a raise."
Should be seeing one unsuited 2, 3, 4, 5, or 6 flips it to a raise?
Another thing, before you consider this hand 98s, there is another hand T8s relatively more important to consider.

I think this work is a Nature Magazine material.
link to original post

Yes, you are right to be confused. I think I might have been looking at the x axis instead of translating the positive yellow bars into card ranks.

I actually set my MacBook to work doing every single case of XXs. I should have them all done by tomorrow.
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April 2nd, 2024 at 9:38:41 AM permalink
Quote: Mental


What is your guess about 98s? Can we just subtract off the base EV to get the answer?
link to original post



Close. But technically, the fraction of ranks that are overs (or unders) plays a role.

Basically, what counts is how much the observed two cards varies from a statistically averaged '2-card ensemble'. When considering K4 or K2s, there is only one overcard rank - Aces. So overcards to the K are relatively unexpected in a probabilisticly-weighted 2-card ensemble. And what you will find is that the observation of an Ace has a very strong positive effect on the EV of a two-card King-high hand.

T9s has 4 over-ranks and 7 under-ranks. Similarly, 98s has 5 over-ranks and 6 under-ranks. So, I would expect the overcards for 98s to have approximately 4/5 the effect of overcards for T9s, and the 98s undercards to have 7/6 of the influence of undercards for T9s.
*************************************
This is similar to the fact that the EV of a 33 pair is significantly degraded by the removal from the deck of a 2, whereas the EV of an 88 pair is much less affected by the removal of a single undercard, 2-7.
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Mental
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April 4th, 2024 at 12:33:56 PM permalink
Quote: gordonm888

Quote: Mental


What is your guess about 98s? Can we just subtract off the base EV to get the answer?
link to original post



Close. But technically, the fraction of ranks that are overs (or unders) plays a role.

Basically, what counts is how much the observed two cards varies from a statistically averaged '2-card ensemble'. When considering K4 or K2s, there is only one overcard rank - Aces. So overcards to the K are relatively unexpected in a probabilisticly-weighted 2-card ensemble. And what you will find is that the observation of an Ace has a very strong positive effect on the EV of a two-card King-high hand.

T9s has 4 over-ranks and 7 under-ranks. Similarly, 98s has 5 over-ranks and 6 under-ranks. So, I would expect the overcards for 98s to have approximately 4/5 the effect of overcards for T9s, and the 98s undercards to have 7/6 of the influence of undercards for T9s.
*************************************
This is similar to the fact that the EV of a 33 pair is significantly degraded by the removal from the deck of a 2, whereas the EV of an 88 pair is much less affected by the removal of a single undercard, 2-7.
link to original post


I started a big calculation on the MacBook two days ago without realizing I didn't match up the new program with the new indexing file that matches my new fast indexing method. The results were garbage. I restarted the run after recreating the index file and testing. I will post the entire set when I am done.

Here is a pair of graphs that gets at the point I was making. In the top graph, I compare Tc2c, J22c, Qc2c, and Kc2c against the whole set of single exposed cards, 3c-Ad. The y axis is the EV difference between raising and checking. Each increase in rank improves the difference by about 0.18. The only triplets showing deltas that are positive are Kc2c with the Ac and Kc2c with the off-suit cards that don't match your hole cards. These are the only raises among the 96 triplets.

In the bottom graph, I subtract off the average delta from the deltas of each of the triplets. This allows me to focus on what the exposed card is doing to the delta. Note that the scale is greatly expanded in the lower graph. The deltas for the four triplets with the 3c exposed only span -0.0054 in EV. The triplets with 4c and 5c are also tightly bunched. Then, starting with 6c, you see the SF penalties coming in to play. On the right, all triplets are tightly bunched (except when the exposed cards pairs the high card).

This rank of the hole cards dominates, of course, with a single rank being worth about 0.18. A suited exposed card lowers the EV by about 0.06 versus unsuited. A straight flush penalty if worth less than 0.01 for each step closer to the card it is interfering with. Straight penalties are about the same size.



Note that an exposed card matching the high card is worse than matching the low card by quite a lot. Also, you are hurt less by matching either card the higher the rank of the high card. The higher cards have more showdown value by themselves without improving.
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aceside
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April 4th, 2024 at 2:34:27 PM permalink
Excellent! We can call each of these results a spectrum. For each spectrum, the x-axis varies in the range of {2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K, A} and the y-axis is the value of DeltaEV=EV_Raise - EV_Check. The center of the spectrum is at x=8. The effect of removal (EOR) on DeltaEV is mirror symmetric around x=8, for flush, for straight penalties, straight flush penalties. The EOR of offsuit card rank is linearly increasing. The rank-matching exposure is just hole-burning.

With your results, I roughly got these numbers:

#1. For each rank-matching exposure card, EOR is ~0.12 for each card. Around the center line of x=8, EOR is ~0.15. Far away from x=8, EOR is ~ 1.0;

#2. For each suit-matching exposure card, EOR is ~ 0.03; Therefore, this contribution of suit exposure is about 1/4 of that of rank exposure;

#3. For each near-gap exposure card, EOR is about 0.02 or what? This number depends on the gap size of the player’s hand, such as suited connector 98 and suited one-gapper T-8. Close to the center line of x=8, the EOR should be relatively larger. I believe.
Last edited by: aceside on Apr 4, 2024
gordonm888
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April 4th, 2024 at 2:42:09 PM permalink
"Note that an exposed card matching the high card is worse than matching the low card by quite a lot. "

Yes, I've seen that too. Ex: almost all of the equity in A2 comes from pairing the Ace (once or multiple times). If all you do is pair the deuce, then you can only beat an Ace-High or lower -and you already have an Ace in your hand and thus a competitive Ace high!
**************
That last chart of yours is δ(ΔEVdecision)/ δ(removal of one card of ithrank) - something I've done when modeling computer perfect play on blackjack, but definitely on the edge of the frontier of published game analysis. (Wordy way of saying "Good stuff!")
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April 4th, 2024 at 2:43:27 PM permalink
I just want you guys to know how much I appreciate this thread. Although i have not been participating I read it and learn something everyday.
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Mental
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April 4th, 2024 at 3:05:28 PM permalink
I Casino Holdem, there is only one decision point. You don't get any gain from preserving optionality.

In UTH, if you check a hand because one of your cards is seen, you can gain some of the EV back by raising on a later street when you pair your somewhat dead card. Clearly, you recover more value when this happens with a high card. A low pair might won't be decisive in as many hands. This option value only accrues to the value of checking, so the delta, (EVr - EVc) should be smaller for seeing a card that matches a high cards.

I hope I am thinking about this correctly. I could investigate by doing a calculation with the decision on the later streets disabled.
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gordonm888
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April 4th, 2024 at 3:58:24 PM permalink
Quote: Mental

I Casino Holdem, there is only one decision point. You don't get any gain from preserving optionality.

In UTH, if you check a hand because one of your cards is seen, you can gain some of the EV back by raising on a later street when you pair your somewhat dead card. Clearly, you recover more value when this happens with a high card. A low pair might won't be decisive in as many hands. This option value only accrues to the value of checking, so the delta, (EVr - EVc) should be smaller for seeing a card that matches a high cards.

I hope I am thinking about this correctly. I could investigate by doing a calculation with the decision on the later streets disabled.
link to original post



That would be interesting.

My general impression is that the decision on the river bet is usually not as important as other decisions. There is only one unit at stake, most of the decisions depend upon "how good is my kicker on this strong board" and the margins are surprisingly thin.

Ages ago I looked at J9o and found that this hand was raised post flop over 40% of the time! Jacks, nines, straight draws, etc. So, for a close-call hand like J9o with two connected medium ranks the value of information to later decisions is probably key to why it is checked preflop.
Last edited by: gordonm888 on Apr 4, 2024
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aceside
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April 4th, 2024 at 8:33:13 PM permalink
Quote: Mental

In the top graph, I compare Tc2c, J22c, Qc2c, and Kc2c against the whole set of single exposed cards, 3c-Ad.


Upon more careful examination on these two graphs, I found a minor problem with your presentation. The situation with an exposed card Jc is missing in both figures on the left side.

Also, you wrote “The deltas for the four triplets with the 3c exposed only span -0.0054 in EV,” but I observed about -0.03 in EV in your graph. I don’t understand this part. Maybe you mean the difference among these four hands is only 0.0054?
Last edited by: aceside on Apr 4, 2024
Mental
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April 5th, 2024 at 6:01:15 AM permalink
Quote: aceside

Quote: Mental

In the top graph, I compare Tc2c, J22c, Qc2c, and Kc2c against the whole set of single exposed cards, 3c-Ad.


Upon more careful examination on these two graphs, I found a minor problem with your presentation. The situation with an exposed card Jc is missing in both figures on the left side.

Also, you wrote “The deltas for the four triplets with the 3c exposed only span -0.0054 in EV,” but I observed about -0.03 in EV in your graph. I don’t understand this part. Maybe you mean the difference among these four hands is only 0.0054?
link to original post

The 2c is missing in all four hands. A high card is missing in all four hands. I just arbitrarily used a set of labels with the Jc missing. You have to count bars to see which card is really missing. In the raw data set, the correct card is missing on the CSV row.

Here are the values for the first four bars of the second chart.
-0.03349 -0.03137 -0.03042 -0.02803
I claimed "The deltas for the four triplets with the 3c exposed only span -0.0054 in EV." Span means the difference from largest to smallest value. All this is saying is that if you have a 2c hole card and an exposed 3c, the EOR is almost the same if the high card is a Tc or Kc.
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Mental
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April 6th, 2024 at 8:46:29 AM permalink
This is a complete set of calculations for all combinations of two cards suited in clubs versus one exposed card of the club suit or of the diamond suit. I also include the reference case of two cards suited in clubs with no exposed card. The data is too large to fit in one post.

