EOR and EV of each card in dealer’s hand for UTH?
May 22nd, 2026 at 6:41:57 AM
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Subtracting the original house edge of 0.02185 from each of your calculation EV numbers, we get the list of EV changes after removing the whole rank of four cards:
= -0.003925
= -0.001571
= -0.000036
= 0.000562
= 0.00426
= -0.002556
= -0.007087
= -0.014476
= -0.048625
= -0.047436
= -0.043571
= -0.034223
= -0.024949.
So, the EV change is snake shaped.
= -0.003925
= -0.001571
= -0.000036
= 0.000562
= 0.00426
= -0.002556
= -0.007087
= -0.014476
= -0.048625
= -0.047436
= -0.043571
= -0.034223
= -0.024949.
So, the EV change is snake shaped.
May 22nd, 2026 at 7:25:09 AM
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Any starting 2-card hand in UTH for which you bet 4X is profitable for player.
Let's count the number of times that a rank appears in a (+EV) 4X opening hand. Unsuited hands, including pairs, will count as 1 and suited hands will count as 0.25.
Ace___13
King___10.75
Queen___7.5
Jack___5
Ten___5
Nine___4
Eight___4_____A8, K8, Q8, 88
Seven__3.25
Six___3.25
Five___3
Four___2.25
Three___2.25_____A2, K2s, 33
Deuce___1.25_____A2, K2s
When eliminating ranks, this is a relative frequency of profitable starting hands in UTH that are eliminated. Of course, AA is far more profitable than 33 so this is far from a complete story.
Let's count the number of times that a rank appears in a (+EV) 4X opening hand. Unsuited hands, including pairs, will count as 1 and suited hands will count as 0.25.
Ace___13
King___10.75
Queen___7.5
Jack___5
Ten___5
Nine___4
Eight___4_____A8, K8, Q8, 88
Seven__3.25
Six___3.25
Five___3
Four___2.25
Three___2.25_____A2, K2s, 33
Deuce___1.25_____A2, K2s
When eliminating ranks, this is a relative frequency of profitable starting hands in UTH that are eliminated. Of course, AA is far more profitable than 33 so this is far from a complete story.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
May 22nd, 2026 at 3:56:20 PM
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A little revision here. For every pair, you count once; however, for every none-pair, you should count twice. For example, the 8-containing hands have these possibilities: A8, 8A, K8, 8K, Q8, 8Q, 88. So, there are seven counts of appearing.
There are also suited 8-containing hands: J8, 8J.
There are also suited 8-containing hands: J8, 8J.
May 22nd, 2026 at 7:05:57 PM
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Quote: acesideA little revision here. For every pair, you count once; however, for every none-pair, you should count twice. For example, the 8-containing hands have these possibilities: A8, 8A, K8, 8K, Q8, 8Q, 88. So, there are seven counts of appearing.
There are also suited 8-containing hands: J8, 8J.
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My nomenclature was bad: when I referred to an unsuited starting hand, I really meant {both unsuited and suited}.
As for pairs having fewer combinations than unpaired hands -yes, but pairs tend to have a larger +EV than unpaired hands. And all ranks except deuces had a pair in their frequency count, so it didn't seem like a big deal. I was just trying to illustrate the principal that EV vs rank removed should have a choppy declining trend because the number of profitable hands varies non-smoothly with rank. I was too lazy to do actual math.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
May 30th, 2026 at 7:53:09 PM
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I had a calculation running when I left for the Indy 500, but I inadvertently ran the wrong calculation. I am 9/13ths of the way through the right calculation, but it won't finish before I leave tomorrow for a 7-day bike trip. I am posting the partial results, and I will update with full results when I can.
Red bars are computer perfect optimal strategy EVs for when a dealer is know to have a certain card. Blue bars are the EV when you play BS when the dealers hand contains a certain card. The ranks left-to-right are 23456789TJQKA.
If the dealer hand is known to contain a nine of clubs, your EV is +0.08 if you play optimally. Your EV is -0.03 if you play BS.
Playing BS when you know the dealer holds an ace of clubs is very bad. You will often be raising 4x with hands like TJo or 9Ko that are dominated. You will seldom win when the dealer qualifies.
Red bars are computer perfect optimal strategy EVs for when a dealer is know to have a certain card. Blue bars are the EV when you play BS when the dealers hand contains a certain card. The ranks left-to-right are 23456789TJQKA.
If the dealer hand is known to contain a nine of clubs, your EV is +0.08 if you play optimally. Your EV is -0.03 if you play BS.
Playing BS when you know the dealer holds an ace of clubs is very bad. You will often be raising 4x with hands like TJo or 9Ko that are dominated. You will seldom win when the dealer qualifies.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
May 31st, 2026 at 6:11:59 AM
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This is a lot of calculation, but probably not much usefulness to players. Let’s be straightforward. If one dealer card is a known Ace, should player 4x raise his AJ offsuit hand? And 10-10 pair hand?
May 31st, 2026 at 7:17:07 AM
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Quote: acesideThis is a lot of calculation, but probably not much usefulness to players. Let’s be straightforward. If one dealer card is a known Ace, should player 4x raise his AJ offsuit hand? And 10-10 pair hand?
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It is a slow calculation because I recalculate the basic strategy for every hand and then do the quicker calculation of the EV for the hand that is constrained to have a particular card in the dealer hand. I could speed this up a lot if it mattered to me. I cannot run these calculations on battery power for very long -- an hour at most.Will try to finish it in the hotel tonight.
I include a snippet of the results files for high cards against ace (suited or not suited to the players hole cards). ALL means normal game, DLR means the particular card is in the dealer hand. Note that the presence of an ace improves the player's EV for some hands. You would be shocked to find that some very weak hands are not harmed by having a dealer ace. EV columns are Raise, Check, Best EV.
