UTH, the 21 Outs

Quote: Mission146

Quote: aceside

This is very helpful! There should be some way of calculating the effect of removal on the basic strategy of UTH if a certain card is removed, just like the illustrious-18 deviations in blackjack card counting. Based on the discountgambling information, I judge it is not very helpful for a player to peek at their neighbor’s hand cards because Only a few marginal decisions matter.

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That's true, but value is value if you can memorize the known card exceptions. It's a low HE game to begin with.

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And the preflop bet decision is not the only decision on which the cards you see may be decisive.

I looked at all this extensively several years ago but never posted any of my findings.

Here are the calculated gain in +EVs for Not Raising K5o,Q8o, K2s, Q6s, and J8s when match cards for the High or Low Card were observed in the 4 cards you see in your 2 neighbor's hands. The last column is the +EV for deciding to Raise the T-8s for the 58% of the time when no Match cards (T or 8) were seen in the neighboring 4 cards.

Gain in Player EV when peeking at 4 other cards and checking for 'match cards" and changing preflop UTH decisions

Observed Cards	Player Hand:	K5o	Q8o	K2s	Q6s	J8s	T8s	Sum
	Probability of Hands	0.009049774	0.009049774	0.003016591	0.003016591	0.003016591	0.003016591
	Prob of OC
No Matches(xxxx)	0.589452888						0.019684
High-xxx	0.172522796	0.054482	0.056866	0.082587	0.057954	0.060932
Low-xxx	0.172522796		0.024866		0.009954	0.036932
HH-xx	0.012323057	0.162482	0.176866	0.190587	0.177954	0.172932
LL-xx	0.012323057	0.042482	0.112866	0.022587	0.079954	0.124932
HL-xx	0.036969171	0.112482	0.124866	0.116587	0.109954	0.128932
HHH-x	0.000191055	0.260482	0.296866	0.288587	0.297954	0.284932
HHL-x	0.001719496	0.120482	0.264866	0.124587	0.249954	0.260932
HLL-x	0.001719496	0.170482	0.232866	0.150587	0.201954	0.236932
LLL-x	0.000191055	0.100482	0.198866	0.056587	0.151954	0.210932
HHHL	1.30265E-05	0.306482	0.360866	0.310587	0.353954	0.348932
HHLL	3.90795E-05	0.166482	0.342866	0.146587	0.311954	0.338932
LLLH	1.30265E-05	0.228482	0.320866	0.184587	0.273954	0.324932
Advantage		0.016666287	0.02326005	0.021736507	0.019842183	0.026293711	0.011602791
Adv*Hand Prob		0.000150826	0.000210498	6.55702E-05	5.98558E-05	7.93174E-05	3.50009E-05	0.000601068

As you can see, the overall increase in Player EV for peeking at your 2 neighbors cards and changing preflop decisions on these 6 starting hands was only +0.06%. It is low because the frequency of getting these six hands is cumulatively only about 3% and you change decisions (usually) about 41% of the time (except for T-8s, where you alter the preflop decision about 59% of the time.)

Caveats: These are not all the hands that you would change for preflop decisions, dependent on the match cards. Also, these results are approximate based on sampling, rather than running through every possible combination of suits and ranks for the 4 cards that you are peeking at.

So I've been thinking about the 20 outs or less rule.

Unpaired board and there is 1 unseen over is 19 outs.
Paired board with 2 unseen overs is 19 outs.
2pair or trips board with 3 unseen overs is also 19 outs.

Unpaired board and giving the dealer a gutshot with no unseen overs is 18 outs. (You hold one of the gutshot cards)

What situation is there 20 outs?

Quote: odiousgambit

[paraphrase Wiz]: If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

Quote: 100xOdds

So I've been thinking about the 20 outs or less rule.

Unpaired board and there is 1 unseen over is 19 outs.

Your use of 'unseen' throws me a bit. An unpaired board will represent 15 outs, which I have called the initial board. These outs are typically the 3 cards the dealer could have for each of the cards on the board, it would give the dealer a pair to have one. 5 cards, 15 outs. Then you consider your best kicker and what cards are higher in rank than that kicker, but not on the board; the dealer could have those cards and there are 4 each. If you have a King, only the Ace, that adds 4 more possible outs = 19. If you have a Queen best kicker, the Ace and King make 8 more dealer outs for 23 and the odds are against you and you fold.

Quote:

Paired board with 2 unseen overs is 19 outs.
2pair or trips board with 3 unseen overs is also 19 outs.

Unpaired board and giving the dealer a gutshot with no unseen overs is 18 outs. (You hold one of the gutshot cards)

What situation is there 20 outs?

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chew on the above and I'm thinking we don't need to visit these

Quote: 100xOdds

Quote: odiousgambit

If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

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well, I hope this was something that I posted early on. Looks like it is wrong, you don't count 3 possible 10s as 3 outs, although it is true that it would be bad if the dealer had a 10. A weak second kicker can be a consideration, but not for a simple strategy. 15+8 is sufficient anyway in this case to tell you to fold.

the 2 does not give 3 outs!

Quote: 100xOdds

Quote: odiousgambit

If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

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With T2 and the board is J655, the two is not decisive You have 55-JT6 and the only Tx that beats you are T9,T8 and T7; you will tie T4,T3,T2. That is half the possible unpaired tens, no card higher than J and not pairing the board. DSO this might count at 1/2 of 3 of 3 outs (Since there are only 3 tens left for the dealer's hand. The outs are 19 + 1½ = 20.5 which is less than 21.