0,12,4,1,0.270450,0.077217,0.193233,,2c,Ac,,,3c
0,12,4,1,0.278019,0.080240,0.197779,,2c,Ac,,,4c
0,12,4,1,0.285705,0.083426,0.202279,,2c,Ac,,,5c
0,12,4,1,0.350158,0.131384,0.218774,,2c,Ac,,,6c
0,12,4,1,0.349681,0.130098,0.219583,,2c,Ac,,,7c
0,12,4,1,0.346639,0.128318,0.218321,,2c,Ac,,,8c
0,12,4,1,0.346621,0.128463,0.218158,,2c,Ac,,,9c
0,12,4,1,0.329497,0.114693,0.214803,,2c,Ac,,,Tc
0,12,4,1,0.322010,0.111469,0.210541,,2c,Ac,,,Jc
0,12,4,1,0.314499,0.108168,0.206331,,2c,Ac,,,Qc
0,12,4,1,0.306963,0.104794,0.202169,,2c,Ac,,,Kc
0,12,4,1,0.219556,0.068389,0.151167,,2c,Ac,,,2d
0,12,4,1,0.429431,0.190170,0.239262,,2c,Ac,,,3d
0,12,4,1,0.437662,0.193413,0.244249,,2c,Ac,,,4d
0,12,4,1,0.445854,0.196739,0.249115,,2c,Ac,,,5d
0,12,4,1,0.490778,0.221945,0.268833,,2c,Ac,,,6d
0,12,4,1,0.490079,0.220467,0.269612,,2c,Ac,,,7d
0,12,4,1,0.486489,0.218551,0.267938,,2c,Ac,,,8d
0,12,4,1,0.486599,0.218727,0.267873,,2c,Ac,,,9d
0,12,4,1,0.479264,0.215895,0.263369,,2c,Ac,,,Td
0,12,4,1,0.470995,0.212416,0.258580,,2c,Ac,,,Jd
0,12,4,1,0.462736,0.208868,0.253868,,2c,Ac,,,Qd
0,12,4,1,0.454486,0.205283,0.249203,,2c,Ac,,,Kd
0,12,4,1,0.143573,0.009147,0.134426,,2c,Ac,,,Ad
0,12,4,0,0.399855,0.166518,0.233337,,2c,Ac,,
1,12,4,1,0.336105,0.113830,0.222275,,3c,Ac,,,2c
1,12,4,1,0.373181,0.133809,0.239372,,3c,Ac,,,4c
1,12,4,1,0.380876,0.137049,0.243827,,3c,Ac,,,5c
1,12,4,1,0.444608,0.184868,0.259740,,3c,Ac,,,6c
1,12,4,1,0.443916,0.183395,0.260521,,3c,Ac,,,7c
1,12,4,1,0.452521,0.188152,0.264369,,3c,Ac,,,8c
1,12,4,1,0.449954,0.186713,0.263241,,3c,Ac,,,9c
1,12,4,1,0.432836,0.172877,0.259959,,3c,Ac,,,Tc
1,12,4,1,0.425349,0.169613,0.255737,,3c,Ac,,,Jc
1,12,4,1,0.417838,0.166307,0.251531,,3c,Ac,,,Qc
1,12,4,1,0.410302,0.162964,0.247338,,3c,Ac,,,Kc
1,12,4,1,0.492826,0.225893,0.266933,,3c,Ac,,,2d
1,12,4,1,0.316188,0.121546,0.194642,,3c,Ac,,,3d
1,12,4,1,0.531596,0.247153,0.284444,,3c,Ac,,,4d
1,12,4,1,0.539786,0.250545,0.289241,,3c,Ac,,,5d
1,12,4,1,0.584095,0.275893,0.308201,,3c,Ac,,,6d
1,12,4,1,0.583156,0.274207,0.308949,,3c,Ac,,,7d
1,12,4,1,0.591749,0.278314,0.313434,,3c,Ac,,,8d
1,12,4,1,0.589032,0.276843,0.312189,,3c,Ac,,,9d
1,12,4,1,0.581704,0.273933,0.307771,,3c,Ac,,,Td
1,12,4,1,0.573435,0.270414,0.303021,,3c,Ac,,,Jd
1,12,4,1,0.565176,0.266876,0.298300,,3c,Ac,,,Qd
1,12,4,1,0.556925,0.263318,0.293608,,3c,Ac,,,Kd
1,12,4,1,0.250401,0.069374,0.181027,,3c,Ac,,,Ad
1,12,4,0,0.496714,0.221372,0.275342,,3c,Ac,,
2,12,4,1,0.436235,0.169484,0.266751,,4c,Ac,,,2c
2,12,4,1,0.436145,0.168854,0.267291,,4c,Ac,,,3c
2,12,4,1,0.473149,0.188930,0.284219,,4c,Ac,,,5c
2,12,4,1,0.536179,0.236578,0.299601,,4c,Ac,,,6c
2,12,4,1,0.535274,0.234959,0.300314,,4c,Ac,,,7c
2,12,4,1,0.543524,0.239497,0.304027,,4c,Ac,,,8c
2,12,4,1,0.551840,0.244026,0.307814,,4c,Ac,,,9c
2,12,4,1,0.532323,0.228825,0.303498,,4c,Ac,,,Tc
2,12,4,1,0.524836,0.225544,0.299292,,4c,Ac,,,Jc
2,12,4,1,0.517326,0.222208,0.295118,,4c,Ac,,,Qc
2,12,4,1,0.509789,0.218900,0.290889,,4c,Ac,,,Kc
2,12,4,1,0.592136,0.281279,0.310857,,4c,Ac,,,2d
2,12,4,1,0.592363,0.281292,0.311072,,4c,Ac,,,3d
2,12,4,1,0.409376,0.172666,0.236709,,4c,Ac,,,4d
2,12,4,1,0.630919,0.302615,0.328304,,4c,Ac,,,5d
2,12,4,1,0.674470,0.327917,0.346552,,4c,Ac,,,6d
2,12,4,1,0.673291,0.326067,0.347224,,4c,Ac,,,7d
2,12,4,1,0.681650,0.330032,0.351618,,4c,Ac,,,8d
2,12,4,1,0.690303,0.334016,0.356287,,4c,Ac,,,9d
2,12,4,1,0.680322,0.329692,0.350631,,4c,Ac,,,Td
2,12,4,1,0.672054,0.326153,0.345901,,4c,Ac,,,Jd
2,12,4,1,0.663794,0.322604,0.341190,,4c,Ac,,,Qd
2,12,4,1,0.655544,0.319063,0.336481,,4c,Ac,,,Kd
2,12,4,1,0.353312,0.127211,0.226101,,4c,Ac,,,Ad
2,12,4,0,0.590105,0.274105,0.316000,,4c,Ac,,
3,12,4,1,0.542233,0.227836,0.314397,,5c,Ac,,,2c
3,12,4,1,0.542335,0.227186,0.315149,,5c,Ac,,,3c
3,12,4,1,0.542341,0.226676,0.315665,,5c,Ac,,,4c
3,12,4,1,0.635438,0.291685,0.343753,,5c,Ac,,,6c
3,12,4,1,0.634325,0.289941,0.344383,,5c,Ac,,,7c
3,12,4,1,0.642199,0.294256,0.347943,,5c,Ac,,,8c
3,12,4,1,0.650156,0.298533,0.351623,,5c,Ac,,,9c
3,12,4,1,0.641284,0.289059,0.352225,,5c,Ac,,,Tc
3,12,4,1,0.631405,0.284469,0.346936,,5c,Ac,,,Jc
3,12,4,1,0.623894,0.281119,0.342775,,5c,Ac,,,Qc
3,12,4,1,0.616358,0.277778,0.338580,,5c,Ac,,,Kc
3,12,4,1,0.697024,0.339347,0.357677,,5c,Ac,,,2d
3,12,4,1,0.697457,0.339342,0.358115,,5c,Ac,,,3d
3,12,4,1,0.697797,0.339507,0.358290,,5c,Ac,,,4d
3,12,4,1,0.510965,0.227345,0.283619,,5c,Ac,,,5d
3,12,4,1,0.772439,0.383404,0.389035,,5c,Ac,,,6d
3,12,4,1,0.771018,0.381377,0.389641,,5c,Ac,,,7d
3,12,4,1,0.778994,0.385171,0.393823,,5c,Ac,,,8d
3,12,4,1,0.787409,0.389035,0.398374,,5c,Ac,,,9d
3,12,4,1,0.788524,0.389856,0.398668,,5c,Ac,,,Td
3,12,4,1,0.777610,0.384976,0.392634,,5c,Ac,,,Jd
3,12,4,1,0.769351,0.381397,0.387953,,5c,Ac,,,Qd
3,12,4,1,0.761100,0.377744,0.383357,,5c,Ac,,,Kd
3,12,4,1,0.459935,0.186213,0.273722,,5c,Ac,,,Ad
3,12,4,0,0.690217,0.329747,0.360470,,5c,Ac,,
4,12,4,1,0.551554,0.223497,0.328057,,6c,Ac,,,2c
4,12,4,1,0.552009,0.223186,0.328823,,6c,Ac,,,3c
4,12,4,1,0.552241,0.222694,0.329547,,6c,Ac,,,4c
4,12,4,1,0.552352,0.222218,0.330135,,6c,Ac,,,5c
4,12,4,1,0.583484,0.239408,0.344077,,6c,Ac,,,7c
4,12,4,1,0.591272,0.243528,0.347744,,6c,Ac,,,8c
4,12,4,1,0.598856,0.247553,0.351303,,6c,Ac,,,9c
4,12,4,1,0.589617,0.237856,0.351761,,6c,Ac,,,Tc
4,12,4,1,0.590267,0.238858,0.351409,,6c,Ac,,,Jc
4,12,4,1,0.580370,0.234225,0.346145,,6c,Ac,,,Qc
4,12,4,1,0.572834,0.230900,0.341934,,6c,Ac,,,Kc
4,12,4,1,0.686818,0.313388,0.373429,,6c,Ac,,,2d
4,12,4,1,0.687581,0.313665,0.373916,,6c,Ac,,,3d
4,12,4,1,0.688159,0.313805,0.374354,,6c,Ac,,,4d
4,12,4,1,0.688625,0.313985,0.374639,,6c,Ac,,,5d
4,12,4,1,0.447620,0.168886,0.278733,,6c,Ac,,,6d
4,12,4,1,0.720241,0.331555,0.388687,,6c,Ac,,,7d
4,12,4,1,0.728138,0.335181,0.392958,,6c,Ac,,,8d
4,12,4,1,0.736172,0.338818,0.397355,,6c,Ac,,,9d
4,12,4,1,0.737038,0.339556,0.397482,,6c,Ac,,,Td
4,12,4,1,0.737088,0.339683,0.397404,,6c,Ac,,,Jd
4,12,4,1,0.726190,0.334752,0.391438,,6c,Ac,,,Qd
4,12,4,1,0.717940,0.331156,0.386784,,6c,Ac,,,Kd
4,12,4,1,0.414681,0.138658,0.276023,,6c,Ac,,,Ad
4,12,4,0,0.649275,0.285699,0.363575,,6c,Ac,,
5,12,4,1,0.675912,0.291930,0.383982,,7c,Ac,,,2c
5,12,4,1,0.676781,0.291807,0.384974,,7c,Ac,,,3c
5,12,4,1,0.677381,0.291513,0.385868,,7c,Ac,,,4c
5,12,4,1,0.677741,0.291064,0.386677,,7c,Ac,,,5c
5,12,4,1,0.675685,0.289951,0.385734,,7c,Ac,,,6c
5,12,4,1,0.709471,0.309737,0.399735,,7c,Ac,,,8c
5,12,4,1,0.716897,0.313668,0.403228,,7c,Ac,,,9c
5,12,4,1,0.707281,0.303863,0.403418,,7c,Ac,,,Tc
5,12,4,1,0.707534,0.304636,0.402898,,7c,Ac,,,Jc
5,12,4,1,0.708063,0.305539,0.402524,,7c,Ac,,,Qc
5,12,4,1,0.698146,0.300763,0.397383,,7c,Ac,,,Kc
5,12,4,1,0.810304,0.382089,0.428215,,7c,Ac,,,2d
5,12,4,1,0.811330,0.382569,0.428761,,7c,Ac,,,3d
5,12,4,1,0.812251,0.382895,0.429356,,7c,Ac,,,4d
5,12,4,1,0.812974,0.383091,0.429884,,7c,Ac,,,5d
5,12,4,1,0.810637,0.381787,0.428851,,7c,Ac,,,6d
5,12,4,1,0.557574,0.228440,0.329134,,7c,Ac,,,7d
5,12,4,1,0.844776,0.401970,0.442806,,7c,Ac,,,8d
5,12,4,1,0.852665,0.405679,0.446986,,7c,Ac,,,9d
5,12,4,1,0.853149,0.406277,0.446872,,7c,Ac,,,Td
5,12,4,1,0.852912,0.406316,0.446596,,7c,Ac,,,Jd
5,12,4,1,0.852859,0.406408,0.446450,,7c,Ac,,,Qd
5,12,4,1,0.841978,0.401192,0.440786,,7c,Ac,,,Kd
5,12,4,1,0.533475,0.205109,0.328367,,7c,Ac,,,Ad
5,12,4,0,0.767431,0.351951,0.415480,,7c,Ac,,
6,12,4,1,0.782340,0.352076,0.430263,,8c,Ac,,,2c
6,12,4,1,0.789753,0.355383,0.434370,,8c,Ac,,,3c
6,12,4,1,0.790755,0.355329,0.435426,,8c,Ac,,,4c
6,12,4,1,0.791487,0.355078,0.436409,,8c,Ac,,,5c
6,12,4,1,0.789592,0.353963,0.435629,,8c,Ac,,,6c
6,12,4,1,0.779860,0.348804,0.431057,,8c,Ac,,,7c
6,12,4,1,0.816634,0.370356,0.446277,,8c,Ac,,,9c
6,12,4,1,0.806853,0.360417,0.446435,,8c,Ac,,,Tc
6,12,4,1,0.806717,0.361058,0.445659,,8c,Ac,,,Jc
6,12,4,1,0.806813,0.361783,0.445029,,8c,Ac,,,Qc
6,12,4,1,0.807218,0.362695,0.444523,,8c,Ac,,,Kc
6,12,4,1,0.915118,0.442258,0.472860,,8c,Ac,,,2d
6,12,4,1,0.923522,0.445889,0.477632,,8c,Ac,,,3d
6,12,4,1,0.924703,0.446441,0.478262,,8c,Ac,,,4d
6,12,4,1,0.925779,0.446816,0.478963,,8c,Ac,,,5d
6,12,4,1,0.923594,0.445483,0.478111,,8c,Ac,,,6d
6,12,4,1,0.913284,0.440653,0.472631,,8c,Ac,,,7d
6,12,4,1,0.650302,0.279029,0.371273,,8c,Ac,,,8d
6,12,4,1,0.950830,0.462630,0.488200,,8c,Ac,,,9d
6,12,4,1,0.951159,0.463097,0.488062,,8c,Ac,,,Td
6,12,4,1,0.950527,0.463042,0.487485,,8c,Ac,,,Jd
6,12,4,1,0.950144,0.463073,0.487071,,8c,Ac,,,Qd
6,12,4,1,0.949988,0.463192,0.486797,,8c,Ac,,,Kd
6,12,4,1,0.629879,0.259587,0.370292,,8c,Ac,,,Ad
6,12,4,0,0.868890,0.409619,0.459271,,8c,Ac,,
7,12,4,1,0.869927,0.402212,0.467714,,9c,Ac,,,2c
7,12,4,1,0.878136,0.405981,0.472155,,9c,Ac,,,3c
7,12,4,1,0.885549,0.409436,0.476112,,9c,Ac,,,4c
7,12,4,1,0.886682,0.409444,0.477238,,9c,Ac,,,5c
7,12,4,1,0.885071,0.408497,0.476574,,9c,Ac,,,6c
7,12,4,1,0.875607,0.403201,0.472407,,9c,Ac,,,7c
7,12,4,1,0.867875,0.398971,0.468904,,9c,Ac,,,8c
7,12,4,1,0.894373,0.410915,0.483458,,9c,Ac,,,Tc
7,12,4,1,0.894059,0.411442,0.482616,,9c,Ac,,,Jc
7,12,4,1,0.893771,0.412027,0.481744,,9c,Ac,,,Qc
7,12,4,1,0.893699,0.412748,0.480952,,9c,Ac,,,Kc
7,12,4,1,1.001410,0.492126,0.509285,,9c,Ac,,,2d
7,12,4,1,1.010359,0.496279,0.514080,,9c,Ac,,,3d
7,12,4,1,1.018763,0.500144,0.518620,,9c,Ac,,,4d
7,12,4,1,1.020100,0.500747,0.519353,,9c,Ac,,,5d
7,12,4,1,1.018160,0.499543,0.518616,,9c,Ac,,,6d
7,12,4,1,1.008128,0.494482,0.513646,,9c,Ac,,,7d
7,12,4,1,1.000066,0.490490,0.509575,,9c,Ac,,,8d
7,12,4,1,0.724294,0.319972,0.404323,,9c,Ac,,,9d
7,12,4,1,1.037076,0.513204,0.523872,,9c,Ac,,,Td
7,12,4,1,1.036277,0.513042,0.523235,,9c,Ac,,,Jd
7,12,4,1,1.035505,0.512945,0.522559,,9c,Ac,,,Qd
7,12,4,1,1.034967,0.513001,0.521966,,9c,Ac,,,Kd
7,12,4,1,0.706043,0.303432,0.402611,,9c,Ac,,,Ad
7,12,4,0,0.953564,0.458240,0.495324,,9c,Ac,,
8,12,4,1,1.352315,0.804482,0.547833,,Tc,Ac,,,2c
8,12,4,1,1.360535,0.808349,0.552186,,Tc,Ac,,,3c
8,12,4,1,1.368754,0.812403,0.556352,,Tc,Ac,,,4c
8,12,4,1,1.376166,0.815987,0.560178,,Tc,Ac,,,5c
8,12,4,1,1.374860,0.815285,0.559575,,Tc,Ac,,,6c
8,12,4,1,1.365774,0.809952,0.555822,,Tc,Ac,,,7c
8,12,4,1,1.358295,0.805589,0.552706,,Tc,Ac,,,8c
8,12,4,1,1.356069,0.805132,0.550937,,Tc,Ac,,,9c
8,12,4,1,1.087918,0.535471,0.552446,,Tc,Ac,,,Jc
8,12,4,1,1.087454,0.535949,0.551505,,Tc,Ac,,,Qc
8,12,4,1,1.087010,0.536481,0.550529,,Tc,Ac,,,Kc
8,12,4,1,1.481176,0.893293,0.587883,,Tc,Ac,,,2d
8,12,4,1,1.490139,0.897535,0.592604,,Tc,Ac,,,3d
8,12,4,1,1.499102,0.901964,0.597138,,Tc,Ac,,,4d
8,12,4,1,1.507506,0.906048,0.601458,,Tc,Ac,,,5d
8,12,4,1,1.505710,0.905043,0.600667,,Tc,Ac,,,6d
8,12,4,1,1.496036,0.899859,0.596177,,Tc,Ac,,,7d
8,12,4,1,1.488229,0.895760,0.592469,,Tc,Ac,,,8d
8,12,4,1,1.485843,0.895282,0.590561,,Tc,Ac,,,9d
8,12,4,1,1.193792,0.712474,0.481319,,Tc,Ac,,,Td
8,12,4,1,1.480895,0.890996,0.589900,,Tc,Ac,,,Jd
8,12,4,1,1.479948,0.890802,0.589146,,Tc,Ac,,,Qd
8,12,4,1,1.479037,0.890688,0.588349,,Tc,Ac,,,Kd
8,12,4,1,1.176072,0.697499,0.478572,,Tc,Ac,,,Ad
8,12,4,0,1.409312,0.837884,0.571428,,Tc,Ac,,
9,12,4,1,1.434946,0.854175,0.580770,,Jc,Ac,,,2c
9,12,4,1,1.443177,0.858148,0.585029,,Jc,Ac,,,3c
9,12,4,1,1.451408,0.862170,0.589237,,Jc,Ac,,,4c
9,12,4,1,1.459636,0.866362,0.593275,,Jc,Ac,,,5c
9,12,4,1,1.464321,0.869351,0.594970,,Jc,Ac,,,6c
9,12,4,1,1.455635,0.863959,0.591677,,Jc,Ac,,,7c
9,12,4,1,1.448545,0.859708,0.588837,,Jc,Ac,,,8c
9,12,4,1,1.446522,0.859289,0.587233,,Jc,Ac,,,9c
9,12,4,1,1.142103,0.567131,0.574972,,Jc,Ac,,,Tc
9,12,4,1,1.171650,0.586420,0.585230,,Jc,Ac,,,Qc
9,12,4,1,1.171019,0.586831,0.584188,,Jc,Ac,,,Kc
9,12,4,1,1.562652,0.942415,0.620238,,Jc,Ac,,,2d
9,12,4,1,1.571629,0.946824,0.624805,,Jc,Ac,,,3d
9,12,4,1,1.580606,0.951252,0.629354,,Jc,Ac,,,4d
9,12,4,1,1.589583,0.955797,0.633786,,Jc,Ac,,,5d
9,12,4,1,1.594517,0.958415,0.636102,,Jc,Ac,,,6d
9,12,4,1,1.585103,0.953154,0.631949,,Jc,Ac,,,7d
9,12,4,1,1.577666,0.949132,0.628533,,Jc,Ac,,,8d
9,12,4,1,1.575506,0.948702,0.626803,,Jc,Ac,,,9d
9,12,4,1,1.534682,0.922428,0.612254,,Jc,Ac,,,Td
9,12,4,1,1.253181,0.747238,0.505943,,Jc,Ac,,,Jd
9,12,4,1,1.563019,0.940759,0.622260,,Jc,Ac,,,Qd
9,12,4,1,1.561929,0.940519,0.621409,,Jc,Ac,,,Kd
9,12,4,1,1.245385,0.739549,0.505837,,Jc,Ac,,,Ad
9,12,4,0,1.489507,0.886020,0.603486,,Jc,Ac,,
10,12,4,1,1.521024,0.905581,0.615443,,Qc,Ac,,,2c
10,12,4,1,1.529267,0.909774,0.619493,,Qc,Ac,,,3c
10,12,4,1,1.537508,0.913911,0.623597,,Qc,Ac,,,4c
10,12,4,1,1.545748,0.918049,0.627699,,Qc,Ac,,,5c
10,12,4,1,1.551223,0.921578,0.629645,,Qc,Ac,,,6c
10,12,4,1,1.548238,0.919752,0.628486,,Qc,Ac,,,7c
10,12,4,1,1.541537,0.915577,0.625960,,Qc,Ac,,,8c
10,12,4,1,1.539718,0.915168,0.624550,,Qc,Ac,,,9c
10,12,4,1,1.236376,0.623359,0.613016,,Qc,Ac,,,Tc
10,12,4,1,1.228146,0.619238,0.608908,,Qc,Ac,,,Jc
10,12,4,1,1.257483,0.638420,0.619063,,Qc,Ac,,,Kc
10,12,4,1,1.647568,0.993246,0.654322,,Qc,Ac,,,2d
10,12,4,1,1.656558,0.997865,0.658693,,Qc,Ac,,,3d
10,12,4,1,1.665549,1.002439,0.663110,,Qc,Ac,,,4d
10,12,4,1,1.674540,1.006995,0.667545,,Qc,Ac,,,5d
10,12,4,1,1.680011,1.010013,0.669998,,Qc,Ac,,,6d
10,12,4,1,1.677005,1.008245,0.668760,,Qc,Ac,,,7d
10,12,4,1,1.669815,1.004247,0.665567,,Qc,Ac,,,8d
10,12,4,1,1.667881,1.003845,0.664036,,Qc,Ac,,,9d
10,12,4,1,1.628182,0.977972,0.650209,,Qc,Ac,,,Td
10,12,4,1,1.619187,0.973358,0.645829,,Qc,Ac,,,Jd
10,12,4,1,1.315493,0.783181,0.532311,,Qc,Ac,,,Qd
10,12,4,1,1.647062,0.991408,0.655654,,Qc,Ac,,,Kd
10,12,4,1,1.317473,0.782855,0.534618,,Qc,Ac,,,Ad
10,12,4,0,1.572705,0.935691,0.637014,,Qc,Ac,,
11,12,4,1,1.609895,0.958433,0.651462,,Kc,Ac,,,2c
11,12,4,1,1.618148,0.962771,0.655378,,Kc,Ac,,,3c
11,12,4,1,1.626401,0.967099,0.659302,,Kc,Ac,,,4c
11,12,4,1,1.634652,0.971384,0.663268,,Kc,Ac,,,5c
11,12,4,1,1.640042,0.974824,0.665218,,Kc,Ac,,,6c
11,12,4,1,1.638207,0.973533,0.664675,,Kc,Ac,,,7c
11,12,4,1,1.636312,0.972636,0.663676,,Kc,Ac,,,8c
11,12,4,1,1.634697,0.972249,0.662448,,Kc,Ac,,,9c
11,12,4,1,1.332196,0.680752,0.651444,,Kc,Ac,,,Tc
11,12,4,1,1.323956,0.676486,0.647470,,Kc,Ac,,,Jc
11,12,4,1,1.315714,0.672094,0.643620,,Kc,Ac,,,Qc
11,12,4,1,1.735277,1.045561,0.689716,,Kc,Ac,,,2d
11,12,4,1,1.744281,1.050331,0.693950,,Kc,Ac,,,3d
11,12,4,1,1.753285,1.055083,0.698202,,Kc,Ac,,,4d
11,12,4,1,1.762290,1.059785,0.702505,,Kc,Ac,,,5d
11,12,4,1,1.767658,1.062781,0.704877,,Kc,Ac,,,6d
11,12,4,1,1.765602,1.061415,0.704187,,Kc,Ac,,,7d
11,12,4,1,1.763834,1.060591,0.703243,,Kc,Ac,,,8d
11,12,4,1,1.762127,1.060196,0.701931,,Kc,Ac,,,9d
11,12,4,1,1.723046,1.034552,0.688493,,Kc,Ac,,,Td
11,12,4,1,1.714037,1.029831,0.684206,,Kc,Ac,,,Jd
11,12,4,1,1.705029,1.024952,0.680077,,Kc,Ac,,,Qd
11,12,4,1,1.380054,0.820044,0.560010,,Kc,Ac,,,Kd
11,12,4,1,1.392179,0.827246,0.564933,,Kc,Ac,,,Ad
11,12,4,0,1.658326,0.986740,0.671586,,Kc,Ac,,