9,10,1,1.024156,0.693598,1.024156,Jc,Qc,Jc_Qc,Ac,ALL
9,10,1,-1.332715,-0.593780,-1.332715,Jc,Qc,Jc_Qc,Ac,DLR
9,10,3,1.024156,0.693598,1.024156,Jc,Qc,Jc_Qc,Ad,ALL
9,10,3,-0.884039,-0.236196,-0.884039,Jc,Qc,Jc_Qc,Ad,DLR
9,11,1,1.227500,0.767587,1.227500,Jc,Kc,Jc_Kc,Ac,ALL
9,11,1,-1.477953,-0.761039,-1.477953,Jc,Kc,Jc_Kc,Ac,DLR
9,11,3,1.227500,0.767587,1.227500,Jc,Kc,Jc_Kc,Ad,ALL
9,11,3,-1.020862,-0.395739,-1.020862,Jc,Kc,Jc_Kc,Ad,DLR
9,12,3,1.489507,0.886020,1.489507,Jc,Ac,Jc_Ac,Ad,ALL
9,12,3,1.155341,0.646318,1.155341,Jc,Ac,Jc_Ac,Ad,DLR
9,22,3,2.749739,1.650960,2.749739,Jc,Jd,Jc_Jd,Ac,ALL
9,22,3,1.330751,0.693211,1.330751,Jc,Jd,Jc_Jd,Ac,DLR
9,22,3,2.749739,1.650960,2.749739,Jc,Jd,Jc_Jd,Ah,ALL
9,22,3,1.365341,0.723279,1.365341,Jc,Jd,Jc_Jd,Ah,DLR
9,23,3,0.455681,0.224297,0.455681,Jc,Qd,Jc_Qd,Ac,ALL
9,23,3,-1.668766,-0.765439,-1.668766,Jc,Qd,Jc_Qd,Ac,DLR
9,23,3,0.455681,0.224297,0.455681,Jc,Qd,Jc_Qd,Ad,ALL
9,23,3,-1.670806,-0.766850,-1.670806,Jc,Qd,Jc_Qd,Ad,DLR
9,23,6,0.455681,0.224297,0.455681,Jc,Qd,Jc_Qd,Ah,ALL
9,23,6,-1.623147,-0.736860,-1.623147,Jc,Qd,Jc_Qd,Ah,DLR
9,24,3,0.691991,0.318649,0.691991,Jc,Kd,Jc_Kd,Ac,ALL
9,24,3,-1.794351,-0.926809,-1.794351,Jc,Kd,Jc_Kd,Ac,DLR
9,24,3,0.691991,0.318649,0.691991,Jc,Kd,Jc_Kd,Ad,ALL
9,24,3,-1.798003,-0.928510,-1.798003,Jc,Kd,Jc_Kd,Ad,DLR
9,24,6,0.691991,0.318649,0.691991,Jc,Kd,Jc_Kd,Ah,ALL
9,24,6,-1.747178,-0.900762,-1.747178,Jc,Kd,Jc_Kd,Ah,DLR
9,25,3,0.991767,0.461261,0.991767,Jc,Ad,Jc_Ad,Ac,ALL
9,25,3,0.609950,0.196573,0.609950,Jc,Ad,Jc_Ad,Ac,DLR
9,25,6,0.991767,0.461261,0.991767,Jc,Ad,Jc_Ad,Ah,ALL
9,25,6,0.632165,0.231214,0.632165,Jc,Ad,Jc_Ad,Ah,DLR
10,11,1,1.312620,0.816408,1.312620,Qc,Kc,Qc_Kc,Ac,ALL
10,11,1,-1.477453,-0.775550,-1.477453,Qc,Kc,Qc_Kc,Ac,DLR
10,11,3,1.312620,0.816408,1.312620,Qc,Kc,Qc_Kc,Ad,ALL
10,11,3,-1.019966,-0.407208,-1.019966,Qc,Kc,Qc_Kc,Ad,DLR
10,12,3,1.572705,0.935691,1.572705,Qc,Ac,Qc_Ac,Ad,ALL
10,12,3,1.578266,0.872101,1.578266,Qc,Ac,Qc_Ac,Ad,DLR
10,23,3,3.018649,1.821642,3.018649,Qc,Qd,Qc_Qd,Ac,ALL
10,23,3,1.449309,0.762683,1.449309,Qc,Qd,Qc_Qd,Ac,DLR
10,23,3,3.018649,1.821642,3.018649,Qc,Qd,Qc_Qd,Ah,ALL
10,23,3,1.484579,0.793271,1.484579,Qc,Qd,Qc_Qd,Ah,DLR
10,24,3,0.782942,0.370490,0.782942,Qc,Kd,Qc_Kd,Ac,ALL
10,24,3,-1.795186,-0.941404,-1.795186,Qc,Kd,Qc_Kd,Ac,DLR
10,24,3,0.782942,0.370490,0.782942,Qc,Kd,Qc_Kd,Ad,ALL
10,24,3,-1.797227,-0.942414,-1.797227,Qc,Kd,Qc_Kd,Ad,DLR
10,24,6,0.782942,0.370490,0.782942,Qc,Kd,Qc_Kd,Ah,ALL
10,24,6,-1.746476,-0.912429,-1.746476,Qc,Kd,Qc_Kd,Ah,DLR
10,25,3,1.080609,0.514408,1.080609,Qc,Ad,Qc_Ad,Ac,ALL
10,25,3,1.062666,0.437359,1.062666,Qc,Ad,Qc_Ad,Ac,DLR
10,25,6,1.080609,0.514408,1.080609,Qc,Ad,Qc_Ad,Ah,ALL
10,25,6,1.081814,0.470766,1.081814,Qc,Ad,Qc_Ad,Ah,DLR
11,12,3,1.658326,0.986740,1.658326,Kc,Ac,Kc_Ac,Ad,ALL
11,12,3,1.989133,1.094723,1.989133,Kc,Ac,Kc_Ac,Ad,DLR
11,24,3,3.289359,1.993532,3.289359,Kc,Kd,Kc_Kd,Ac,ALL
11,24,3,1.564299,0.830017,1.564299,Kc,Kd,Kc_Kd,Ac,DLR
11,24,3,3.289359,1.993532,3.289359,Kc,Kd,Kc_Kd,Ah,ALL
11,24,3,1.600228,0.861114,1.600228,Kc,Kd,Kc_Kd,Ah,DLR
11,25,3,1.171914,0.568928,1.171914,Kc,Ad,Kc_Ad,Ac,ALL
11,25,3,1.501538,0.675084,1.501538,Kc,Ad,Kc_Ad,Ac,DLR
11,25,6,1.171914,0.568928,1.171914,Kc,Ad,Kc_Ad,Ah,ALL
11,25,6,1.517642,0.706500,1.517642,Kc,Ad,Kc_Ad,Ah,DLR
12,25,3,3.601073,2.192924,3.601073,Ac,Ad,Ac_Ad,Ah,ALL
12,25,3,3.991335,2.221799,3.991335,Ac,Ad,Ac_Ad,Ah,DLR
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
May 31st, 2026 at 8:18:12 AM
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Quote: MentalYou would be shocked to find that some very weak hands are not harmed by having a dealer ace.