Quote: gordonm888

Quote: 100xOdds

Quote: odiousgambit

If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

link to original post

With T2 and the board is J655, the two is not decisive You have 55-JT6 and the only Tx that beats you are T9,T8 and T7; you will tie T4,T3,T2. That is half the possible unpaired tens, no card higher than J and not pairing the board. DSO this might count at 1/2 of 3 of 3 outs (Since there are only 3 tens left for the dealer's hand. The outs are 19 + 1½ = 20.5 which is less than 21.

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I thought the break even was not 21 but somewhere between 20 and 21 though. So not immediately clear to me that 20.5 is playable.

Quote: gordonm888

Quote: 100xOdds

Quote: odiousgambit

[paraphrase Wiz] If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

link to original post

With T2 and the board is J655, the two is not decisive. You have 55-JT6 and the only Tx that beats you are T9,T8 and T7; you will tie T4,T3,T2. That is half the possible unpaired tens, no card higher than J and not pairing the board. DSO this might count at 1/2 of 3 of 3 outs (Since there are only 3 tens left for the dealer's hand. The outs are 19 + 1½ = 20.5 which is less than 21.

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ahh.. never thought about ties in my example thus the kicker in my hand doesnt matter.

so basically count what % of unpaired Tens have me beat and multiple that by # of outs. (thus your 1.5 outs in my T2 on J6K55 example)

So dealer's outs for T2 on 99JJ4: 12+2+2+3 + (4/5 * 3outs) = 21.4 outs = fold.
but on 99JJ5: 12+2+2+3 + (3/5 * 3outs) = 20.8 outs = bet ante (1x)

so to simplify for every hand, if the kicker is 5 or above, dont worry about it?
and add 3 dealer outs if it isnt?
(and by kicker, i mean whether it's in your hand or you're using the lowest card on the board)

Quote: odiousgambit

Quote: 100xOdds

Quote: odiousgambit

[Paraphrase Wiz] If the dealer also has a Ten then you lose because everything beats your 2 kicker.

Dealer outs:
15+8+3 is 26 thus fold

interesting.. never thought of having a 2 as a kicker meant giving the dealer 3 more outs.

Let say the board was j6k55 and i had T2:
Normally,I would bet ante because 11+8 is 19outs.

But now with this additional knowledge that with the 2 kicker means the dealer has 3 more outs thus it's a fold.

At what point do you NOT consider the kicker as useless?
Ie: not assign 3 more outs to the dealer
T5? T7?

link to original post

well, I hope this was something that I posted early on. Looks like it is wrong, you don't count 3 possible 10s as 3 outs, although it is true that it would be bad if the dealer had a 10. A weak second kicker can be a consideration, but not for a simple strategy. 15+8 is sufficient anyway in this case to tell you to fold.

the 2 does not give 3 outs!

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I was quoting your OP (1st post in this thread).

due to my editing of that post multiple times, i left out of the part where it was the Wiz who said 3 additional dealer outs if you have a 2 kicker.
(it made it look like you said that.)

i edited my posts.

Quote: gordonm888

With T2 and the board is J655, the two is not decisive You have 55-JT6 and the only Tx that beats you are T9,T8 and T7; you will tie T4,T3,T2. That is half the possible unpaired tens, no card higher than J and not pairing the board. DSO this might count at 1/2 of 3 of 3 outs (Since there are only 3 tens left for the dealer's hand. The outs are 19 + 1½ = 20.5 which is less than 21.

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I count 11 initial outs [3+3+2] and 12 other outs for A,K,Q [4+4+4] ... 23 not 19, never mind the additional consideration which would not be a simple strategy. Or I made a mistake I can't see.

Mission and someone else said they might count a certain situation as one out, such as maybe having a bad second kicker, whereas in a simple strategy there are few situations where something is only one out, not 2,3, or 4 outs. This is a deviation from simple strategy *which they conceded.* Here we have 100xodds showing that a simple strategy gives him some problems, so do we want to go there? Just saying.

Quote: 100xOdds

[snipped to shorten to something reasonable]





[Paraphrase Wiz] If the dealer also has a Ten then you lose because everything beats your 2 kicker. 


I was quoting your OP (1st post in this thread).


due to my editing of that post multiple times, i left out of the part where it was the Wiz who said 3 additional dealer outs if you have a 2 kicker.
(it made  it look like you said that.)


i edited my posts.

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I see that the above example has been removed from the wizard page [and replaced I think], see link below. I'd like to think it is because he realized he was deviating from a simple strategy


the consideration that both dealer and player have the same card usually means a wash. If you are sharpening your game and want to in fact go deeper than simple strategy, you can expect to be getting iinto the weeds. Check out these using the Wiz calculator:


Here I changed the original so you have a 9 for second kicker instead of a 2. Having a 2 doesn't have much to do with it, because dealer outs are 23 just using simple strategy. Fold. 





Note that this time I have changed the original so that there is an Ace on the board. Now the dealer outs are 19 using simple strategy. Player cards are still 10,2, but it is now a Raise. This is not a situation where a weak second kicker matters enough. I've noticed it is more likely with K,2 or Q,2 .





https://wizardofodds.com/games/ultimate-texas-hold-em/
https://wizardofodds.com/games/ultimate-texas-hold-em/calculator/

Well this is something new that most people tend to make mistakes on. I think it is normal for us to find a way to see which is the best way to either make use of since there are so many factors that affect the way we do our work on this one at the very least. That is what makes it hard for us to try more new things.