0,11,4,1,-0.166345,-0.135889,-0.030456,,2c,Kc,,,3c
0,11,4,1,-0.159245,-0.133323,-0.025922,,2c,Kc,,,4c
0,11,4,1,-0.152028,-0.130535,-0.021493,,2c,Kc,,,5c
0,11,4,1,-0.144369,-0.126795,-0.017574,,2c,Kc,,,6c
0,11,4,1,-0.135668,-0.122336,-0.013332,,2c,Kc,,,7c
0,11,4,1,-0.138288,-0.123883,-0.014405,,2c,Kc,,,8c
0,11,4,1,-0.145915,-0.127261,-0.018654,,2c,Kc,,,9c
0,11,4,1,-0.163060,-0.140693,-0.022368,,2c,Kc,,,Tc
0,11,4,1,-0.170085,-0.143390,-0.026695,,2c,Kc,,,Jc
0,11,4,1,-0.177128,-0.145984,-0.031144,,2c,Kc,,,Qc
0,11,4,1,-0.104592,-0.111245,0.006653,,2c,Kc,,,Ac
0,11,4,1,-0.290594,-0.189085,-0.101509,,2c,Kc,,,2d
0,11,4,1,-0.021237,-0.044637,0.023400,,2c,Kc,,,3d
0,11,4,1,-0.013555,-0.041985,0.028429,,2c,Kc,,,4d
0,11,4,1,-0.005912,-0.039151,0.033239,,2c,Kc,,,5d
0,11,4,1,0.001863,-0.036077,0.037940,,2c,Kc,,,6d
0,11,4,1,0.010552,-0.032400,0.042952,,2c,Kc,,,7d
0,11,4,1,0.007745,-0.033954,0.041699,,2c,Kc,,,8d
0,11,4,1,-0.000725,-0.036878,0.036153,,2c,Kc,,,9d
0,11,4,1,-0.007837,-0.039169,0.031331,,2c,Kc,,,Td
0,11,4,1,-0.015555,-0.041990,0.026435,,2c,Kc,,,Jd
0,11,4,1,-0.023265,-0.044707,0.021442,,2c,Kc,,,Qd
0,11,4,1,-0.367642,-0.251488,-0.116153,,2c,Kc,,,Kd
0,11,4,1,0.036625,-0.015087,0.051712,,2c,Kc,,,Ad
0,11,4,0,-0.074507,-0.079920,0.005413,,2c,Kc,
1,11,4,1,-0.064162,-0.084189,0.020027,,3c,Kc,,,4c
1,11,4,1,-0.056936,-0.081406,0.024469,,3c,Kc,,,5c
1,11,4,1,-0.049681,-0.077994,0.028313,,3c,Kc,,,6c
1,11,4,1,-0.041344,-0.073784,0.032440,,3c,Kc,,,7c
1,11,4,1,-0.032993,-0.070237,0.037244,,3c,Kc,,,8c
1,11,4,1,-0.043119,-0.074569,0.031451,,3c,Kc,,,9c
1,11,4,1,-0.060258,-0.088024,0.027766,,3c,Kc,,,Tc
1,11,4,1,-0.067283,-0.090687,0.023404,,3c,Kc,,,Jc
1,11,4,1,-0.074326,-0.093275,0.018949,,3c,Kc,,,Qc
1,11,4,1,-0.001767,-0.058218,0.056451,,3c,Kc,,,Ac
1,11,4,1,0.042002,-0.012601,0.054604,,3c,Kc,,,2d
1,11,4,1,-0.195131,-0.141985,-0.053146,,3c,Kc,,,3d
1,11,4,1,0.080282,0.007600,0.072682,,3c,Kc,,,4d
1,11,4,1,0.087922,0.010423,0.077499,,3c,Kc,,,5d
1,11,4,1,0.095290,0.013170,0.082120,,3c,Kc,,,6d
1,11,4,1,0.103761,0.016722,0.087039,,3c,Kc,,,7d
1,11,4,1,0.112419,0.019518,0.092901,,3c,Kc,,,8d
1,11,4,1,0.101196,0.015674,0.085521,,3c,Kc,,,9d
1,11,4,1,0.094090,0.013365,0.080725,,3c,Kc,,,Td
1,11,4,1,0.086373,0.010575,0.075799,,3c,Kc,,,Jd
1,11,4,1,0.078663,0.007844,0.070818,,3c,Kc,,,Qd
1,11,4,1,-0.261186,-0.196905,-0.064281,,3c,Kc,,,Kd
1,11,4,1,0.138599,0.037732,0.100867,,3c,Kc,,,Ad
1,11,4,0,0.022000,-0.030195,0.052195,,3c,Kc,
2,11,4,1,0.000190,-0.051924,0.052115,,4c,Kc,,,3c
2,11,4,1,0.036865,-0.032715,0.069580,,4c,Kc,,,5c
2,11,4,1,0.043738,-0.029607,0.073345,,4c,Kc,,,6c
2,11,4,1,0.051731,-0.025644,0.077375,,4c,Kc,,,7c
2,11,4,1,0.059721,-0.022314,0.082034,,4c,Kc,,,8c
2,11,4,1,0.060488,-0.021637,0.082125,,4c,Kc,,,9c
2,11,4,1,0.040855,-0.036051,0.076907,,4c,Kc,,,Tc
2,11,4,1,0.033830,-0.038702,0.072532,,4c,Kc,,,Jc
2,11,4,1,0.026788,-0.041262,0.068049,,4c,Kc,,,Qc
2,11,4,1,0.099494,-0.005731,0.105224,,4c,Kc,,,Ac
2,11,4,1,0.142881,0.039387,0.103494,,4c,Kc,,,2d
2,11,4,1,0.142498,0.039261,0.103237,,4c,Kc,,,3d
2,11,4,1,-0.100794,-0.095286,-0.005508,,4c,Kc,,,4d
2,11,4,1,0.180520,0.059607,0.120913,,4c,Kc,,,5d
2,11,4,1,0.187464,0.062040,0.125424,,4c,Kc,,,6d
2,11,4,1,0.195596,0.065343,0.130253,,4c,Kc,,,7d
2,11,4,1,0.204035,0.068041,0.135995,,4c,Kc,,,8d
2,11,4,1,0.204186,0.068459,0.135727,,4c,Kc,,,9d
2,11,4,1,0.194336,0.065213,0.129123,,4c,Kc,,,Td
2,11,4,1,0.186618,0.062428,0.124191,,4c,Kc,,,Jd
2,11,4,1,0.178908,0.059716,0.119192,,4c,Kc,,,Qd
2,11,4,1,-0.156504,-0.143214,-0.013290,,4c,Kc,,,Kd
2,11,4,1,0.239037,0.090053,0.148984,,4c,Kc,,,Ad
2,11,4,0,0.117016,0.018917,0.098099,,4c,Kc,
3,11,4,1,0.108294,0.002721,0.105572,,5c,Kc,,,3c
3,11,4,1,0.107808,0.001941,0.105867,,5c,Kc,,,4c
3,11,4,1,0.145157,0.021800,0.123358,,5c,Kc,,,6c
3,11,4,1,0.152826,0.025534,0.127293,,5c,Kc,,,7c
3,11,4,1,0.160437,0.028626,0.131810,,5c,Kc,,,8c
3,11,4,1,0.160843,0.029080,0.131763,,5c,Kc,,,9c
3,11,4,1,0.151999,0.019709,0.132290,,5c,Kc,,,Tc
3,11,4,1,0.142481,0.016107,0.126374,,5c,Kc,,,Jc
3,11,4,1,0.135438,0.013500,0.121939,,5c,Kc,,,Qc
3,11,4,1,0.208311,0.049666,0.158645,,5c,Kc,,,Ac
3,11,4,1,0.249652,0.093798,0.155854,,5c,Kc,,,2d
3,11,4,1,0.249456,0.093688,0.155768,,5c,Kc,,,3d
3,11,4,1,0.249185,0.093641,0.155545,,5c,Kc,,,4d
3,11,4,1,0.002431,-0.045471,0.047902,,5c,Kc,,,5d
3,11,4,1,0.287551,0.113921,0.173630,,5c,Kc,,,6d
3,11,4,1,0.295324,0.116997,0.178327,,5c,Kc,,,7d
3,11,4,1,0.303381,0.119481,0.183900,,5c,Kc,,,8d
3,11,4,1,0.303314,0.119781,0.183533,,5c,Kc,,,9d
3,11,4,1,0.304718,0.120836,0.183882,,5c,Kc,,,Td
3,11,4,1,0.294256,0.117098,0.177158,,5c,Kc,,,Jd
3,11,4,1,0.286546,0.114314,0.172232,,5c,Kc,,,Qd
3,11,4,1,-0.047661,-0.088189,0.040529,,5c,Kc,,,Kd
3,11,4,1,0.346888,0.145356,0.201532,,5c,Kc,,,Ad
3,11,4,0,0.219148,0.070638,0.148510,,5c,Kc,
4,11,4,1,0.208398,0.053602,0.154796,,6c,Kc,,,3c
4,11,4,1,0.208124,0.052874,0.155250,,6c,Kc,,,4c
4,11,4,1,0.207743,0.052171,0.155573,,6c,Kc,,,5c
4,11,4,1,0.240708,0.070780,0.169928,,6c,Kc,,,7c
4,11,4,1,0.248099,0.073785,0.174314,,6c,Kc,,,8c
4,11,4,1,0.248127,0.074010,0.174117,,6c,Kc,,,9c
4,11,4,1,0.238908,0.064389,0.174518,,6c,Kc,,,Tc
4,11,4,1,0.240068,0.065663,0.174405,,6c,Kc,,,Jc
4,11,4,1,0.230539,0.061932,0.168607,,6c,Kc,,,Qc
4,11,4,1,0.309582,0.101593,0.207989,,6c,Kc,,,Ac
4,11,4,1,0.348582,0.143718,0.204864,,6c,Kc,,,2d
4,11,4,1,0.348733,0.143812,0.204921,,6c,Kc,,,3d
4,11,4,1,0.348682,0.143763,0.204919,,6c,Kc,,,4d
4,11,4,1,0.348537,0.143783,0.204754,,6c,Kc,,,5d
4,11,4,1,0.079322,-0.008817,0.088139,,6c,Kc,,,6d
4,11,4,1,0.381908,0.162591,0.219317,,6c,Kc,,,7d
4,11,4,1,0.389743,0.165041,0.224702,,6c,Kc,,,8d
4,11,4,1,0.389296,0.165119,0.224177,,6c,Kc,,,9d
4,11,4,1,0.390463,0.166013,0.224450,,6c,Kc,,,Td
4,11,4,1,0.391130,0.166440,0.224690,,6c,Kc,,,Jd
4,11,4,1,0.380683,0.162509,0.218174,,6c,Kc,,,Qd
4,11,4,1,0.044480,-0.041149,0.085629,,6c,Kc,,,Kd
4,11,4,1,0.448010,0.196655,0.251354,,6c,Kc,,,Ad
4,11,4,0,0.309149,0.116480,0.192669,,6c,Kc,
5,11,4,1,0.314365,0.109466,0.204899,,7c,Kc,,,3c
5,11,4,1,0.314455,0.108941,0.205514,,7c,Kc,,,4c
5,11,4,1,0.314308,0.108296,0.206012,,7c,Kc,,,5c
5,11,4,1,0.305660,0.104229,0.201431,,7c,Kc,,,6c
5,11,4,1,0.340808,0.123778,0.217030,,7c,Kc,,,8c
5,11,4,1,0.340677,0.123869,0.216808,,7c,Kc,,,9c
5,11,4,1,0.331078,0.114036,0.217041,,7c,Kc,,,Tc
5,11,4,1,0.331833,0.115103,0.216730,,7c,Kc,,,Jc
5,11,4,1,0.332878,0.116209,0.216669,,7c,Kc,,,Qc
5,11,4,1,0.409909,0.156121,0.253788,,7c,Kc,,,Ac
5,11,4,1,0.453453,0.198693,0.254760,,7c,Kc,,,2d
5,11,4,1,0.453864,0.198950,0.254915,,7c,Kc,,,3d
5,11,4,1,0.454157,0.199126,0.255031,,7c,Kc,,,4d
5,11,4,1,0.454252,0.199156,0.255096,,7c,Kc,,,5d
5,11,4,1,0.445062,0.195515,0.249547,,7c,Kc,,,6d
5,11,4,1,0.163904,0.034524,0.129381,,7c,Kc,,,7d
5,11,4,1,0.481002,0.215475,0.265528,,7c,Kc,,,8d
5,11,4,1,0.480406,0.215453,0.264953,,7c,Kc,,,9d
5,11,4,1,0.481193,0.216121,0.265072,,7c,Kc,,,Td
5,11,4,1,0.481586,0.216419,0.265167,,7c,Kc,,,Jd
5,11,4,1,0.482147,0.216654,0.265493,,7c,Kc,,,Qd
5,11,4,1,0.136977,0.008919,0.128057,,7c,Kc,,,Kd
5,11,4,1,0.546982,0.250935,0.296047,,7c,Kc,,,Ad
5,11,4,0,0.403899,0.167172,0.236727,,7c,Kc,
6,11,4,1,0.401664,0.155624,0.246039,,8c,Kc,,,3c
6,11,4,1,0.402148,0.155319,0.246828,,8c,Kc,,,4c
6,11,4,1,0.402370,0.154920,0.247450,,8c,Kc,,,5c
6,11,4,1,0.393964,0.150638,0.243325,,8c,Kc,,,6c
6,11,4,1,0.385590,0.146958,0.238632,,8c,Kc,,,7c
6,11,4,1,0.421317,0.168014,0.253303,,8c,Kc,,,9c
6,11,4,1,0.411523,0.157979,0.253544,,8c,Kc,,,Tc
6,11,4,1,0.411887,0.158778,0.253109,,8c,Kc,,,Jc
6,11,4,1,0.412489,0.159693,0.252795,,8c,Kc,,,Qc
6,11,4,1,0.491363,0.200479,0.290884,,8c,Kc,,,Ac
6,11,4,1,0.532575,0.241887,0.290688,,8c,Kc,,,2d
6,11,4,1,0.540529,0.244480,0.296049,,8c,Kc,,,3d
6,11,4,1,0.541096,0.244844,0.296252,,8c,Kc,,,4d
6,11,4,1,0.541544,0.245137,0.296407,,8c,Kc,,,5d
6,11,4,1,0.532603,0.241179,0.291423,,8c,Kc,,,6d
6,11,4,1,0.523750,0.238053,0.285697,,8c,Kc,,,7d
6,11,4,1,0.229541,0.067970,0.161571,,8c,Kc,,,8d
6,11,4,1,0.559610,0.259372,0.300238,,8c,Kc,,,9d
6,11,4,1,0.560232,0.259786,0.300446,,8c,Kc,,,Td
6,11,4,1,0.560231,0.259848,0.300383,,8c,Kc,,,Jd
6,11,4,1,0.560480,0.260012,0.300468,,8c,Kc,,,Qd
6,11,4,1,0.207769,0.047539,0.160229,,8c,Kc,,,Kd
6,11,4,1,0.627249,0.295048,0.332201,,8c,Kc,,,Ad
6,11,4,0,0.481611,0.209086,0.272526,,8c,Kc,
7,11,4,1,0.625608,0.298465,0.327143,,9c,Kc,,,3c
7,11,4,1,0.632651,0.300984,0.331667,,9c,Kc,,,4c
7,11,4,1,0.633267,0.300757,0.332511,,9c,Kc,,,5c
7,11,4,1,0.625217,0.296522,0.328694,,9c,Kc,,,6c
7,11,4,1,0.617121,0.292787,0.324334,,9c,Kc,,,7c
7,11,4,1,0.615340,0.292937,0.322403,,9c,Kc,,,8c
7,11,4,1,0.586635,0.261624,0.325011,,9c,Kc,,,Tc
7,11,4,1,0.586812,0.262269,0.324544,,9c,Kc,,,Jc
7,11,4,1,0.587031,0.263037,0.323994,,9c,Kc,,,Qc
7,11,4,1,0.721551,0.349098,0.372453,,9c,Kc,,,Ac
7,11,4,1,0.753282,0.383441,0.369841,,9c,Kc,,,2d
7,11,4,1,0.761683,0.386833,0.374849,,9c,Kc,,,3d
7,11,4,1,0.769636,0.389609,0.380028,,9c,Kc,,,4d
7,11,4,1,0.770359,0.390049,0.380310,,9c,Kc,,,5d
7,11,4,1,0.761753,0.386165,0.375588,,9c,Kc,,,6d
7,11,4,1,0.753188,0.382913,0.370275,,9c,Kc,,,7d
7,11,4,1,0.751324,0.383167,0.368157,,9c,Kc,,,8d
7,11,4,1,0.437906,0.199828,0.238079,,9c,Kc,,,9d
7,11,4,1,0.752542,0.384366,0.368176,,9c,Kc,,,Td
7,11,4,1,0.752354,0.384279,0.368076,,9c,Kc,,,Jd
7,11,4,1,0.752211,0.384384,0.367827,,9c,Kc,,,Qd
7,11,4,1,0.421430,0.184557,0.236873,,9c,Kc,,,Kd
7,11,4,1,0.855475,0.442729,0.412747,,9c,Kc,,,Ad
7,11,4,0,0.694571,0.344751,0.349820,,9c,Kc,
8,11,4,1,1.105996,0.697536,0.408460,,Tc,Kc,,,3c
8,11,4,1,1.113746,0.700807,0.412939,,Tc,Kc,,,4c
8,11,4,1,1.120730,0.703611,0.417119,,Tc,Kc,,,5c
8,11,4,1,1.113182,0.699349,0.413833,,Tc,Kc,,,6c
8,11,4,1,1.105450,0.695772,0.409678,,Tc,Kc,,,7c
8,11,4,1,1.103550,0.695817,0.407732,,Tc,Kc,,,8c
8,11,4,1,1.047500,0.653151,0.394349,,Tc,Kc,,,9c
8,11,4,1,0.779096,0.382928,0.396168,,Tc,Kc,,,Jc
8,11,4,1,0.779123,0.383574,0.395549,,Tc,Kc,,,Qc
8,11,4,1,0.912037,0.469792,0.442245,,Tc,Kc,,,Ac
8,11,4,1,1.231021,0.781535,0.449487,,Tc,Kc,,,2d
8,11,4,1,1.239435,0.784953,0.454482,,Tc,Kc,,,3d
8,11,4,1,1.247850,0.788404,0.459446,,Tc,Kc,,,4d
8,11,4,1,1.255738,0.791468,0.464270,,Tc,Kc,,,5d
8,11,4,1,1.247524,0.787491,0.460033,,Tc,Kc,,,6d
8,11,4,1,1.239303,0.784398,0.454905,,Tc,Kc,,,7d
8,11,4,1,1.237314,0.784545,0.452768,,Tc,Kc,,,8d
8,11,4,1,1.200371,0.763609,0.436762,,Tc,Kc,,,9d
8,11,4,1,0.907304,0.590823,0.316481,,Tc,Kc,,,Td
8,11,4,1,1.195451,0.759074,0.436377,,Tc,Kc,,,Jd
8,11,4,1,1.195114,0.759051,0.436063,,Tc,Kc,,,Qd
8,11,4,1,0.888383,0.575943,0.312440,,Tc,Kc,,,Kd
8,11,4,1,1.296793,0.817601,0.479192,,Tc,Kc,,,Ad
8,11,4,0,1.148469,0.721297,0.427172,,Tc,Kc,
9,11,4,1,1.187442,0.745488,0.441954,,Jc,Kc,,,3c
9,11,4,1,1.195204,0.748770,0.446433,,Jc,Kc,,,4c
9,11,4,1,1.202963,0.752190,0.450774,,Jc,Kc,,,5c
9,11,4,1,1.201343,0.750783,0.450560,,Jc,Kc,,,6c
9,11,4,1,1.193993,0.747370,0.446623,,Jc,Kc,,,7c
9,11,4,1,1.192285,0.747484,0.444801,,Jc,Kc,,,8c
9,11,4,1,1.137126,0.705023,0.432103,,Jc,Kc,,,9c
9,11,4,1,0.832183,0.413391,0.418792,,Jc,Kc,,,Tc
9,11,4,1,0.862346,0.432372,0.429974,,Jc,Kc,,,Qc
9,11,4,1,0.994704,0.518418,0.476286,,Jc,Kc,,,Ac
9,11,4,1,1.311286,0.829058,0.482228,,Jc,Kc,,,2d
9,11,4,1,1.319714,0.832493,0.487221,,Jc,Kc,,,3d
9,11,4,1,1.328142,0.835970,0.492172,,Jc,Kc,,,4d
9,11,4,1,1.336571,0.839593,0.496978,,Jc,Kc,,,5d
9,11,4,1,1.335023,0.838119,0.496905,,Jc,Kc,,,6d
9,11,4,1,1.327063,0.835123,0.491940,,Jc,Kc,,,7d
9,11,4,1,1.325286,0.835361,0.489925,,Jc,Kc,,,8d
9,11,4,1,1.289272,0.814621,0.474651,,Jc,Kc,,,9d
9,11,4,1,1.248102,0.789304,0.458798,,Jc,Kc,,,Td
9,11,4,1,0.965959,0.624660,0.341299,,Jc,Kc,,,Jd
9,11,4,1,1.277253,0.807472,0.469782,,Jc,Kc,,,Qd
9,11,4,1,0.956600,0.617254,0.339346,,Jc,Kc,,,Kd
9,11,4,1,1.378311,0.865762,0.512549,,Jc,Kc,,,Ad
9,11,4,0,1.227500,0.767587,0.459913,,Jc,Kc,
10,11,4,1,1.275616,0.796335,0.479281,,Qc,Kc,,,3c
10,11,4,1,1.283388,0.799654,0.483735,,Qc,Kc,,,4c
10,11,4,1,1.291159,0.803102,0.488057,,Qc,Kc,,,5c
10,11,4,1,1.290611,0.802321,0.488290,,Qc,Kc,,,6c
10,11,4,1,1.288078,0.801476,0.486602,,Qc,Kc,,,7c
10,11,4,1,1.286562,0.801658,0.484904,,Qc,Kc,,,8c
10,11,4,1,1.232115,0.759408,0.472707,,Qc,Kc,,,9c
10,11,4,1,0.928244,0.468248,0.459996,,Qc,Kc,,,Tc
10,11,4,1,0.920483,0.464996,0.455487,,Qc,Kc,,,Jc
10,11,4,1,1.083387,0.569651,0.513736,,Qc,Kc,,,Ac
10,11,4,1,1.398237,0.879476,0.518761,,Qc,Kc,,,2d
10,11,4,1,1.406678,0.883016,0.523662,,Qc,Kc,,,3d
10,11,4,1,1.415120,0.886537,0.528583,,Qc,Kc,,,4d
10,11,4,1,1.423562,0.890199,0.533363,,Qc,Kc,,,5d
10,11,4,1,1.422886,0.889278,0.533608,,Qc,Kc,,,6d
10,11,4,1,1.420373,0.888491,0.531883,,Qc,Kc,,,7d
10,11,4,1,1.418810,0.888759,0.530051,,Qc,Kc,,,8d
10,11,4,1,1.383355,0.868177,0.515178,,Qc,Kc,,,9d
10,11,4,1,1.343317,0.843337,0.499980,,Qc,Kc,,,Td
10,11,4,1,1.334871,0.839792,0.495079,,Qc,Kc,,,Jd
10,11,4,1,1.031147,0.660938,0.370209,,Qc,Kc,,,Qd
10,11,4,1,1.030522,0.660640,0.369882,,Qc,Kc,,,Kd
10,11,4,1,1.465632,0.916387,0.549245,,Qc,Kc,,,Ad
10,11,4,0,1.312620,0.816408,0.496213,,Qc,Kc,
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
Mental
  • Threads: 16
  • Posts: 1549
Joined: Dec 10, 2018
April 6th, 2024 at 8:48:37 AM permalink
0,10,4,1,-0.485057,-0.275342,-0.209714,,2c,Qc,,,3c
0,10,4,1,-0.478411,-0.273567,-0.204844,,2c,Qc,,,4c
0,10,4,1,-0.471648,-0.271618,-0.200030,,2c,Qc,,,5c
0,10,4,1,-0.463867,-0.268334,-0.195534,,2c,Qc,,,6c
0,10,4,1,-0.455455,-0.264902,-0.190553,,2c,Qc,,,7c
0,10,4,1,-0.465639,-0.268205,-0.197434,,2c,Qc,,,8c
0,10,4,1,-0.473221,-0.271134,-0.202088,,2c,Qc,,,9c
0,10,4,1,-0.490345,-0.284021,-0.206324,,2c,Qc,,,Tc
0,10,4,1,-0.496918,-0.285919,-0.210999,,2c,Qc,,,Jc
0,10,4,1,-0.427703,-0.253673,-0.174031,,2c,Qc,,,Kc
0,10,4,1,-0.427766,-0.253995,-0.173771,,2c,Qc,,,Ac
0,10,4,1,-0.632293,-0.336449,-0.295844,,2c,Qc,,,2d
0,10,4,1,-0.335962,-0.184826,-0.151136,,2c,Qc,,,3d
0,10,4,1,-0.328810,-0.182969,-0.145842,,2c,Qc,,,4d
0,10,4,1,-0.321697,-0.180944,-0.140754,,2c,Qc,,,5d
0,10,4,1,-0.313737,-0.178272,-0.135464,,2c,Qc,,,6d
0,10,4,1,-0.305044,-0.175526,-0.129518,,2c,Qc,,,7d
0,10,4,1,-0.316372,-0.178375,-0.137997,,2c,Qc,,,8d
0,10,4,1,-0.324598,-0.180855,-0.143743,,2c,Qc,,,9d
0,10,4,1,-0.331579,-0.182597,-0.148982,,2c,Qc,,,Td
0,10,4,1,-0.338765,-0.184646,-0.154119,,2c,Qc,,,Jd
0,10,4,1,-0.700462,-0.394388,-0.306074,,2c,Qc,,,Qd
0,10,4,1,-0.281150,-0.156901,-0.124249,,2c,Qc,,,Kd
0,10,4,1,-0.281300,-0.157293,-0.124007,,2c,Qc,,,Ad
0,10,4,0,-0.391427,-0.220440,-0.170987,,2c,Qc,
1,10,4,1,-0.382560,-0.225739,-0.156820,,3c,Qc,,,4c
1,10,4,1,-0.375788,-0.223773,-0.152015,,3c,Qc,,,5c
1,10,4,1,-0.368413,-0.220694,-0.147719,,3c,Qc,,,6c
1,10,4,1,-0.360374,-0.217600,-0.142774,,3c,Qc,,,7c
1,10,4,1,-0.359513,-0.216539,-0.142974,,3c,Qc,,,8c
1,10,4,1,-0.369679,-0.220187,-0.149492,,3c,Qc,,,9c
1,10,4,1,-0.386796,-0.233171,-0.153625,,3c,Qc,,,Tc
1,10,4,1,-0.393370,-0.235134,-0.158235,,3c,Qc,,,Jc
1,10,4,1,-0.324265,-0.202159,-0.122106,,3c,Qc,,,Kc
1,10,4,1,-0.324127,-0.202351,-0.121776,,3c,Qc,,,Ac
1,10,4,1,-0.271828,-0.153814,-0.118014,,3c,Qc,,,2d
1,10,4,1,-0.536277,-0.291642,-0.244634,,3c,Qc,,,3d
1,10,4,1,-0.234228,-0.134557,-0.099671,,3c,Qc,,,4d
1,10,4,1,-0.227118,-0.132547,-0.094571,,3c,Qc,,,5d
1,10,4,1,-0.219563,-0.130073,-0.089490,,3c,Qc,,,6d
1,10,4,1,-0.211075,-0.127605,-0.083470,,3c,Qc,,,7d
1,10,4,1,-0.210866,-0.126784,-0.084081,,3c,Qc,,,8d
1,10,4,1,-0.221925,-0.129947,-0.091978,,3c,Qc,,,9d
1,10,4,1,-0.228899,-0.131774,-0.097125,,3c,Qc,,,Td
1,10,4,1,-0.236085,-0.133884,-0.102201,,3c,Qc,,,Jd
1,10,4,1,-0.593145,-0.341321,-0.251824,,3c,Qc,,,Qd
1,10,4,1,-0.178569,-0.105529,-0.073040,,3c,Qc,,,Kd
1,10,4,1,-0.178518,-0.105795,-0.072723,,3c,Qc,,,Ad
1,10,4,0,-0.294160,-0.172115,-0.122045,,3c,Qc,
2,10,4,1,-0.317412,-0.194731,-0.122681,,4c,Qc,,,3c
2,10,4,1,-0.281288,-0.176458,-0.104831,,4c,Qc,,,5c
2,10,4,1,-0.274296,-0.173602,-0.100694,,4c,Qc,,,6c
2,10,4,1,-0.266603,-0.170679,-0.095924,,4c,Qc,,,7c
2,10,4,1,-0.266105,-0.169978,-0.096127,,4c,Qc,,,8c
2,10,4,1,-0.265312,-0.169269,-0.096044,,4c,Qc,,,9c
2,10,4,1,-0.285007,-0.183017,-0.101991,,4c,Qc,,,Tc
2,10,4,1,-0.291581,-0.185107,-0.106474,,4c,Qc,,,Jc
2,10,4,1,-0.222571,-0.151450,-0.071121,,4c,Qc,,,Kc
2,10,4,1,-0.222109,-0.151417,-0.070693,,4c,Qc,,,Ac
2,10,4,1,-0.170260,-0.103498,-0.066762,,4c,Qc,,,2d
2,10,4,1,-0.171155,-0.103994,-0.067161,,4c,Qc,,,3d
2,10,4,1,-0.441437,-0.247233,-0.194204,,4c,Qc,,,4d
2,10,4,1,-0.133846,-0.084638,-0.049208,,4c,Qc,,,5d
2,10,4,1,-0.126715,-0.082442,-0.044273,,4c,Qc,,,6d
2,10,4,1,-0.118564,-0.080154,-0.038411,,4c,Qc,,,7d
2,10,4,1,-0.118554,-0.079599,-0.038955,,4c,Qc,,,8d
2,10,4,1,-0.118174,-0.079129,-0.039044,,4c,Qc,,,9d
2,10,4,1,-0.127973,-0.081687,-0.046286,,4c,Qc,,,Td
2,10,4,1,-0.135159,-0.083919,-0.051240,,4c,Qc,,,Jd
2,10,4,1,-0.487673,-0.289198,-0.198476,,4c,Qc,,,Qd
2,10,4,1,-0.077726,-0.054959,-0.022767,,4c,Qc,,,Kd
2,10,4,1,-0.077326,-0.054992,-0.022333,,4c,Qc,,,Ad
2,10,4,0,-0.198448,-0.124449,-0.073998,,4c,Qc,
3,10,4,1,-0.208690,-0.142151,-0.066539,,5c,Qc,,,3c
3,10,4,1,-0.209586,-0.143255,-0.066331,,5c,Qc,,,4c
3,10,4,1,-0.172249,-0.123813,-0.048436,,5c,Qc,,,6c
3,10,4,1,-0.164880,-0.121171,-0.043709,,5c,Qc,,,7c
3,10,4,1,-0.164759,-0.120686,-0.044073,,5c,Qc,,,8c
3,10,4,1,-0.164334,-0.120312,-0.044022,,5c,Qc,,,9c
3,10,4,1,-0.173174,-0.129722,-0.043453,,5c,Qc,,,Tc
3,10,4,1,-0.182325,-0.132712,-0.049613,,5c,Qc,,,Jc
3,10,4,1,-0.113393,-0.098165,-0.015228,,5c,Qc,,,Kc
3,10,4,1,-0.112609,-0.097876,-0.014733,,5c,Qc,,,Ac
3,10,4,1,-0.062852,-0.051204,-0.011647,,5c,Qc,,,2d
3,10,4,1,-0.063578,-0.051546,-0.012032,,5c,Qc,,,3d
3,10,4,1,-0.064360,-0.051924,-0.012436,,5c,Qc,,,4d
3,10,4,1,-0.337759,-0.199802,-0.137958,,5c,Qc,,,5d
3,10,4,1,-0.026024,-0.032118,0.006094,,5c,Qc,,,6d
3,10,4,1,-0.018232,-0.030159,0.011927,,5c,Qc,,,7d
3,10,4,1,-0.018596,-0.029800,0.011203,,5c,Qc,,,8d
3,10,4,1,-0.018421,-0.029555,0.011134,,5c,Qc,,,9d
3,10,4,1,-0.016900,-0.028553,0.011653,,5c,Qc,,,Td
3,10,4,1,-0.026911,-0.031647,0.004736,,5c,Qc,,,Jd
3,10,4,1,-0.378112,-0.235945,-0.142167,,5c,Qc,,,Qd
3,10,4,1,0.030456,-0.001849,0.032305,,5c,Qc,,,Kd
3,10,4,1,0.031206,-0.001619,0.032825,,5c,Qc,,,Ad
3,10,4,0,-0.095682,-0.074470,-0.021212,,5c,Qc,
4,10,4,1,-0.108886,-0.091309,-0.017576,,6c,Qc,,,3c
4,10,4,1,-0.109586,-0.092235,-0.017351,,6c,Qc,,,4c
4,10,4,1,-0.110377,-0.093166,-0.017211,,6c,Qc,,,5c
4,10,4,1,-0.077414,-0.075206,-0.002207,,6c,Qc,,,7c
4,10,4,1,-0.077520,-0.075042,-0.002479,,6c,Qc,,,8c
4,10,4,1,-0.077477,-0.074906,-0.002571,,6c,Qc,,,9c
4,10,4,1,-0.086700,-0.084624,-0.002076,,6c,Qc,,,Tc
4,10,4,1,-0.085105,-0.083200,-0.001906,,6c,Qc,,,Jc
4,10,4,1,-0.018636,-0.049047,0.030411,,6c,Qc,,,Kc
4,10,4,1,-0.011578,-0.045849,0.034271,,6c,Qc,,,Ac
4,10,4,1,0.035855,-0.001517,0.037372,,6c,Qc,,,2d
4,10,4,1,0.035476,-0.001557,0.037034,,6c,Qc,,,3d
4,10,4,1,0.034895,-0.001771,0.036667,,6c,Qc,,,4d
4,10,4,1,0.034238,-0.001981,0.036219,,6c,Qc,,,5d
4,10,4,1,-0.261441,-0.162460,-0.098981,,6c,Qc,,,6d
4,10,4,1,0.067919,0.016246,0.051673,,6c,Qc,,,7d
4,10,4,1,0.067321,0.016267,0.051054,,6c,Qc,,,8d
4,10,4,1,0.067118,0.016294,0.050824,,6c,Qc,,,9d
4,10,4,1,0.068415,0.017115,0.051301,,6c,Qc,,,Td
4,10,4,1,0.069598,0.017647,0.051952,,6c,Qc,,,Jd
4,10,4,1,-0.286436,-0.187986,-0.098450,,6c,Qc,,,Qd
4,10,4,1,0.124243,0.046970,0.077272,,6c,Qc,,,Kd
4,10,4,1,0.132130,0.049613,0.082517,,6c,Qc,,,Ad
4,10,4,0,-0.006074,-0.028120,0.022046,,6c,Qc,
5,10,4,1,-0.030871,-0.051653,0.020782,,7c,Qc,,,3c
5,10,4,1,-0.031210,-0.052329,0.021119,,7c,Qc,,,4c
5,10,4,1,-0.031772,-0.053134,0.021363,,7c,Qc,,,5c
5,10,4,1,-0.040417,-0.056914,0.016497,,7c,Qc,,,6c
5,10,4,1,-0.005881,-0.036423,0.030542,,7c,Qc,,,8c
5,10,4,1,-0.006024,-0.036546,0.030522,,7c,Qc,,,9c
5,10,4,1,-0.015632,-0.046500,0.030867,,7c,Qc,,,Tc
5,10,4,1,-0.014457,-0.045393,0.030936,,7c,Qc,,,Jc
5,10,4,1,0.053605,-0.011317,0.064922,,7c,Qc,,,Kc
5,10,4,1,0.061055,-0.007529,0.068585,,7c,Qc,,,Ac
5,10,4,1,0.112957,0.037035,0.075921,,7c,Qc,,,2d
5,10,4,1,0.112853,0.037234,0.075618,,7c,Qc,,,3d
5,10,4,1,0.112616,0.037252,0.075365,,7c,Qc,,,4d
5,10,4,1,0.112194,0.037152,0.075041,,7c,Qc,,,5d
5,10,4,1,0.102974,0.033895,0.069079,,7c,Qc,,,6d
5,10,4,1,-0.206367,-0.135562,-0.070805,,7c,Qc,,,7d
5,10,4,1,0.137743,0.054714,0.083029,,7c,Qc,,,8d
5,10,4,1,0.137380,0.054463,0.082917,,7c,Qc,,,9d
5,10,4,1,0.138299,0.055033,0.083266,,7c,Qc,,,Td
5,10,4,1,0.139227,0.055393,0.083834,,7c,Qc,,,Jd
5,10,4,1,-0.221843,-0.153380,-0.068463,,7c,Qc,,,Qd
5,10,4,1,0.195498,0.084416,0.111082,,7c,Qc,,,Kd
5,10,4,1,0.203529,0.087652,0.115877,,7c,Qc,,,Ad
5,10,4,0,0.062776,0.007850,0.054926,,7c,Qc,
6,10,4,1,0.202964,0.090268,0.112695,,8c,Qc,,,3c
6,10,4,1,0.203012,0.089848,0.113163,,8c,Qc,,,4c
6,10,4,1,0.202806,0.089255,0.113551,,8c,Qc,,,5c
6,10,4,1,0.194438,0.085505,0.108933,,8c,Qc,,,6c
6,10,4,1,0.192593,0.085895,0.106698,,8c,Qc,,,7c
6,10,4,1,0.171051,0.063980,0.107070,,8c,Qc,,,9c
6,10,4,1,0.161252,0.053895,0.107357,,8c,Qc,,,Tc
6,10,4,1,0.162041,0.054630,0.107411,,8c,Qc,,,Jc
6,10,4,1,0.288313,0.133114,0.155199,,8c,Qc,,,Kc
6,10,4,1,0.286754,0.131265,0.155489,,8c,Qc,,,Ac
6,10,4,1,0.337201,0.175846,0.161355,,8c,Qc,,,2d
6,10,4,1,0.344704,0.177769,0.166935,,8c,Qc,,,3d
6,10,4,1,0.344756,0.178034,0.166722,,8c,Qc,,,4d
6,10,4,1,0.344675,0.178134,0.166540,,8c,Qc,,,5d
6,10,4,1,0.335745,0.174871,0.160874,,8c,Qc,,,6d
6,10,4,1,0.333807,0.175434,0.158373,,8c,Qc,,,7d
6,10,4,1,0.005104,-0.006000,0.011104,,8c,Qc,,,8d
6,10,4,1,0.331366,0.175993,0.155373,,8c,Qc,,,9d
6,10,4,1,0.332092,0.176359,0.155733,,8c,Qc,,,Td
6,10,4,1,0.332621,0.176342,0.156279,,8c,Qc,,,Jd
6,10,4,1,-0.002359,-0.017017,0.014657,,8c,Qc,,,Qd
6,10,4,1,0.428381,0.227708,0.200674,,8c,Qc,,,Kd
6,10,4,1,0.426928,0.225666,0.201262,,8c,Qc,,,Ad
6,10,4,0,0.278932,0.140199,0.138732,,8c,Qc,
7,10,4,1,0.424061,0.231637,0.192424,,9c,Qc,,,3c
7,10,4,1,0.430677,0.233580,0.197097,,9c,Qc,,,4c
7,10,4,1,0.430857,0.233226,0.197631,,9c,Qc,,,5c
7,10,4,1,0.422843,0.229568,0.193275,,9c,Qc,,,6c
7,10,4,1,0.420908,0.229864,0.191044,,9c,Qc,,,7c
7,10,4,1,0.363247,0.187319,0.175928,,9c,Qc,,,8c
7,10,4,1,0.334014,0.156162,0.177853,,9c,Qc,,,Tc
7,10,4,1,0.334602,0.156702,0.177900,,9c,Qc,,,Jc
7,10,4,1,0.459303,0.234882,0.224421,,9c,Qc,,,Kc
7,10,4,1,0.514136,0.277768,0.236369,,9c,Qc,,,Ac
7,10,4,1,0.555161,0.315726,0.239434,,9c,Qc,,,2d
7,10,4,1,0.563031,0.318572,0.244458,,9c,Qc,,,3d
7,10,4,1,0.570468,0.320674,0.249794,,9c,Qc,,,4d
7,10,4,1,0.570675,0.321007,0.249668,,9c,Qc,,,5d
7,10,4,1,0.562082,0.317763,0.244319,,9c,Qc,,,6d
7,10,4,1,0.560052,0.318251,0.241801,,9c,Qc,,,7d
7,10,4,1,0.521185,0.297854,0.223331,,9c,Qc,,,8d
7,10,4,1,0.212108,0.125498,0.086611,,9c,Qc,,,9d
7,10,4,1,0.522156,0.299470,0.222686,,9c,Qc,,,Td
7,10,4,1,0.522480,0.299272,0.223208,,9c,Qc,,,Jd
7,10,4,1,0.207754,0.118450,0.089304,,9c,Qc,,,Qd
7,10,4,1,0.616639,0.350529,0.266109,,9c,Qc,,,Kd
7,10,4,1,0.652380,0.371323,0.281057,,9c,Qc,,,Ad
7,10,4,0,0.489199,0.274093,0.215105,,9c,Qc,
8,10,4,1,0.905109,0.628000,0.277109,,Tc,Qc,,,3c
8,10,4,1,0.912405,0.630753,0.281652,,Tc,Qc,,,4c
8,10,4,1,0.918739,0.632894,0.285845,,Tc,Qc,,,5c
8,10,4,1,0.911220,0.629300,0.281920,,Tc,Qc,,,6c
8,10,4,1,0.909431,0.629639,0.279792,,Tc,Qc,,,7c
8,10,4,1,0.852477,0.587151,0.265326,,Tc,Qc,,,8c
8,10,4,1,0.796122,0.545179,0.250942,,Tc,Qc,,,9c
8,10,4,1,0.527290,0.274973,0.252316,,Tc,Qc,,,Jc
8,10,4,1,0.650850,0.352982,0.297868,,Tc,Qc,,,Kc
8,10,4,1,0.704769,0.395676,0.309093,,Tc,Qc,,,Ac
8,10,4,1,1.033553,0.711318,0.322235,,Tc,Qc,,,2d
8,10,4,1,1.041436,0.714186,0.327251,,Tc,Qc,,,3d
8,10,4,1,1.049320,0.717032,0.332288,,Tc,Qc,,,4d
8,10,4,1,1.056446,0.719309,0.337137,,Tc,Qc,,,5d
8,10,4,1,1.048258,0.716115,0.332144,,Tc,Qc,,,6d
8,10,4,1,1.046391,0.716647,0.329744,,Tc,Qc,,,7d
8,10,4,1,1.008244,0.696242,0.312002,,Tc,Qc,,,8d
8,10,4,1,0.971166,0.676235,0.294931,,Tc,Qc,,,9d
8,10,4,1,0.682933,0.514528,0.168405,,Tc,Qc,,,Td
8,10,4,1,0.965952,0.672011,0.293941,,Tc,Qc,,,Jd
8,10,4,1,0.674721,0.507325,0.167396,,Tc,Qc,,,Qd
8,10,4,1,1.058955,0.722697,0.336259,,Tc,Qc,,,Kd
8,10,4,1,1.093797,0.743638,0.350159,,Tc,Qc,,,Ad
8,10,4,0,0.943595,0.648023,0.295572,,Tc,Qc,
9,10,4,1,0.988273,0.675393,0.312880,,Jc,Qc,,,3c
9,10,4,1,0.995580,0.678164,0.317416,,Jc,Qc,,,4c
9,10,4,1,1.002885,0.681055,0.321831,,Jc,Qc,,,5c
9,10,4,1,1.000422,0.679715,0.320707,,Jc,Qc,,,6c
9,10,4,1,0.998825,0.680094,0.318730,,Jc,Qc,,,7c
9,10,4,1,0.942610,0.637795,0.304815,,Jc,Qc,,,8c
9,10,4,1,0.887142,0.596095,0.291047,,Jc,Qc,,,9c
9,10,4,1,0.581752,0.305390,0.276363,,Jc,Qc,,,Tc
9,10,4,1,0.735738,0.400998,0.334741,,Jc,Qc,,,Kc
9,10,4,1,0.789144,0.443564,0.345580,,Jc,Qc,,,Ac
9,10,4,1,1.115503,0.758227,0.357275,,Jc,Qc,,,2d
9,10,4,1,1.123400,0.761178,0.362222,,Jc,Qc,,,3d
9,10,4,1,1.131298,0.764044,0.367254,,Jc,Qc,,,4d
9,10,4,1,1.139196,0.767059,0.372137,,Jc,Qc,,,5d
9,10,4,1,1.136728,0.765642,0.371085,,Jc,Qc,,,6d
9,10,4,1,1.135073,0.766218,0.368856,,Jc,Qc,,,7d
9,10,4,1,1.097539,0.745934,0.351604,,Jc,Qc,,,8d
9,10,4,1,1.061396,0.726190,0.335207,,Jc,Qc,,,9d
9,10,4,1,1.019810,0.702060,0.317749,,Jc,Qc,,,Td
9,10,4,1,0.744007,0.548555,0.195453,,Jc,Qc,,,Jd
9,10,4,1,0.744478,0.548732,0.195746,,Jc,Qc,,,Qd
9,10,4,1,1.142734,0.770275,0.372459,,Jc,Qc,,,Kd
9,10,4,1,1.177001,0.791083,0.385917,,Jc,Qc,,,Ad
9,10,4,0,1.024156,0.693598,0.330558,,Jc,Qc,,