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No, that's poker.
In conventional poker you can open with, say, a 76s. When the flop comes if it is 2 or 3 high cards you will be folding (unless they're in your suit); what you are hoping for is a flop with 2 or ideally 3 low cards that pair you or give you straight possibilities. If you know your opponent has an Ace then that is no different than when he has a Jack -they are both 'overcards', higher than your 7 or 6. You assume he has high cards like T,J,Q,K,A and you are only continuing only if the flop is low cards or gives you a flush draw.
In UTH, it is the same principle. If you open with 54, you are checking and you should expect that dealer has higher cards than yours. Doesn't matter whether dealer has an AK as opposed to a 98 - they're all higher than your two crappy cards. You are hoping that dealer doesn't pair and you get one pair - or that you make a straight or two pair.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
May 31st, 2026 at 8:10:12 PM
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Quote: MentalPlaying BS when you know the dealer holds an ace of clubs is very bad. You will often be raising 4x with hands like TJo or 9Ko that are dominated. You will seldom win when the dealer qualifies.
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I’ve been thinking about this part. Knowing a dealer Ace is still very different from knowing a dealer Ace of clubs. So, here is my question. Is your basic strategy the same for these two different situations?
June 1st, 2026 at 3:51:04 AM
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The calculation finished, but the average of the EORs is off by 0.3%. The average EV for placing all 13 ranks in the dealers hole cards should be the same as the EV of the base game (assuming I use the same BS). I am not sure what to make of the small discrepancy.
0 0.473939
1 0.389140
2 0.303292
3 0.218642
4 0.162909
5 0.104732
6 0.042896
7 -0.026492
8 -0.120932
9 -0.191599
10 -0.310372
11 -0.518471
12 -0.847202
Average -0.024578
I will be riding on the Erie Canalway bike trail until Sunday, and I won't be spending any time on this problem until I get home.
0 0.473939
1 0.389140
2 0.303292
3 0.218642
4 0.162909
5 0.104732
6 0.042896
7 -0.026492
8 -0.120932
9 -0.191599
10 -0.310372
11 -0.518471
12 -0.847202
Average -0.024578
I will be riding on the Erie Canalway bike trail until Sunday, and I won't be spending any time on this problem until I get home.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
June 1st, 2026 at 5:39:13 AM
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Quote: acesideThis is a lot of calculation, but probably not much usefulness to players. Let’s be straightforward. If one dealer card is a known Ace, should player 4x raise his AJ offsuit hand? And 10-10 pair hand?
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"Poker is a game of high cards"
The fact that an observed Ace in the dealer's hand is a certain suit is immaterial unless both your cards are that suit or unless the board comes out with 3 or more of that suit. Which are infrequent circumstances.
High cards make the dealers hand strong. Low cards make it weak. Why? Read above. "Poker is a game of high cards"
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 1st, 2026 at 5:53:19 AM
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I just looked into the list of hands you calculated. I see you have calculated this (player two cards, dealer exposed)
Jc_Qd,Ad.
But it looks like you haven’t calculated another suit combination, like this one
Jc_Qd,Ah.
By the way, enjoy your bike ride. Are you talking about the 350-mile long route from Buffalo to Albany?
Jc_Qd,Ad.
But it looks like you haven’t calculated another suit combination, like this one
Jc_Qd,Ah.
By the way, enjoy your bike ride. Are you talking about the 350-mile long route from Buffalo to Albany?
June 1st, 2026 at 7:36:23 PM
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Quote: acesideI just looked into the list of hands you calculated. I see you have calculated this (player two cards, dealer exposed)
Jc_Qd,Ad.
But it looks like you haven’t calculated another suit combination, like this one
Jc_Qd,Ah.
By the way, enjoy your bike ride. Are you talking about the 350-mile long route from Buffalo to Albany?
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Maybe you overlooked it or it is missing from the post you received.
9,23,6,-1.623147,-0.736860,-1.623147,Jc,Qd,Jc_Qd,Ah,DLR
Yes, we left Buffalo this morning and logged 67 miles into a headwind today. We are riding e-bikes, since we we both born in the first Eisenhower administration and we now need a little extra power to make the trip more enjoyable.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
June 1st, 2026 at 10:43:40 PM
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I actually rode a road bike on a small segment of this trail dozens of times. It was converted from a railroad to a bike trail.
August 3rd, 2026 at 7:13:15 PM
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Quote: MentalThe calculation finished, but the average of the EORs is off by 0.3%. The average EV for placing all 13 ranks in the dealers hole cards should be the same as the EV of the base game (assuming I use the same BS). I am not sure what to make of the small discrepancy.
0 0.473939
1 0.389140
2 0.303292
3 0.218642
4 0.162909
5 0.104732
6 0.042896
7 -0.026492
8 -0.120932
9 -0.191599
10 -0.310372
11 -0.518471
12 -0.847202
Average -0.024578
I will be riding on the Erie Canalway bike trail until Sunday, and I won't be spending any time on this problem until I get home.
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I revisited this problem because I realized I could do the calculation much more efficiently. In the end, the EV numbers came out slightly different and are probably more accurate than my previous attempt.
0.4972237334
0.4080658742
0.3181753448
0.2294870515
0.1711200214
0.1104881192
0.0463495828
-0.0250372845
-0.1224322786
-0.1979561768
-0.3219571567
-0.5332806646
-0.8642924452
With my new program, I can calculate the EV for every case of two known dealer hole cards, and from these results, I can calculate the EV for the case of one known dealer hole card. Thus, I get both sets of EV's simultaneously. The new algorithm takes a tenth the time as my previous algorithm and yields more information.
-0.2840462789 / 13 = TOT EV: -0.0218497138
This is the average of all 13 different ranks of one known card in the dealer's hand. Mike gives the EV as -0.021850, which agrees with my EV after rounding.
-28.9727204494 / 1326 = TOT EV: -0.0218497138
I also calculate the EV for every possible two cards in the dealer's hand. The average of these 1326 EV's is the same number, as expected.