0,9,4,1,-0.776599,-0.391479,-0.385120,,2c,Jc,,,3c
0,9,4,1,-0.770393,-0.389891,-0.380502,,2c,Jc,,,4c
0,9,4,1,-0.764069,-0.387987,-0.376082,,2c,Jc,,,5c
0,9,4,1,-0.756433,-0.385238,-0.371195,,2c,Jc,,,6c
0,9,4,1,-0.755588,-0.384175,-0.371413,,2c,Jc,,,7c
0,9,4,1,-0.765806,-0.387456,-0.378351,,2c,Jc,,,8c
0,9,4,1,-0.773322,-0.390376,-0.382946,,2c,Jc,,,9c
0,9,4,1,-0.790644,-0.403641,-0.387003,,2c,Jc,,,Tc
0,9,4,1,-0.724697,-0.371616,-0.353081,,2c,Jc,,,Qc
0,9,4,1,-0.723003,-0.370366,-0.352637,,2c,Jc,,,Kc
0,9,4,1,-0.723404,-0.370727,-0.352677,,2c,Jc,,,Ac
0,9,4,1,-0.943692,-0.456822,-0.486869,,2c,Jc,,,2d
0,9,4,1,-0.624054,-0.302391,-0.321664,,2c,Jc,,,3d
0,9,4,1,-0.617415,-0.300745,-0.316670,,2c,Jc,,,4d
0,9,4,1,-0.610814,-0.298768,-0.312046,,2c,Jc,,,5d
0,9,4,1,-0.602667,-0.296638,-0.306029,,2c,Jc,,,6d
0,9,4,1,-0.602505,-0.295793,-0.306712,,2c,Jc,,,7d
0,9,4,1,-0.613683,-0.298545,-0.315138,,2c,Jc,,,8d
0,9,4,1,-0.621738,-0.300978,-0.320761,,2c,Jc,,,9d
0,9,4,1,-0.628893,-0.303080,-0.325814,,2c,Jc,,,Td
0,9,4,1,-1.002599,-0.508774,-0.493825,,2c,Jc,,,Jd
0,9,4,1,-0.573087,-0.274648,-0.298439,,2c,Jc,,,Qd
0,9,4,1,-0.571524,-0.274147,-0.297377,,2c,Jc,,,Kd
0,9,4,1,-0.572116,-0.274566,-0.297551,,2c,Jc,,,Ad
0,9,4,0,-0.681566,-0.336220,-0.345346,,2c,Jc,
1,9,4,1,-0.674113,-0.343036,-0.331077,,3c,Jc,,,4c
1,9,4,1,-0.667781,-0.341129,-0.326651,,3c,Jc,,,5c
1,9,4,1,-0.660554,-0.338678,-0.321876,,3c,Jc,,,6c
1,9,4,1,-0.660083,-0.337924,-0.322159,,3c,Jc,,,7c
1,9,4,1,-0.659271,-0.337059,-0.322211,,3c,Jc,,,8c
1,9,4,1,-0.669440,-0.340845,-0.328596,,3c,Jc,,,9c
1,9,4,1,-0.686756,-0.354112,-0.332645,,3c,Jc,,,Tc
1,9,4,1,-0.620830,-0.321706,-0.299124,,3c,Jc,,,Qc
1,9,4,1,-0.619142,-0.320462,-0.298679,,3c,Jc,,,Kc
1,9,4,1,-0.619356,-0.320685,-0.298671,,3c,Jc,,,Ac
1,9,4,1,-0.559412,-0.272415,-0.286997,,3c,Jc,,,2d
1,9,4,1,-0.847522,-0.413422,-0.434099,,3c,Jc,,,3d
1,9,4,1,-0.522411,-0.253303,-0.269108,,3c,Jc,,,4d
1,9,4,1,-0.515812,-0.251361,-0.264451,,3c,Jc,,,5d
1,9,4,1,-0.508070,-0.249531,-0.258539,,3c,Jc,,,6d
1,9,4,1,-0.508093,-0.248900,-0.259193,,3c,Jc,,,7d
1,9,4,1,-0.507766,-0.248200,-0.259566,,3c,Jc,,,8d
1,9,4,1,-0.518717,-0.251460,-0.267257,,3c,Jc,,,9d
1,9,4,1,-0.525865,-0.253559,-0.272306,,3c,Jc,,,Td
1,9,4,1,-0.894848,-0.457214,-0.437634,,3c,Jc,,,Jd
1,9,4,1,-0.470075,-0.224698,-0.245377,,3c,Jc,,,Qd
1,9,4,1,-0.468519,-0.224204,-0.244315,,3c,Jc,,,Kd
1,9,4,1,-0.468929,-0.224501,-0.244428,,3c,Jc,,,Ad
1,9,4,0,-0.583907,-0.289096,-0.294811,,3c,Jc,
2,9,4,1,-0.608549,-0.313072,-0.295477,,4c,Jc,,,3c
2,9,4,1,-0.572913,-0.294729,-0.278183,,4c,Jc,,,5c
2,9,4,1,-0.566068,-0.292548,-0.273521,,4c,Jc,,,6c
2,9,4,1,-0.565942,-0.292092,-0.273850,,4c,Jc,,,7c
2,9,4,1,-0.565500,-0.291589,-0.273911,,4c,Jc,,,8c
2,9,4,1,-0.564725,-0.291139,-0.273585,,4c,Jc,,,9c
2,9,4,1,-0.584688,-0.305281,-0.279408,,4c,Jc,,,Tc
2,9,4,1,-0.518770,-0.272534,-0.246235,,4c,Jc,,,Qc
2,9,4,1,-0.517087,-0.271297,-0.245790,,4c,Jc,,,Kc
2,9,4,1,-0.516979,-0.271291,-0.245688,,4c,Jc,,,Ac
2,9,4,1,-0.457552,-0.223200,-0.234352,,4c,Jc,,,2d
2,9,4,1,-0.458860,-0.223715,-0.235145,,4c,Jc,,,3d
2,9,4,1,-0.752572,-0.370220,-0.382352,,4c,Jc,,,4d
2,9,4,1,-0.422178,-0.204244,-0.217934,,4c,Jc,,,5d
2,9,4,1,-0.414860,-0.202696,-0.212164,,4c,Jc,,,6d
2,9,4,1,-0.415213,-0.202357,-0.212856,,4c,Jc,,,7d
2,9,4,1,-0.415071,-0.201963,-0.213108,,4c,Jc,,,8d
2,9,4,1,-0.414615,-0.201679,-0.212936,,4c,Jc,,,9d
2,9,4,1,-0.424651,-0.204669,-0.219982,,4c,Jc,,,Td
2,9,4,1,-0.789003,-0.406467,-0.382537,,4c,Jc,,,Jd
2,9,4,1,-0.368864,-0.175382,-0.193482,,4c,Jc,,,Qd
2,9,4,1,-0.367314,-0.174897,-0.192417,,4c,Jc,,,Kd
2,9,4,1,-0.367376,-0.174957,-0.192418,,4c,Jc,,,Ad
2,9,4,0,-0.487857,-0.242526,-0.245331,,4c,Jc,
3,9,4,1,-0.499601,-0.262254,-0.237346,,5c,Jc,,,3c
3,9,4,1,-0.500827,-0.263292,-0.237535,,5c,Jc,,,4c
3,9,4,1,-0.463714,-0.244580,-0.219134,,5c,Jc,,,6c
3,9,4,1,-0.463905,-0.244354,-0.219551,,5c,Jc,,,7c
3,9,4,1,-0.463843,-0.244123,-0.219720,,5c,Jc,,,8c
3,9,4,1,-0.463443,-0.243939,-0.219505,,5c,Jc,,,9c
3,9,4,1,-0.472566,-0.253718,-0.218849,,5c,Jc,,,Tc
3,9,4,1,-0.409289,-0.221530,-0.187759,,5c,Jc,,,Qc
3,9,4,1,-0.407613,-0.220304,-0.187309,,5c,Jc,,,Kc
3,9,4,1,-0.407182,-0.220076,-0.187105,,5c,Jc,,,Ac
3,9,4,1,-0.349894,-0.172323,-0.177571,,5c,Jc,,,2d
3,9,4,1,-0.351051,-0.172691,-0.178361,,5c,Jc,,,3d
3,9,4,1,-0.352247,-0.173046,-0.179201,,5c,Jc,,,4d
3,9,4,1,-0.648826,-0.324616,-0.324210,,5c,Jc,,,5d
3,9,4,1,-0.313867,-0.153813,-0.160054,,5c,Jc,,,6d
3,9,4,1,-0.314573,-0.153739,-0.160833,,5c,Jc,,,7d
3,9,4,1,-0.314805,-0.153626,-0.161178,,5c,Jc,,,8d
3,9,4,1,-0.314540,-0.153551,-0.160989,,5c,Jc,,,9d
3,9,4,1,-0.313289,-0.152879,-0.160410,,5c,Jc,,,Td
3,9,4,1,-0.679131,-0.355020,-0.324111,,5c,Jc,,,Jd
3,9,4,1,-0.260378,-0.124263,-0.136115,,5c,Jc,,,Qd
3,9,4,1,-0.258835,-0.123786,-0.135049,,5c,Jc,,,Kd
3,9,4,1,-0.258546,-0.123610,-0.134936,,5c,Jc,,,Ad
3,9,4,0,-0.384807,-0.194062,-0.190745,,5c,Jc,
4,9,4,1,-0.429492,-0.228653,-0.200839,,6c,Jc,,,3c
4,9,4,1,-0.430526,-0.229599,-0.200927,,6c,Jc,,,4c
4,9,4,1,-0.431712,-0.230589,-0.201124,,6c,Jc,,,5c
4,9,4,1,-0.398957,-0.211329,-0.187628,,6c,Jc,,,7c
4,9,4,1,-0.399148,-0.211278,-0.187871,,6c,Jc,,,8c
4,9,4,1,-0.399135,-0.211335,-0.187801,,6c,Jc,,,9c
4,9,4,1,-0.408658,-0.221380,-0.187278,,6c,Jc,,,Tc
4,9,4,1,-0.344006,-0.190086,-0.153920,,6c,Jc,,,Qc
4,9,4,1,-0.342353,-0.188862,-0.153491,,6c,Jc,,,Kc
4,9,4,1,-0.335507,-0.185921,-0.149586,,6c,Jc,,,Ac
4,9,4,1,-0.280664,-0.139407,-0.141256,,6c,Jc,,,2d
4,9,4,1,-0.281472,-0.139545,-0.141927,,6c,Jc,,,3d
4,9,4,1,-0.282472,-0.139806,-0.142666,,6c,Jc,,,4d
4,9,4,1,-0.283620,-0.140115,-0.143505,,6c,Jc,,,5d
4,9,4,1,-0.603766,-0.305201,-0.298565,,6c,Jc,,,6d
4,9,4,1,-0.250630,-0.120507,-0.130123,,6c,Jc,,,7d
4,9,4,1,-0.251109,-0.120584,-0.130524,,6c,Jc,,,8d
4,9,4,1,-0.251221,-0.120730,-0.130491,,6c,Jc,,,9d
4,9,4,1,-0.250173,-0.120223,-0.129951,,6c,Jc,,,Td
4,9,4,1,-0.617167,-0.323999,-0.293169,,6c,Jc,,,Jd
4,9,4,1,-0.195911,-0.092937,-0.102974,,6c,Jc,,,Qd
4,9,4,1,-0.194402,-0.092452,-0.101950,,6c,Jc,,,Kd
4,9,4,1,-0.186822,-0.090193,-0.096629,,6c,Jc,,,Ad
4,9,4,0,-0.322729,-0.163644,-0.159085,,6c,Jc,
5,9,4,1,-0.195564,-0.089981,-0.105584,,7c,Jc,,,3c
5,9,4,1,-0.196250,-0.090722,-0.105529,,7c,Jc,,,4c
5,9,4,1,-0.197157,-0.091534,-0.105623,,7c,Jc,,,5c
5,9,4,1,-0.198777,-0.091246,-0.107531,,7c,Jc,,,6c
5,9,4,1,-0.223390,-0.114067,-0.109323,,7c,Jc,,,8c
5,9,4,1,-0.223561,-0.114229,-0.109332,,7c,Jc,,,9c
5,9,4,1,-0.233456,-0.124493,-0.108963,,7c,Jc,,,Tc
5,9,4,1,-0.108278,-0.048724,-0.059555,,7c,Jc,,,Qc
5,9,4,1,-0.116230,-0.053183,-0.063048,,7c,Jc,,,Kc
5,9,4,1,-0.108972,-0.049591,-0.059380,,7c,Jc,,,Ac
5,9,4,1,-0.049090,-0.002525,-0.046565,,7c,Jc,,,2d
5,9,4,1,-0.049611,-0.002441,-0.047169,,7c,Jc,,,3d
5,9,4,1,-0.050277,-0.002491,-0.047786,,7c,Jc,,,4d
5,9,4,1,-0.051131,-0.002617,-0.048514,,7c,Jc,,,5d
5,9,4,1,-0.052823,-0.002287,-0.050535,,7c,Jc,,,6d
5,9,4,1,-0.393174,-0.179145,-0.214029,,7c,Jc,,,7d
5,9,4,1,-0.058612,-0.002507,-0.056104,,7c,Jc,,,8d
5,9,4,1,-0.058912,-0.002759,-0.056152,,7c,Jc,,,9d
5,9,4,1,-0.058250,-0.002477,-0.055773,,7c,Jc,,,Td
5,9,4,1,-0.394257,-0.188214,-0.206043,,7c,Jc,,,Jd
5,9,4,1,0.038180,0.047113,-0.008932,,7c,Jc,,,Qd
5,9,4,1,0.029497,0.042337,-0.012840,,7c,Jc,,,Kd
5,9,4,1,0.037253,0.045265,-0.008013,,7c,Jc,,,Ad
5,9,4,0,-0.106608,-0.034445,-0.072162,,7c,Jc,
6,9,4,1,0.035975,0.050367,-0.014392,,8c,Jc,,,3c
6,9,4,1,0.035668,0.049877,-0.014208,,8c,Jc,,,4c
6,9,4,1,0.035115,0.049252,-0.014138,,8c,Jc,,,5c
6,9,4,1,0.033406,0.049467,-0.016061,,8c,Jc,,,6c
6,9,4,1,-0.026211,0.007203,-0.033413,,8c,Jc,,,7c
6,9,4,1,-0.048297,-0.015060,-0.033238,,8c,Jc,,,9c
6,9,4,1,-0.058398,-0.025383,-0.033015,,8c,Jc,,,Tc
6,9,4,1,0.065172,0.049212,0.015960,,8c,Jc,,,Qc
6,9,4,1,0.116234,0.089800,0.026433,,8c,Jc,,,Kc
6,9,4,1,0.114378,0.087684,0.026694,,8c,Jc,,,Ac
6,9,4,1,0.172953,0.134921,0.038031,,8c,Jc,,,2d
6,9,4,1,0.179940,0.136536,0.043403,,8c,Jc,,,3d
6,9,4,1,0.179574,0.136702,0.042872,,8c,Jc,,,4d
6,9,4,1,0.179063,0.136758,0.042305,,8c,Jc,,,5d
6,9,4,1,0.177280,0.136992,0.040288,,8c,Jc,,,6d
6,9,4,1,0.136081,0.116922,0.019158,,8c,Jc,,,7d
6,9,4,1,-0.182467,-0.050410,-0.132058,,8c,Jc,,,8d
6,9,4,1,0.133356,0.117359,0.015997,,8c,Jc,,,9d
6,9,4,1,0.133807,0.117510,0.016297,,8c,Jc,,,Td
6,9,4,1,-0.177831,-0.053375,-0.124456,,8c,Jc,,,Jd
6,9,4,1,0.228610,0.165923,0.062688,,8c,Jc,,,Qd
6,9,4,1,0.260154,0.184183,0.075971,,8c,Jc,,,Kd
6,9,4,1,0.258325,0.181810,0.076515,,8c,Jc,,,Ad
6,9,4,0,0.107386,0.096318,0.011068,,8c,Jc,
7,9,4,1,0.257368,0.189860,0.067508,,9c,Jc,,,3c
7,9,4,1,0.263348,0.191471,0.071877,,9c,Jc,,,4c
7,9,4,1,0.263174,0.191050,0.072123,,9c,Jc,,,5c
7,9,4,1,0.261610,0.191315,0.070295,,9c,Jc,,,6c
7,9,4,1,0.202690,0.149135,0.053555,,9c,Jc,,,7c
7,9,4,1,0.144744,0.106871,0.037873,,9c,Jc,,,8c
7,9,4,1,0.114599,0.074995,0.039604,,9c,Jc,,,Tc
7,9,4,1,0.237026,0.149323,0.087703,,9c,Jc,,,Qc
7,9,4,1,0.287171,0.189305,0.097866,,9c,Jc,,,Kc
7,9,4,1,0.342117,0.231988,0.110129,,9c,Jc,,,Ac
7,9,4,1,0.391208,0.272782,0.118426,,9c,Jc,,,2d
7,9,4,1,0.398566,0.275340,0.123226,,9c,Jc,,,3d
7,9,4,1,0.405260,0.277058,0.128203,,9c,Jc,,,4d
7,9,4,1,0.405050,0.277322,0.127728,,9c,Jc,,,5d
7,9,4,1,0.403429,0.277589,0.125840,,9c,Jc,,,6d
7,9,4,1,0.362949,0.257565,0.105384,,9c,Jc,,,7d
7,9,4,1,0.323965,0.237561,0.086403,,9c,Jc,,,8d
7,9,4,1,0.025559,0.079694,-0.054135,,9c,Jc,,,9d
7,9,4,1,0.324098,0.238763,0.085335,,9c,Jc,,,Td
7,9,4,1,0.032196,0.080709,-0.048513,,9c,Jc,,,Jd
7,9,4,1,0.417736,0.286950,0.130786,,9c,Jc,,,Qd
7,9,4,1,0.448332,0.304769,0.143563,,9c,Jc,,,Kd
7,9,4,1,0.484142,0.325165,0.158977,,9c,Jc,,,Ad
7,9,4,0,0.317837,0.228196,0.089641,,9c,Jc,
8,9,4,1,0.745484,0.586060,0.159424,,Tc,Jc,,,3c
8,9,4,1,0.752340,0.588622,0.163719,,Tc,Jc,,,4c
8,9,4,1,0.757448,0.590004,0.167444,,Tc,Jc,,,5c
8,9,4,1,0.756196,0.590308,0.165888,,Tc,Jc,,,6c
8,9,4,1,0.698010,0.548436,0.149574,,Tc,Jc,,,7c
8,9,4,1,0.640757,0.506211,0.134547,,Tc,Jc,,,8c
8,9,4,1,0.584060,0.464246,0.119814,,Tc,Jc,,,9c
8,9,4,1,0.435304,0.267751,0.167553,,Tc,Jc,,,Qc
8,9,4,1,0.484890,0.307516,0.177374,,Tc,Jc,,,Kc
8,9,4,1,0.538904,0.349939,0.188965,,Tc,Jc,,,Ac
8,9,4,1,0.876616,0.668222,0.208394,,Tc,Jc,,,2d
8,9,4,1,0.883988,0.670885,0.213103,,Tc,Jc,,,3d
8,9,4,1,0.891360,0.673544,0.217816,,Tc,Jc,,,4d
8,9,4,1,0.897122,0.675052,0.222070,,Tc,Jc,,,5d
8,9,4,1,0.895846,0.675370,0.220476,,Tc,Jc,,,6d
8,9,4,1,0.855996,0.655578,0.200418,,Tc,Jc,,,7d
8,9,4,1,0.817727,0.635536,0.182190,,Tc,Jc,,,8d
8,9,4,1,0.780342,0.615682,0.164661,,Tc,Jc,,,9d
8,9,4,1,0.503899,0.468904,0.034995,,Tc,Jc,,,Td
8,9,4,1,0.505913,0.469899,0.036013,,Tc,Jc,,,Jd
8,9,4,1,0.866540,0.659713,0.206826,,Tc,Jc,,,Qd
8,9,4,1,0.896545,0.677422,0.219124,,Tc,Jc,,,Kd
8,9,4,1,0.931450,0.697938,0.233512,,Tc,Jc,,,Ad
8,9,4,0,0.778841,0.601905,0.176936,,Tc,Jc,,

0,8,4,1,-1.040797,-0.483755,-0.557042,,2c,Tc,,,3c
0,8,4,1,-1.035015,-0.482328,-0.552688,,2c,Tc,,,4c
0,8,4,1,-1.029247,-0.481708,-0.547539,,2c,Tc,,,5c
0,8,4,1,-1.029069,-0.481143,-0.547926,,2c,Tc,,,6c
0,8,4,1,-1.028359,-0.480337,-0.548022,,2c,Tc,,,7c
0,8,4,1,-1.038590,-0.483727,-0.554863,,2c,Tc,,,8c
0,8,4,1,-1.046210,-0.486576,-0.559634,,2c,Tc,,,9c
0,8,4,1,-0.995642,-0.469989,-0.525654,,2c,Tc,,,Jc
0,8,4,1,-0.993442,-0.468598,-0.524844,,2c,Tc,,,Qc
0,8,4,1,-0.991564,-0.467214,-0.524350,,2c,Tc,,,Kc
0,8,4,1,-0.991966,-0.467442,-0.524525,,2c,Tc,,,Ac
0,8,4,1,-1.224575,-0.549806,-0.674769,,2c,Tc,,,2d
0,8,4,1,-0.885327,-0.396986,-0.488341,,2c,Tc,,,3d
0,8,4,1,-0.879181,-0.395565,-0.483616,,2c,Tc,,,4d
0,8,4,1,-0.872931,-0.394911,-0.478019,,2c,Tc,,,5d
0,8,4,1,-0.873135,-0.394404,-0.478730,,2c,Tc,,,6d
0,8,4,1,-0.872987,-0.393756,-0.479231,,2c,Tc,,,7d
0,8,4,1,-0.884066,-0.396536,-0.487530,,2c,Tc,,,8d
0,8,4,1,-0.892192,-0.398725,-0.493467,,2c,Tc,,,9d
0,8,4,1,-1.273818,-0.596991,-0.676827,,2c,Tc,,,Td
0,8,4,1,-0.839640,-0.373725,-0.465914,,2c,Tc,,,Jd
0,8,4,1,-0.837539,-0.373060,-0.464480,,2c,Tc,,,Qd
0,8,4,1,-0.835798,-0.372394,-0.463404,,2c,Tc,,,Kd
0,8,4,1,-0.836422,-0.372704,-0.463718,,2c,Tc,,,Ad
0,8,4,0,-0.944855,-0.429841,-0.515013,,2c,Tc,
1,8,4,1,-0.938648,-0.436768,-0.501880,,3c,Tc,,,4c
1,8,4,1,-0.932871,-0.436141,-0.496730,,3c,Tc,,,5c
1,8,4,1,-0.933099,-0.435860,-0.497239,,3c,Tc,,,6c
1,8,4,1,-0.932771,-0.435367,-0.497404,,3c,Tc,,,7c
1,8,4,1,-0.932067,-0.434721,-0.497345,,3c,Tc,,,8c
1,8,4,1,-0.942396,-0.438398,-0.503998,,3c,Tc,,,9c
1,8,4,1,-0.891753,-0.421882,-0.469872,,3c,Tc,,,Jc
1,8,4,1,-0.889559,-0.420486,-0.469073,,3c,Tc,,,Qc
1,8,4,1,-0.887687,-0.419106,-0.468581,,3c,Tc,,,Kc
1,8,4,1,-0.887917,-0.419217,-0.468700,,3c,Tc,,,Ac
1,8,4,1,-0.820561,-0.368214,-0.452347,,3c,Tc,,,2d
1,8,4,1,-1.128650,-0.507981,-0.620669,,3c,Tc,,,3d
1,8,4,1,-0.784077,-0.349449,-0.434628,,3c,Tc,,,4d
1,8,4,1,-0.777830,-0.348813,-0.429017,,3c,Tc,,,5d
1,8,4,1,-0.778431,-0.348559,-0.429872,,3c,Tc,,,6d
1,8,4,1,-0.778454,-0.348115,-0.430339,,3c,Tc,,,7d
1,8,4,1,-0.778161,-0.347629,-0.430532,,3c,Tc,,,8d
1,8,4,1,-0.789226,-0.350635,-0.438591,,3c,Tc,,,9d
1,8,4,1,-1.166059,-0.547391,-0.618668,,3c,Tc,,,Td
1,8,4,1,-0.736600,-0.325463,-0.411137,,3c,Tc,,,Jd
1,8,4,1,-0.734507,-0.324800,-0.409706,,3c,Tc,,,Qd
1,8,4,1,-0.732772,-0.324141,-0.408630,,3c,Tc,,,Kd
1,8,4,1,-0.733233,-0.324356,-0.408876,,3c,Tc,,,Ad
1,8,4,0,-0.847170,-0.384250,-0.462920,,3c,Tc,
2,8,4,1,-0.873049,-0.408211,-0.464838,,4c,Tc,,,3c
2,8,4,1,-0.837965,-0.391285,-0.446680,,4c,Tc,,,5c
2,8,4,1,-0.838570,-0.391246,-0.447323,,4c,Tc,,,6c
2,8,4,1,-0.838589,-0.391012,-0.447577,,4c,Tc,,,7c
2,8,4,1,-0.838263,-0.390711,-0.447552,,4c,Tc,,,8c
2,8,4,1,-0.837742,-0.390421,-0.447321,,4c,Tc,,,9c
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6,8,4,1,0.123696,0.160110,-0.036414,,8c,Tc,,,Ad
6,8,4,0,-0.030267,0.075411,-0.105679,,8c,Tc,
7,8,4,1,0.130518,0.172580,-0.042062,,9c,Tc,,,3c
7,8,4,1,0.135353,0.173173,-0.037819,,9c,Tc,,,4c
7,8,4,1,0.141449,0.176050,-0.034601,,9c,Tc,,,5c
7,8,4,1,0.081796,0.134632,-0.052836,,9c,Tc,,,6c
7,8,4,1,0.022597,0.092880,-0.070283,,9c,Tc,,,7c
7,8,4,1,-0.035793,0.051102,-0.086895,,9c,Tc,,,8c
7,8,4,1,0.051674,0.086766,-0.035092,,9c,Tc,,,Jc
7,8,4,1,0.103621,0.126661,-0.023041,,9c,Tc,,,Qc
7,8,4,1,0.154299,0.166763,-0.012464,,9c,Tc,,,Kc
7,8,4,1,0.210120,0.209422,0.000698,,9c,Tc,,,Ac
7,8,4,1,0.266402,0.254706,0.011696,,9c,Tc,,,2d
7,8,4,1,0.273266,0.256353,0.016913,,9c,Tc,,,3d
7,8,4,1,0.278695,0.256968,0.021727,,9c,Tc,,,4d
7,8,4,1,0.285406,0.260044,0.025362,,9c,Tc,,,5d
7,8,4,1,0.243811,0.240631,0.003179,,9c,Tc,,,6d
7,8,4,1,0.203229,0.221156,-0.017926,,9c,Tc,,,7d
7,8,4,1,0.163819,0.201754,-0.037935,,9c,Tc,,,8d
7,8,4,1,-0.117079,0.061441,-0.178520,,9c,Tc,,,9d
7,8,4,1,-0.100017,0.070766,-0.170783,,9c,Tc,,,Td
7,8,4,1,0.254551,0.245949,0.008602,,9c,Tc,,,Jd
7,8,4,1,0.287214,0.263442,0.023773,,9c,Tc,,,Qd
7,8,4,1,0.318409,0.281323,0.037086,,9c,Tc,,,Kd
7,8,4,1,0.355200,0.301651,0.053549,,9c,Tc,,,Ad
7,8,4,0,0.185169,0.205485,-0.020316,,9c,Tc,
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
Mental
  • Threads: 16
  • Posts: 1549
Joined: Dec 10, 2018
April 6th, 2024 at 8:51:04 AM permalink
0,7,4,1,-1.313140,-0.582098,-0.731042,,2c,9c,,,3c
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0,7,4,1,-1.102006,-0.473910,-0.628096,,2c,9c,,,Ad
0,7,4,0,-1.213506,-0.527903,-0.685603,,2c,9c,,
1,7,4,1,-1.246718,-0.552929,-0.693789,,3c,9c,,,2c
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1,7,4,1,-1.154815,-0.513095,-0.641720,,3c,9c,,,Tc
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1,7,4,1,-1.149773,-0.510042,-0.639732,,3c,9c,,,Qc
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1,7,4,1,-1.000968,-0.426697,-0.574271,,3c,9c,,,Qd
1,7,4,1,-0.998825,-0.425777,-0.573049,,3c,9c,,,Kd
1,7,4,1,-0.999199,-0.425757,-0.573441,,3c,9c,,,Ad
1,7,4,0,-1.116141,-0.482501,-0.633641,,3c,9c,,
2,7,4,1,-1.175617,-0.521165,-0.654451,,4c,9c,,,2c
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2,7,4,1,-0.928817,-0.394161,-0.534656,,4c,9c,,,Ad
2,7,4,0,-1.049228,-0.452472,-0.596757,,4c,9c,,
3,7,4,1,-0.925949,-0.385628,-0.540322,,5c,9c,,,2c
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3,7,4,1,-0.824430,-0.340726,-0.483705,,5c,9c,,,Tc
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3,7,4,1,-0.829935,-0.343295,-0.486640,,5c,9c,,,Qc
3,7,4,1,-0.827630,-0.341652,-0.485978,,5c,9c,,,Kc
3,7,4,1,-0.826804,-0.340972,-0.485832,,5c,9c,,,Ac
3,7,4,1,-0.773054,-0.301759,-0.471295,,5c,9c,,,2d
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3,7,4,1,-0.768419,-0.299496,-0.468923,,5c,9c,,,4d
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4,5,4,1,-0.790333,-0.180654,-0.609679,,6c,7c,,,Tc
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4,5,4,1,-0.600200,-0.068598,-0.531602,,6c,7c,,,Kd
4,5,4,1,-0.598892,-0.069411,-0.529481,,6c,7c,,,Ad
4,5,4,0,-0.746324,-0.140962,-0.605362,,6c,7c,,
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
Mental
Mental
  • Threads: 16
  • Posts: 1549
Joined: Dec 10, 2018
Thanked by
acesideMrCasinoGames
April 6th, 2024 at 8:54:22 AM permalink
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3,4,4,1,-0.870802,-0.171237,-0.699565,,5c,6c,,,9d
3,4,4,1,-0.827626,-0.150371,-0.677255,,5c,6c,,,Td
3,4,4,1,-0.835615,-0.154535,-0.681080,,5c,6c,,,Jd
3,4,4,1,-0.842565,-0.157792,-0.684773,,5c,6c,,,Qd
3,4,4,1,-0.845327,-0.159055,-0.686272,,5c,6c,,,Kd
3,4,4,1,-0.841974,-0.157748,-0.684226,,5c,6c,,,Ad
3,4,4,0,-0.984539,-0.226888,-0.757651,,5c,6c,,