To be clear, all EVs assume you use computer-perfect strategy for the situation where you do not know anything about the dealer's hand. Clearly, raising 4x based on this strategy even when you know the dealer holds an ace is sometimes very costly. Not raising when you know the dealer has a deuce is also often a significant lost opportunity.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
August 3rd, 2026 at 7:48:18 PM
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Great work! However, I’m not very sure about your last sentence. Knowing that the dealer has a deuce helps the player, but probably not more than knowing that the dealer has a king does. Is this right?
August 4th, 2026 at 4:32:29 AM
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Quote: acesideGreat work! However, I’m not very sure about your last sentence. Knowing that the dealer has a deuce helps the player, but probably not more than knowing that the dealer has a king does. Is this right?
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Yes.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
August 4th, 2026 at 11:17:19 AM
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Quote: acesideGreat work! However, I’m not very sure about your last sentence. Knowing that the dealer has a deuce helps the player, but probably not more than knowing that the dealer has a king does. Is this right?
link to original post
No.
A deuce helps you much more than a king hurts you if you play CPOS (computer perfect optimal strategy). You can raise 4x preflop a lot more often against a deuce and still have the better of it. Against a king, you will still raise your very good hands preflop and will only check some marginal hands. The good hands will make you less money, especially if the king is an overcard to one or both of your cards. Under CPOS, a deuce helps you 2.7x more than a king hurts you (+64.6% versus -23.4%).
If you play BS despite knowing one of the dealer HCs, a deuce still helps you just a little bit more than a king hurts you.
| Dealer HC | CPOS | BS |
|---|---|---|
| 2 | 62.43% | 49.72% |
| 3 | 52.66% | 40.81% |
| 4 | 43.22% | 31.82% |
| 5 | 33.82% | 22.95% |
| 6 | 28.60% | 17.11% |
| 7 | 22.85% | 11.05% |
| 8 | 16.15% | 4.63% |
| 9 | 8.57% | -2.50% |
| T | -1.25% | -12.24% |
| J | -8.17% | -19.80% |
| Q | -16.25% | -32.20% |
| K | -25.82% | -53.33% |
| A | -40.11% | -86.43% |
Under CPOS, a deuce helps you much more than and ace hurts you. If you play BS, a dealer ace will crush many of your raises.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
August 4th, 2026 at 6:27:27 PM
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Some details on the calculation:
I do the following calculation for every one of the 169 distinct 2-card player hole cards. (52 choose 2) = 1326 unique hands, but these fall into 169 distinct hands ignoring suit permutations.
I calculate the optimal strategy by looping through all possible flops, rivers, and dealer hands. For any two player hole cards, there are 19600 possible flops and 1081 rivers. I use a 1-dimensional array of size 19600 to record the optimal flop decisions for BS. I use a 19600x1081 2-dimensional array to record the optimal river decisions. Once I have all 21,207,200 decision points recorded, I repeat the looping process. At the river, I decide which strategy decision has priority. If there is a preflop raise, this has priority. If not, then I check for a postflop raise. If it is checked to the river, then I use this decision.
Then, when I run out all the 990 possible dealer decisions, I record the W/L result of the hand in a 52x52 array indexed by the two cards in the dealer hand. When I complete the calculation, I know the exact EV for the two player hole cards and two specific dealer cards. From the CSV example below, the EV for player Ac-Ad versus dealer 2c-3c is EV=3.43730465.
In order to find the EV of Ac-Ad versus every dealer hand containing a 2c, I just need to take an average of the 49 cells in the row and column associated with a 2c. The result is EV=3.8052522763 which agrees with Eliot's result, 3.80525228. Note that Eliot is calculating EV using CPOS and I am calculating EV for BS. However, for pocket aces, CPOS and BS both say raise preflop, so the EVs should be the same. For a player hand like 4c-7d, my EV results will be different than Eliot's EVs.
You can copy the CSV array to a file and import it to Excel and check all the Ac-Ad versus XX results against Eliot's results.
I do the following calculation for every one of the 169 distinct 2-card player hole cards. (52 choose 2) = 1326 unique hands, but these fall into 169 distinct hands ignoring suit permutations.
I calculate the optimal strategy by looping through all possible flops, rivers, and dealer hands. For any two player hole cards, there are 19600 possible flops and 1081 rivers. I use a 1-dimensional array of size 19600 to record the optimal flop decisions for BS. I use a 19600x1081 2-dimensional array to record the optimal river decisions. Once I have all 21,207,200 decision points recorded, I repeat the looping process. At the river, I decide which strategy decision has priority. If there is a preflop raise, this has priority. If not, then I check for a postflop raise. If it is checked to the river, then I use this decision.
Then, when I run out all the 990 possible dealer decisions, I record the W/L result of the hand in a 52x52 array indexed by the two cards in the dealer hand. When I complete the calculation, I know the exact EV for the two player hole cards and two specific dealer cards. From the CSV example below, the EV for player Ac-Ad versus dealer 2c-3c is EV=3.43730465.