0,3,4,1,-1.837428,-0.682627,-1.154801,,2c,5c,,,3c
0,3,4,1,-1.840542,-0.684289,-1.156253,,2c,5c,,,4c
0,3,4,1,-1.733525,-0.620364,-1.113161,,2c,5c,,,6c
0,3,4,1,-1.670341,-0.577959,-1.092382,,2c,5c,,,7c
0,3,4,1,-1.675273,-0.580957,-1.094316,,2c,5c,,,8c
0,3,4,1,-1.668594,-0.577950,-1.090644,,2c,5c,,,9c
0,3,4,1,-1.661102,-0.574328,-1.086773,,2c,5c,,,Tc
0,3,4,1,-1.665415,-0.576112,-1.089303,,2c,5c,,,Jc
0,3,4,1,-1.667790,-0.577081,-1.090709,,2c,5c,,,Qc
0,3,4,1,-1.670197,-0.578107,-1.092090,,2c,5c,,,Kc
0,3,4,1,-1.732287,-0.620343,-1.111944,,2c,5c,,,Ac
0,3,4,1,-1.942399,-0.668204,-1.274194,,2c,5c,,,2d
0,3,4,1,-1.641430,-0.558406,-1.083025,,2c,5c,,,3d
0,3,4,1,-1.644841,-0.559459,-1.085382,,2c,5c,,,4d
0,3,4,1,-1.947491,-0.674637,-1.272855,,2c,5c,,,5d
0,3,4,1,-1.557396,-0.518039,-1.039357,,2c,5c,,,6d
0,3,4,1,-1.513135,-0.497862,-1.015273,,2c,5c,,,7d
0,3,4,1,-1.519249,-0.501051,-1.018198,,2c,5c,,,8d
0,3,4,1,-1.512749,-0.498590,-1.014160,,2c,5c,,,9d
0,3,4,1,-1.505464,-0.495629,-1.009835,,2c,5c,,,Td
0,3,4,1,-1.510341,-0.497569,-1.012772,,2c,5c,,,Jd
0,3,4,1,-1.513115,-0.498739,-1.014376,,2c,5c,,,Qd
0,3,4,1,-1.515877,-0.499964,-1.015913,,2c,5c,,,Kd
0,3,4,1,-1.560281,-0.520183,-1.040098,,2c,5c,,,Ad
0,3,4,0,-1.629476,-0.552398,-1.077078,,2c,5c,,
1,3,4,1,-1.614837,-0.562115,-1.052722,,3c,5c,,,2c
1,3,4,1,-1.646218,-0.587300,-1.058918,,3c,5c,,,4c
1,3,4,1,-1.540237,-0.523871,-1.016367,,3c,5c,,,6c
1,3,4,1,-1.477642,-0.481778,-0.995864,,3c,5c,,,7c
1,3,4,1,-1.414658,-0.439063,-0.975595,,3c,5c,,,8c
1,3,4,1,-1.419374,-0.441944,-0.977430,,3c,5c,,,9c
1,3,4,1,-1.411888,-0.438360,-0.973528,,3c,5c,,,Tc
1,3,4,1,-1.416573,-0.440358,-0.976216,,3c,5c,,,Jc
1,3,4,1,-1.418948,-0.441342,-0.977606,,3c,5c,,,Qc
1,3,4,1,-1.421356,-0.442395,-0.978961,,3c,5c,,,Kc
1,3,4,1,-1.482996,-0.484410,-0.998586,,3c,5c,,,Ac
1,3,4,1,-1.421431,-0.439727,-0.981703,,3c,5c,,,2d
1,3,4,1,-1.700169,-0.538067,-1.162102,,3c,5c,,,3d
1,3,4,1,-1.434203,-0.441548,-0.992656,,3c,5c,,,4d
1,3,4,1,-1.692690,-0.536978,-1.155712,,3c,5c,,,5d
1,3,4,1,-1.347883,-0.400669,-0.947214,,3c,5c,,,6d
1,3,4,1,-1.304177,-0.380797,-0.923380,,3c,5c,,,7d
1,3,4,1,-1.260028,-0.360270,-0.899758,,3c,5c,,,8d
1,3,4,1,-1.265688,-0.363359,-0.902330,,3c,5c,,,9d
1,3,4,1,-1.258410,-0.360438,-0.897971,,3c,5c,,,Td
1,3,4,1,-1.263710,-0.362616,-0.901094,,3c,5c,,,Jd
1,3,4,1,-1.266484,-0.363798,-0.902686,,3c,5c,,,Qd
1,3,4,1,-1.269246,-0.365042,-0.904204,,3c,5c,,,Kd
1,3,4,1,-1.313143,-0.385025,-0.928117,,3c,5c,,,Ad
1,3,4,0,-1.393130,-0.423657,-0.969474,,3c,5c,,
2,3,4,1,-1.374301,-0.430223,-0.944078,,4c,5c,,,2c
2,3,4,1,-1.432493,-0.470511,-0.961982,,4c,5c,,,3c
2,3,4,1,-1.355141,-0.430802,-0.924339,,4c,5c,,,6c
2,3,4,1,-1.293158,-0.389046,-0.904112,,4c,5c,,,7c
2,3,4,1,-1.230766,-0.346655,-0.884111,,4c,5c,,,8c
2,3,4,1,-1.167929,-0.303760,-0.864169,,4c,5c,,,9c
2,3,4,1,-1.171851,-0.306214,-0.865637,,4c,5c,,,Tc
2,3,4,1,-1.178107,-0.309143,-0.868964,,4c,5c,,,Jc
2,3,4,1,-1.180482,-0.310144,-0.870339,,4c,5c,,,Qc
2,3,4,1,-1.182890,-0.311205,-0.871685,,4c,5c,,,Kc
2,3,4,1,-1.243934,-0.352886,-0.891048,,4c,5c,,,Ac
2,3,4,1,-1.182973,-0.308538,-0.874434,,4c,5c,,,2d
2,3,4,1,-1.222977,-0.326510,-0.896468,,4c,5c,,,3d
2,3,4,1,-1.467314,-0.411904,-1.055410,,4c,5c,,,4d
2,3,4,1,-1.448762,-0.403960,-1.044802,,4c,5c,,,5d
2,3,4,1,-1.146231,-0.286585,-0.859646,,4c,5c,,,6d
2,3,4,1,-1.103199,-0.267103,-0.836096,,4c,5c,,,7d
2,3,4,1,-1.059598,-0.246859,-0.812739,,4c,5c,,,8d
2,3,4,1,-1.015764,-0.226277,-0.789486,,4c,5c,,,9d
2,3,4,1,-1.020360,-0.228916,-0.791445,,4c,5c,,,Td
2,3,4,1,-1.027360,-0.232067,-0.795292,,4c,5c,,,Jd
2,3,4,1,-1.030133,-0.233265,-0.796868,,4c,5c,,,Qd
2,3,4,1,-1.032896,-0.234518,-0.798378,,4c,5c,,,Kd
2,3,4,1,-1.076117,-0.254169,-0.821948,,4c,5c,,,Ad
2,3,4,0,-1.166242,-0.298984,-0.867258,,4c,5c,,

0,2,4,1,-1.955661,-0.731872,-1.223789,,2c,4c,,,3c
0,2,4,1,-1.922233,-0.714052,-1.208181,,2c,4c,,,5c
0,2,4,1,-1.848845,-0.666677,-1.182167,,2c,4c,,,6c
0,2,4,1,-1.784996,-0.623937,-1.161059,,2c,4c,,,7c
0,2,4,1,-1.789548,-0.626730,-1.162818,,2c,4c,,,8c
0,2,4,1,-1.782416,-0.623352,-1.159064,,2c,4c,,,9c
0,2,4,1,-1.783823,-0.624021,-1.159802,,2c,4c,,,Tc
0,2,4,1,-1.786140,-0.624866,-1.161274,,2c,4c,,,Jc
0,2,4,1,-1.788515,-0.625819,-1.162697,,2c,4c,,,Qc
0,2,4,1,-1.790923,-0.626836,-1.164087,,2c,4c,,,Kc
0,2,4,1,-1.853577,-0.669386,-1.184191,,2c,4c,,,Ac
0,2,4,1,-2.062986,-0.718598,-1.344387,,2c,4c,,,2d
0,2,4,1,-1.759226,-0.608126,-1.151099,,2c,4c,,,3d
0,2,4,1,-2.060393,-0.718078,-1.342314,,2c,4c,,,4d
0,2,4,1,-1.727666,-0.590168,-1.137498,,2c,4c,,,5d
0,2,4,1,-1.672144,-0.565188,-1.106955,,2c,4c,,,6d
0,2,4,1,-1.627231,-0.544683,-1.082547,,2c,4c,,,7d
0,2,4,1,-1.632903,-0.547642,-1.085261,,2c,4c,,,8d
0,2,4,1,-1.626196,-0.544970,-1.081226,,2c,4c,,,9d
0,2,4,1,-1.628116,-0.545659,-1.082457,,2c,4c,,,Td
0,2,4,1,-1.630911,-0.546697,-1.084214,,2c,4c,,,Jd
0,2,4,1,-1.633685,-0.547854,-1.085831,,2c,4c,,,Qd
0,2,4,1,-1.636447,-0.549068,-1.087379,,2c,4c,,,Kd
0,2,4,1,-1.681485,-0.569638,-1.111847,,2c,4c,,,Ad
0,2,4,0,-1.744497,-0.599061,-1.145436,,2c,4c,,
1,2,4,1,-1.737151,-0.613926,-1.123225,,3c,4c,,,2c
1,2,4,1,-1.731431,-0.619160,-1.112272,,3c,4c,,,5c
1,2,4,1,-1.658725,-0.572117,-1.086608,,3c,4c,,,6c
1,2,4,1,-1.595468,-0.529665,-1.065803,,3c,4c,,,7c
1,2,4,1,-1.531610,-0.486539,-1.045071,,3c,4c,,,8c
1,2,4,1,-1.536071,-0.489277,-1.046794,,3c,4c,,,9c
1,2,4,1,-1.539048,-0.490885,-1.048163,,3c,4c,,,Tc
1,2,4,1,-1.541366,-0.491771,-1.049595,,3c,4c,,,Jc
1,2,4,1,-1.543741,-0.492758,-1.050983,,3c,4c,,,Qc
1,2,4,1,-1.546148,-0.493804,-1.052344,,3c,4c,,,Kc
1,2,4,1,-1.608364,-0.536143,-1.072221,,3c,4c,,,Ac
1,2,4,1,-1.543253,-0.492003,-1.051249,,3c,4c,,,2d
1,2,4,1,-1.825130,-0.591357,-1.233773,,3c,4c,,,3d
1,2,4,1,-1.810226,-0.583480,-1.226746,,3c,4c,,,4d
1,2,4,1,-1.520380,-0.474293,-1.046087,,3c,4c,,,5d
1,2,4,1,-1.465609,-0.449701,-1.015909,,3c,4c,,,6d
1,2,4,1,-1.421244,-0.429442,-0.991802,,3c,4c,,,7d
1,2,4,1,-1.376497,-0.408712,-0.967785,,3c,4c,,,8d
1,2,4,1,-1.381868,-0.411654,-0.970214,,3c,4c,,,9d
1,2,4,1,-1.385487,-0.413310,-0.972177,,3c,4c,,,Td
1,2,4,1,-1.388282,-0.414382,-0.973900,,3c,4c,,,Jd
1,2,4,1,-1.391056,-0.415564,-0.975492,,3c,4c,,,Qd
1,2,4,1,-1.393818,-0.416801,-0.977017,,3c,4c,,,Kd
1,2,4,1,-1.438361,-0.437134,-1.001227,,3c,4c,,,Ad
1,2,4,0,-1.511855,-0.472659,-1.039197,,3c,4c,,