Ac Ad,2c,3c,4c,5c,6c,7c,8c,9c,Tc,Jc,Qc,Kc,Ac,2d,3d,4d,5d,6d,7d,8d,9d,Td,Jd,Qd,Kd,Ad,2h,3h,4h,5h,6h,7h,8h,9h,Th,Jh,Qh,Kh,Ah,2s,3s,4s,5s,6s,7s,8s,9s,Ts,Js,Qs,Ks,As,
2c,0.00000000,3.43730465,3.39434440,3.35138416,3.37467033,3.54173850,3.49877825,3.54421411,3.50734274,3.55010676,3.59287078,3.63563479,0.00000000,3.53135717,3.90108999,3.85442830,3.80776661,3.83005646,4.00912805,3.96277647,4.01213278,3.97337914,4.01984461,4.06631007,4.11277554,0.00000000,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,
3c,0.00000000,0.00000000,3.21695067,3.17399042,3.19727659,3.36434477,3.49868014,3.50125387,3.46438249,3.50714651,3.54991053,3.59267455,0.00000000,3.90108999,3.48166155,3.66553603,3.61887434,3.64116419,3.82023578,3.96236825,3.96547108,3.92671745,3.97318292,4.01964838,4.06611384,0.00000000,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,
4c,0.00000000,0.00000000,0.00000000,2.99659669,3.01988286,3.18695103,3.32128641,3.50115575,3.42142225,3.46418627,3.50695028,3.54971430,0.00000000,3.85442830,3.66553603,3.43196594,3.42998206,3.45227191,3.63134350,3.77347597,3.96506286,3.88005576,3.92652123,3.97298669,4.01945215,0.00000000,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,
5c,0.00000000,0.00000000,0.00000000,0.00000000,2.84248913,3.00955730,3.14389267,3.32376202,3.42132413,3.42122602,3.46399004,3.50675406,0.00000000,3.80776661,3.61887434,3.42998206,3.38227032,3.26337963,3.44245122,3.58458370,3.77617059,3.87964754,3.87985953,3.92632500,3.97279046,0.00000000,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,
6c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84439037,2.97872574,3.15859509,3.25615720,3.43335471,3.43325659,3.47602061,0.00000000,3.83005646,3.64116419,3.45227191,3.26337963,3.33124784,3.26640772,3.40854019,3.60012708,3.70360403,3.89230008,3.89251208,3.93897754,0.00000000,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,
7c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.85065736,3.03052671,3.12808882,3.30528633,3.48248383,3.48238572,0.00000000,4.00912805,3.82023578,3.63134350,3.44245122,3.26640772,3.34038640,3.27321142,3.46479831,3.56827526,3.75697131,3.94566736,3.94587935,0.00000000,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,
8c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.89599510,2.99355722,3.17075473,3.34795223,3.52514974,0.00000000,3.96277647,3.96236825,3.77347597,3.58458370,3.40854019,3.27321142,3.33777005,3.32246961,3.42594656,3.61464261,3.80333866,3.99203471,0.00000000,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,
9c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.86658590,3.04378341,3.22098091,3.39817842,0.00000000,4.01213278,3.96547108,3.96506286,3.77617059,3.60012708,3.46479831,3.32246961,3.38223294,3.29030826,3.47900431,3.66770036,3.85639641,0.00000000,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,
Tc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.97694889,3.15414640,3.33134391,0.00000000,3.97337914,3.92671745,3.88005576,3.87964754,3.70360403,3.56827526,3.42594656,3.29030826,3.34082558,3.39803797,3.58673401,3.77543006,0.00000000,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,
Jc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.19691042,3.37410793,0.00000000,4.01984461,3.97318292,3.92652123,3.87985953,3.89230008,3.75697131,3.61464261,3.47900431,3.39803797,3.38528848,3.63319948,3.82189553,0.00000000,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,
Qc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.41687195,0.00000000,4.06631007,4.01964838,3.97298669,3.92632500,3.89251208,3.94566736,3.80333866,3.66770036,3.58673401,3.63319948,3.42975138,3.86836099,0.00000000,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,
Kc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.11277554,4.06611384,4.01945215,3.97279046,3.93897754,3.94587935,3.99203471,3.85639641,3.77543006,3.82189553,3.86836099,3.47421428,0.00000000,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,
Ac,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
2d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.43730465,3.39434440,3.35138416,3.37467033,3.54173850,3.49877825,3.54421411,3.50734274,3.55010676,3.59287078,3.63563479,0.00000000,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,
3d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.21695067,3.17399042,3.19727659,3.36434477,3.49868014,3.50125387,3.46438249,3.50714651,3.54991053,3.59267455,0.00000000,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,
4d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.99659669,3.01988286,3.18695103,3.32128641,3.50115575,3.42142225,3.46418627,3.50695028,3.54971430,0.00000000,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,
5d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84248913,3.00955730,3.14389267,3.32376202,3.42132413,3.42122602,3.46399004,3.50675406,0.00000000,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,
6d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84439037,2.97872574,3.15859509,3.25615720,3.43335471,3.43325659,3.47602061,0.00000000,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,
7d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.85065736,3.03052671,3.12808882,3.30528633,3.48248383,3.48238572,0.00000000,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,
8d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.89599510,2.99355722,3.17075473,3.34795223,3.52514974,0.00000000,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,
9d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.86658590,3.04378341,3.22098091,3.39817842,0.00000000,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,
Td,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.97694889,3.15414640,3.33134391,0.00000000,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,
Jd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.19691042,3.37410793,0.00000000,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,
Qd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.41687195,0.00000000,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,
Kd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,
Ad,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
2h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.31684911,3.27458208,3.23246223,3.25096186,3.41401468,3.37228378,3.41643073,3.39436806,3.43585718,3.47734631,3.51883544,3.68838828,3.39364038,3.74923612,3.70359819,3.65825461,3.67865227,3.85134299,3.80639186,3.85398154,3.82898948,3.87370233,3.91841519,3.96312804,4.19156295,
3h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.10293499,3.06086770,3.07936733,3.24242015,3.37218566,3.37474537,3.35268270,3.39417183,3.43566096,3.47715009,3.64698558,3.74923612,3.34360721,3.51959932,3.47425574,3.49465340,3.66734412,3.80516544,3.80794765,3.78295560,3.82766845,3.87238131,3.91709416,4.14582457,
4h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88923813,2.90777280,3.07082562,3.20059113,3.37464726,3.31099735,3.35248647,3.39397560,3.43546473,3.60558289,3.70359819,3.51959932,3.29436595,3.29065283,3.31105049,3.48374120,3.62156253,3.80711719,3.73731767,3.78203053,3.82674338,3.87145624,4.10048216,