0,1,4,1,-2.022652,-0.764621,-1.258031,,2c,3c,,,4c
0,1,4,1,-2.019438,-0.763619,-1.255819,,2c,3c,,,5c
0,1,4,1,-1.945254,-0.715834,-1.229420,,2c,3c,,,6c
0,1,4,1,-1.880675,-0.672761,-1.207914,,2c,3c,,,7c
0,1,4,1,-1.885014,-0.675415,-1.209600,,2c,3c,,,8c
0,1,4,1,-1.888475,-0.677360,-1.211116,,2c,3c,,,9c
0,1,4,1,-1.887499,-0.676849,-1.210650,,2c,3c,,,Tc
0,1,4,1,-1.889817,-0.677665,-1.212152,,2c,3c,,,Jc
0,1,4,1,-1.892192,-0.678585,-1.213607,,2c,3c,,,Qc
0,1,4,1,-1.894599,-0.679572,-1.215027,,2c,3c,,,Kc
0,1,4,1,-1.957558,-0.722271,-1.235287,,2c,3c,,,Ac
0,1,4,1,-2.170407,-0.772850,-1.397558,,2c,3c,,,2d
0,1,4,1,-2.155418,-0.765168,-1.390250,,2c,3c,,,3d
0,1,4,1,-1.826873,-0.641512,-1.185361,,2c,3c,,,4d
0,1,4,1,-1.824412,-0.640418,-1.183994,,2c,3c,,,5d
0,1,4,1,-1.768148,-0.615064,-1.153084,,2c,3c,,,6d
0,1,4,1,-1.722806,-0.594381,-1.128425,,2c,3c,,,7d
0,1,4,1,-1.728241,-0.597207,-1.131035,,2c,3c,,,8d
0,1,4,1,-1.732569,-0.599217,-1.133352,,2c,3c,,,9d
0,1,4,1,-1.731966,-0.598746,-1.133220,,2c,3c,,,Td
0,1,4,1,-1.734761,-0.599765,-1.134995,,2c,3c,,,Jd
0,1,4,1,-1.737534,-0.600894,-1.136641,,2c,3c,,,Qd
0,1,4,1,-1.740297,-0.602084,-1.138213,,2c,3c,,,Kd
0,1,4,1,-1.785604,-0.622778,-1.162826,,2c,3c,,,Ad
0,1,4,0,-1.842806,-0.649268,-1.193537,,2c,3c,,

I will be very busy in April with travel and tax preparation plus my normal online play. I might be able to answer quick questions, but might not be able to join a lengthy discussion.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
aceside
aceside
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Joined: May 14, 2021
April 6th, 2024 at 9:34:21 AM permalink
Quote: Mental

I hope I am thinking about this correctly. I could investigate by doing a calculation with the decision on the later streets disabled.
link to original post

Regarding the later street strategic decisions, there is not very much gambling to do on the 1x Raise/Check decision. The only thing I can think of is the less than 21 outs rule. There is still some gambling on the 2x Raise/Check decision. Please help think about what edge might still hide in this stage of decision.

Here I present a couple of graphs similar to yours earlier based on your data (some data points of 2c removal are missing), as shown below:
Last edited by: aceside on Apr 6, 2024
CollusionUTH
CollusionUTH
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Joined: Nov 12, 2024
November 12th, 2024 at 3:07:41 PM permalink
All of those links have royal flush at 100:1
It’s 500:1

I’m very confused
CollusionUTH
CollusionUTH
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Joined: Nov 12, 2024
November 12th, 2024 at 3:10:20 PM permalink
All of those links have royal flush at 100:1
It’s 500:1

I’m very confused
Quote: MrCasinoGames

Quote: Wizard

Quote: Mental

After I do some more optimization and checking, I am going to try to calculate EVs with lower numbers of exposed cards. I will create a plot of overall UTH EV versus number of exposed cards. If this curve is noisy, at least it will tell me how much the EV depends on the specific random choice of exposed cards. Maybe 1326 starting hands will not be enough to get good answers. I don't expect that it should take more than a few days to see the results converge. I should be able to run four parallel computations on my MacBook without bogging down. This should produce results for about eight starting hands per minute (115K/day).
link to original post



This is great! I look forward to seeing some numbers for a small number of cards exposed.
link to original post


FYI. Below are 3 Links to Casino Hold'em® with ALL Player's Hole-Cards deal Face-Up:
* GLI-Report on 08/September/2023:
* Math by Charles R. Mousseau on 03/July/3017: /48JvP6o
* Math by Stephen How on 14/Aug/2014: /4360ObK

Casino Hold'em® Face-Up (aka Casino Hold'em® Poker-Plus / Casino Hold'em® Open): /
* Casino Hold'em® at Wizard of Odds:
link to original post

gordonm888
Administrator
gordonm888
  • Threads: 61
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Joined: Feb 18, 2015
November 12th, 2024 at 6:40:13 PM permalink
Quote: CollusionUTH

All of those links have royal flush at 100:1
It’s 500:1

I’m very confused

Quote: MrCasinoGames

Quote: Wizard

Quote: Mental

After I do some more optimization and checking, I am going to try to calculate EVs with lower numbers of exposed cards. I will create a plot of overall UTH EV versus number of exposed cards. If this curve is noisy, at least it will tell me how much the EV depends on the specific random choice of exposed cards. Maybe 1326 starting hands will not be enough to get good answers. I don't expect that it should take more than a few days to see the results converge. I should be able to run four parallel computations on my MacBook without bogging down. This should produce results for about eight starting hands per minute (115K/day).
link to original post



This is great! I look forward to seeing some numbers for a small number of cards exposed.
link to original post


FYI. Below are 3 Links to Casino Hold'em® with ALL Player's Hole-Cards deal Face-Up:
* GLI-Report on 08/September/2023:
* Math by Charles R. Mousseau on 03/July/3017: /48JvP6o
* Math by Stephen How on 14/Aug/2014: /4360ObK

Casino Hold'em® Face-Up (aka Casino Hold'em® Poker-Plus / Casino Hold'em® Open):
/
* Casino Hold'em® at Wizard of Odds:

link to original post


link to original post



These links are not for UTH, they are for a game called Casino Hold'em which was developed and is owned by forum member MrCasinoGames, who made the post. It has several important differences from UTH and, of course, has a different basic strategy than UTH.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
CollusionUTH
CollusionUTH
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Joined: Nov 12, 2024
November 12th, 2024 at 7:44:14 PM permalink
Thank you for the reply, the thread seems to be about uth tho and those links seem to be presented as evidence
Am I missing something
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