5h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73615725,2.89923109,3.02899660,3.20305273,3.31089923,3.31080112,3.35229025,3.39377938,3.56418019,3.65825461,3.47425574,3.29065283,3.24571338,3.12774192,3.30043263,3.43825395,3.62380862,3.73678155,3.73668694,3.78139980,3.82611265,4.05543408,
6h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73790227,2.86767829,3.04173441,3.14958092,3.32097922,3.32088111,3.36237023,3.72309940,3.67865227,3.49465340,3.31105049,3.12774192,3.19624085,3.12949920,3.26732052,3.45287519,3.56584812,3.74852596,3.74843135,3.79314421,4.22555749,
7h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.74292766,2.91698729,3.02483379,3.19623209,3.36763040,3.36753228,3.70597978,3.85134299,3.66734412,3.48374120,3.30043263,3.12949920,3.20239163,3.13476112,3.32031579,3.43328872,3.61596656,3.79864440,3.79854979,4.20707012,
8h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.78698000,2.89482650,3.06622481,3.23762311,3.40902141,3.70588167,3.80639186,3.80516544,3.62156253,3.43825395,3.26732052,3.13476112,3.19968417,3.18220713,3.29518006,3.47785790,3.66053575,3.84321359,4.20692646,
9h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.77094546,2.94234377,3.11374207,3.28514037,3.74708813,3.85398154,3.80794765,3.80711719,3.62380862,3.45287519,3.32031579,3.18220713,3.24220699,3.16278593,3.34546377,3.52814162,3.71081946,4.25132979,
Th,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88091951,3.05231781,3.22371612,3.56058854,3.82898948,3.78295560,3.73731767,3.73678155,3.56584812,3.43328872,3.29518006,3.16278593,3.22675880,3.28086251,3.46354035,3.64621819,4.05116615,
Jh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.09380694,3.26520524,3.60179501,3.87370233,3.82766845,3.78203053,3.73668694,3.74852596,3.61596656,3.47785790,3.34546377,3.28086251,3.26930966,3.50825321,3.69093105,4.09558349,
Qh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.30669437,3.64300148,3.91841519,3.87238131,3.82674338,3.78139980,3.74843135,3.79864440,3.66053575,3.52814162,3.46354035,3.50825321,3.31186051,3.73564390,4.14000084,
Kh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.68420794,3.96312804,3.91709416,3.87145624,3.82611265,3.79314421,3.79854979,3.84321359,3.71081946,3.64621819,3.69093105,3.73564390,3.35441137,4.18441819,
Ah,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.19156295,4.14582457,4.10048216,4.05543408,4.22555749,4.20707012,4.20692646,4.25132979,4.05116615,4.09558349,4.14000084,4.18441819,0.03892066,
2s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.31684911,3.27458208,3.23246223,3.25096186,3.41401468,3.37228378,3.41643073,3.39436806,3.43585718,3.47734631,3.51883544,3.68838828,
3s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.10293499,3.06086770,3.07936733,3.24242015,3.37218566,3.37474537,3.35268270,3.39417183,3.43566096,3.47715009,3.64698558,
4s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88923813,2.90777280,3.07082562,3.20059113,3.37464726,3.31099735,3.35248647,3.39397560,3.43546473,3.60558289,
5s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73615725,2.89923109,3.02899660,3.20305273,3.31089923,3.31080112,3.35229025,3.39377938,3.56418019,
6s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73790227,2.86767829,3.04173441,3.14958092,3.32097922,3.32088111,3.36237023,3.72309940,
7s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.74292766,2.91698729,3.02483379,3.19623209,3.36763040,3.36753228,3.70597978,
8s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.78698000,2.89482650,3.06622481,3.23762311,3.40902141,3.70588167,
9s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.77094546,2.94234377,3.11374207,3.28514037,3.74708813,
Ts,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88091951,3.05231781,3.22371612,3.56058854,
Js,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.09380694,3.26520524,3.60179501,
Qs,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.30669437,3.64300148,
Ks,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.68420794,
As,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
2c,0.00000000,3.43730465,3.39434440,3.35138416,3.37467033,3.54173850,3.49877825,3.54421411,3.50734274,3.55010676,3.59287078,3.63563479,0.00000000,3.53135717,3.90108999,3.85442830,3.80776661,3.83005646,4.00912805,3.96277647,4.01213278,3.97337914,4.01984461,4.06631007,4.11277554,0.00000000,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,
3c,0.00000000,0.00000000,3.21695067,3.17399042,3.19727659,3.36434477,3.49868014,3.50125387,3.46438249,3.50714651,3.54991053,3.59267455,0.00000000,3.90108999,3.48166155,3.66553603,3.61887434,3.64116419,3.82023578,3.96236825,3.96547108,3.92671745,3.97318292,4.01964838,4.06611384,0.00000000,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,
4c,0.00000000,0.00000000,0.00000000,2.99659669,3.01988286,3.18695103,3.32128641,3.50115575,3.42142225,3.46418627,3.50695028,3.54971430,0.00000000,3.85442830,3.66553603,3.43196594,3.42998206,3.45227191,3.63134350,3.77347597,3.96506286,3.88005576,3.92652123,3.97298669,4.01945215,0.00000000,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,
5c,0.00000000,0.00000000,0.00000000,0.00000000,2.84248913,3.00955730,3.14389267,3.32376202,3.42132413,3.42122602,3.46399004,3.50675406,0.00000000,3.80776661,3.61887434,3.42998206,3.38227032,3.26337963,3.44245122,3.58458370,3.77617059,3.87964754,3.87985953,3.92632500,3.97279046,0.00000000,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,
6c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84439037,2.97872574,3.15859509,3.25615720,3.43335471,3.43325659,3.47602061,0.00000000,3.83005646,3.64116419,3.45227191,3.26337963,3.33124784,3.26640772,3.40854019,3.60012708,3.70360403,3.89230008,3.89251208,3.93897754,0.00000000,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,
7c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.85065736,3.03052671,3.12808882,3.30528633,3.48248383,3.48238572,0.00000000,4.00912805,3.82023578,3.63134350,3.44245122,3.26640772,3.34038640,3.27321142,3.46479831,3.56827526,3.75697131,3.94566736,3.94587935,0.00000000,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,
8c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.89599510,2.99355722,3.17075473,3.34795223,3.52514974,0.00000000,3.96277647,3.96236825,3.77347597,3.58458370,3.40854019,3.27321142,3.33777005,3.32246961,3.42594656,3.61464261,3.80333866,3.99203471,0.00000000,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,
9c,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.86658590,3.04378341,3.22098091,3.39817842,0.00000000,4.01213278,3.96547108,3.96506286,3.77617059,3.60012708,3.46479831,3.32246961,3.38223294,3.29030826,3.47900431,3.66770036,3.85639641,0.00000000,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,
Tc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.97694889,3.15414640,3.33134391,0.00000000,3.97337914,3.92671745,3.88005576,3.87964754,3.70360403,3.56827526,3.42594656,3.29030826,3.34082558,3.39803797,3.58673401,3.77543006,0.00000000,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,
Jc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.19691042,3.37410793,0.00000000,4.01984461,3.97318292,3.92652123,3.87985953,3.89230008,3.75697131,3.61464261,3.47900431,3.39803797,3.38528848,3.63319948,3.82189553,0.00000000,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,
Qc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.41687195,0.00000000,4.06631007,4.01964838,3.97298669,3.92632500,3.89251208,3.94566736,3.80333866,3.66770036,3.58673401,3.63319948,3.42975138,3.86836099,0.00000000,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,
Kc,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.11277554,4.06611384,4.01945215,3.97279046,3.93897754,3.94587935,3.99203471,3.85639641,3.77543006,3.82189553,3.86836099,3.47421428,0.00000000,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,
Ac,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
2d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.43730465,3.39434440,3.35138416,3.37467033,3.54173850,3.49877825,3.54421411,3.50734274,3.55010676,3.59287078,3.63563479,0.00000000,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,3.46249877,3.82475396,3.77839303,3.73232644,3.75374729,3.92894574,3.88327160,3.93158429,3.90609290,3.95152876,3.99696462,4.04240047,4.28145557,
3d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.21695067,3.17399042,3.19727659,3.36434477,3.49868014,3.50125387,3.46438249,3.50714651,3.54991053,3.59267455,0.00000000,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,3.82557215,3.41263438,3.59235656,3.54628997,3.56771082,3.74290926,3.88286338,3.88564560,3.86015421,3.90559007,3.95102593,3.99646178,4.23580597,
4d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.99659669,3.01988286,3.18695103,3.32128641,3.50115575,3.42142225,3.46418627,3.50695028,3.54971430,0.00000000,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,3.77963346,3.59277879,3.36316594,3.36025349,3.38167434,3.55687279,3.69682691,3.88523738,3.81421552,3.85965138,3.90508724,3.95052310,4.19015636,
5d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84248913,3.00955730,3.14389267,3.32376202,3.42132413,3.42122602,3.46399004,3.50675406,0.00000000,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,3.73369478,3.54684011,3.36038139,3.31399185,3.19563787,3.37083631,3.51079043,3.69920090,3.81380730,3.81371269,3.85914855,3.90458441,4.14450676,
6d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.84439037,2.97872574,3.15859509,3.25615720,3.43335471,3.43325659,3.47602061,0.00000000,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,3.75496144,3.56810677,3.38164806,3.19548369,3.26374435,3.19728477,3.33723889,3.52564936,3.64025576,3.82578940,3.82569479,3.87113065,4.31717586,
7d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.85065736,3.03052671,3.12808882,3.30528633,3.48248383,3.48238572,0.00000000,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,3.93152530,3.74467063,3.55821192,3.37204755,3.19862215,3.27138902,3.20396349,3.39237396,3.50698036,3.69251400,3.87804765,3.87795304,4.29969591,
8d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.89599510,2.99355722,3.17075473,3.34795223,3.52514974,0.00000000,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,3.88589672,3.88467030,3.69821159,3.51204722,3.33862182,3.20400904,3.26872711,3.25217806,3.36678446,3.55231810,3.73785175,3.92338539,4.29959779,
9d,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.86658590,3.04378341,3.22098091,3.39817842,0.00000000,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,3.93453003,3.88777314,3.88694268,3.70077831,3.52735291,3.39274013,3.25249868,3.31221997,3.23292856,3.41846220,3.60399584,3.78952949,4.34505117,
Td,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.97694889,3.15414640,3.33134391,0.00000000,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,3.89627572,3.84951884,3.80315791,3.80262179,3.62919639,3.49458361,3.35434216,3.22016564,3.28379219,3.33929694,3.52483058,3.71036422,4.12900075,
Jd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.19691042,3.37410793,0.00000000,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,3.94201818,3.89526130,3.84890037,3.80283378,3.81503664,3.68042386,3.54018241,3.40600588,3.33960354,3.32729907,3.57057304,3.75610668,4.17445413,
Qd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.41687195,0.00000000,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,3.98776064,3.94100376,3.89464283,3.84857625,3.81524864,3.86626411,3.72602266,3.59184613,3.52544379,3.57087965,3.37080594,3.80184915,4.21990750,
Kd,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,4.03350310,3.98674622,3.94038529,3.89431871,3.86099110,3.86647610,3.91186291,3.77768638,3.71128404,3.75671989,3.80215575,3.41431282,4.26536088,
Ad,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
2h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.31684911,3.27458208,3.23246223,3.25096186,3.41401468,3.37228378,3.41643073,3.39436806,3.43585718,3.47734631,3.51883544,3.68838828,3.39364038,3.74923612,3.70359819,3.65825461,3.67865227,3.85134299,3.80639186,3.85398154,3.82898948,3.87370233,3.91841519,3.96312804,4.19156295,
3h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.10293499,3.06086770,3.07936733,3.24242015,3.37218566,3.37474537,3.35268270,3.39417183,3.43566096,3.47715009,3.64698558,3.74923612,3.34360721,3.51959932,3.47425574,3.49465340,3.66734412,3.80516544,3.80794765,3.78295560,3.82766845,3.87238131,3.91709416,4.14582457,
4h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88923813,2.90777280,3.07082562,3.20059113,3.37464726,3.31099735,3.35248647,3.39397560,3.43546473,3.60558289,3.70359819,3.51959932,3.29436595,3.29065283,3.31105049,3.48374120,3.62156253,3.80711719,3.73731767,3.78203053,3.82674338,3.87145624,4.10048216,
5h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73615725,2.89923109,3.02899660,3.20305273,3.31089923,3.31080112,3.35229025,3.39377938,3.56418019,3.65825461,3.47425574,3.29065283,3.24571338,3.12774192,3.30043263,3.43825395,3.62380862,3.73678155,3.73668694,3.78139980,3.82611265,4.05543408,
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7h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.74292766,2.91698729,3.02483379,3.19623209,3.36763040,3.36753228,3.70597978,3.85134299,3.66734412,3.48374120,3.30043263,3.12949920,3.20239163,3.13476112,3.32031579,3.43328872,3.61596656,3.79864440,3.79854979,4.20707012,
8h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.78698000,2.89482650,3.06622481,3.23762311,3.40902141,3.70588167,3.80639186,3.80516544,3.62156253,3.43825395,3.26732052,3.13476112,3.19968417,3.18220713,3.29518006,3.47785790,3.66053575,3.84321359,4.20692646,
9h,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.77094546,2.94234377,3.11374207,3.28514037,3.74708813,3.85398154,3.80794765,3.80711719,3.62380862,3.45287519,3.32031579,3.18220713,3.24220699,3.16278593,3.34546377,3.52814162,3.71081946,4.25132979,
Th,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88091951,3.05231781,3.22371612,3.56058854,3.82898948,3.78295560,3.73731767,3.73678155,3.56584812,3.43328872,3.29518006,3.16278593,3.22675880,3.28086251,3.46354035,3.64621819,4.05116615,
Jh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.09380694,3.26520524,3.60179501,3.87370233,3.82766845,3.78203053,3.73668694,3.74852596,3.61596656,3.47785790,3.34546377,3.28086251,3.26930966,3.50825321,3.69093105,4.09558349,
Qh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.30669437,3.64300148,3.91841519,3.87238131,3.82674338,3.78139980,3.74843135,3.79864440,3.66053575,3.52814162,3.46354035,3.50825321,3.31186051,3.73564390,4.14000084,
Kh,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.68420794,3.96312804,3.91709416,3.87145624,3.82611265,3.79314421,3.79854979,3.84321359,3.71081946,3.64621819,3.69093105,3.73564390,3.35441137,4.18441819,
Ah,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,4.19156295,4.14582457,4.10048216,4.05543408,4.22555749,4.20707012,4.20692646,4.25132979,4.05116615,4.09558349,4.14000084,4.18441819,0.03892066,
2s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.31684911,3.27458208,3.23246223,3.25096186,3.41401468,3.37228378,3.41643073,3.39436806,3.43585718,3.47734631,3.51883544,3.68838828,
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4s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88923813,2.90777280,3.07082562,3.20059113,3.37464726,3.31099735,3.35248647,3.39397560,3.43546473,3.60558289,
5s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73615725,2.89923109,3.02899660,3.20305273,3.31089923,3.31080112,3.35229025,3.39377938,3.56418019,
6s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.73790227,2.86767829,3.04173441,3.14958092,3.32097922,3.32088111,3.36237023,3.72309940,
7s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.74292766,2.91698729,3.02483379,3.19623209,3.36763040,3.36753228,3.70597978,
8s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.78698000,2.89482650,3.06622481,3.23762311,3.40902141,3.70588167,
9s,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.77094546,2.94234377,3.11374207,3.28514037,3.74708813,
Ts,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,2.88091951,3.05231781,3.22371612,3.56058854,
Js,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.09380694,3.26520524,3.60179501,
Qs,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.30669437,3.64300148,
Ks,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,3.68420794,
As,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,0.00000000,
In order to find the EV of Ac-Ad versus every dealer hand containing a 2c, I just need to take an average of the 49 cells in the row and column associated with a 2c. The result is EV=3.8052522763 which agrees with Eliot's result, 3.80525228. Note that Eliot is calculating EV using CPOS and I am calculating EV for BS. However, for pocket aces, CPOS and BS both say raise preflop, so the EVs should be the same. For a player hand like 4c-7d, my EV results will be different than Eliot's EVs.
You can copy the CSV array to a file and import it to Excel and check all the Ac-Ad versus XX results against Eliot's results.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
August 5th, 2026 at 12:28:01 AM
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Quote: MentalQuote: acesideGreat work! However, I’m not very sure about your last sentence. Knowing that the dealer has a deuce helps the player, but probably not more than knowing that the dealer has a king does. Is this right?
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No.
A deuce helps you much more than a king hurts you if you play CPOS (computer perfect optimal strategy). You can raise 4x preflop a lot more often against a deuce and still have the better of it. Against a king, you will still raise your very good hands preflop and will only check some marginal hands. The good hands will make you less money, especially if the king is an overcard to one or both of your cards. Under CPOS, a deuce helps you 2.7x more than a king hurts you (+64.6% versus -23.4%).
If you play BS despite knowing one of the dealer HCs, a deuce still helps you just a little bit more than a king hurts you.
Dealer HC CPOS BS 2 62.43% 49.72% 3 52.66% 40.81% 4 43.22% 31.82% 5 33.82% 22.95% 6 28.60% 17.11% 7 22.85% 11.05% 8 16.15% 4.63% 9 8.57% -2.50% T -1.25% -12.24% J -8.17% -19.80% Q -16.25% -32.20% K -25.82% -53.33% A -40.11% -86.43%
Under CPOS, a deuce helps you much more than and ace hurts you. If you play BS, a dealer ace will crush many of your raises.
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Firstly, I'm confused here. As I mentioned earlier, the game UTH probably does not have a Basic Strategy (BS), but you used it above. I would say optimal strategy (CPOS) under certain conditions.
Secondly, I processed your above table:
As shown, I calculated the EV difference between with and without knowing a dealer hole card. Clearly, the EV difference is 46.32% for Ace, 27.51% for King, and 12.71% for Deuce. This means that knowing an Ace helps the player the most, but this is not what you are saying above. Although knowing a dealer deuce guarantees the most 4x/Check switches, I am still not confident if the EV gain is still the largest. Please help.
August 5th, 2026 at 5:18:32 AM
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Quote: aceside
Firstly, I'm confused here. As I mentioned earlier, the game UTH probably does not have a Basic Strategy (BS), but you used it above. I would say optimal strategy (CPOS) under certain conditions.
Secondly, I processed your above table:
As shown, I calculated the EV difference between with and without knowing a dealer hole card. Clearly, the EV difference is 46.32% for Ace, 27.51% for King, and 12.71% for Deuce. This means that knowing an Ace helps the player the most, but this is not what you are saying above. Although knowing a dealer deuce guarantees the most 4x/Check switches, I am still not confident if the EV gain is still the largest. Please help.
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You are calculating the incremental difference between CPOS and BS. Yes, you can gain more EV (make fewer bad raises) by exploiting the knowledge of one dealer card. But, the question you asked was: "Knowing that the dealer has a deuce helps the player, but probably not more than knowing that the dealer has a king does. Is this right?".
The deuce in the dealers hand takes you from an EV of -2.18% to +62.43% or +49.72%. The king takes you from an EV of -2.18% to -25.82% or -53.33% depending on your strategy. For either strategy, the deuce helps you more according to my interpretation of your question.
In your table, you are calculating the incremental benefit that you get from acting on your knowledge of one of the dealer's hole cards by making strategy changes. So, your question is probably better stated as "Which card provides an opportunity for more beneficial strategy changes: a deuce or a king?". The king does.
It is not knowing that the dealer that has a king that helps the player more in your revised table, it is acting on that knowledge that helps you more. The gross benefit of the deuce is still greater.
The reason you are thinking about strategy gain during play rather than pre-deal EV gain is that you don't understand the point of the OP. I cannot discuss the OP's interests without divulging private communications.
Gambling is a math contest where the score is tracked in dollars. Try not to get a negative score.
