Face up holdem.

[Tater10]

Is my logic correct? I first thought this was cut and dry, but i'm racking my brain - I'm decent at probabilites & such, but not game theory.

limit texas holdem, face up.

Button has: Jc Js
Small blind [posts $1]: Ah Kh
Big blind [posts $2]: 8d 7d

according to 2 dimes, the EV for these 3 hands is:
.399
.388
.214

Button acts first and raises with JJ.

now, if the AKh re-raises, this would force the 87d to fold (have a -EV), and bring the respective EV's to:

.539 for JJ, and make a net of 1.546 units (.539 * $14 - $6 put in)
.461 for AKh and make a net of 1.454 units (.461 * $14 - $5 put in)

Now, if the AKh just calls, forcing the BB to call (bb would have a +EV)

EV for Jc Js: 0.788 units (.399 * $12 - $4)
EV for Ah Kh: 1.656 units (.388 * $12 - $3)
EV for 8d 7d: 0.568 units (.214 * $12 - $2)

SO, Ah Kh wants to maximize his EV, so he just calls and plays this 3 handed.

All this came about when it was suggested we just play holdem face up in a home game.

Of course, i'm leaving out the future bets, etc, but i'm pretty sure the EV's for theses hands become pretty clear on the flop.

Grand question: Is face up holdem solvable? Would there be no edge if 10 guys from MIT sat around a poker table playing face up holdem with a computer?

[Tater10]

let me clarify the "grand question".

Wouldn't it be a strategy of the JJ guy to just call, forcing the AKh guy to raise, have the bb call, then JJ re-raise? this would put the 87d into -ev land, but still must call.

[Dan S]

I'm interested in the specific question so maybe I'll get back to it, but first:

[ QUOTE ]

Grand question: Is face up holdem solvable? Would there be no edge if 10 guys from MIT sat around a poker table playing face up holdem with a computer?


[/ QUOTE ]

Yes, that is correct. In a way this is what makes the Fundamental Theorem of Poker work; there is a mathematically optimal face-up strategy, and deviating from it reduces your EV (unless it induces your opponents to deviate from their optimal face-up strategy even worse).

[Louie Landale]

I've never actually seen calculated as EV = ChanceWin*FuturePotSize - Cost, but it works out the same as EV = ChangeWin*PayOff - ChangeLose*Cost. Very curious; but easier to calculate.

Also, the "EV" line at 2-dimes is really their chance to win including ties. The previous "win" columns should read "Win Outright". I wonder how to contact 2-dimes...

Anyway it appears you are correct. (You are even MORE correct since JJ is sure to 4-bet if AKs 3-bets, but I digress...)

I'm sure you are INCORRECT, however, if AKs is currently the "best" hand such as when button really has AQ: AKs should raise out the blind.

I would also like to point out that AKs is A favorite 3-handed where .388 is higher than .333 "fair share", but is a Dog heads up, where .461 is lower than .5 "fair share". I beleive this is because if AKs outdraws JJ that leaves only 4 board cards left over for 87s to outdraw AKs.

But I wonder if this is a general in-the-blind principle. Lets pretend 87s has the only $2 blind, JJ raises from CO, and its up to the AKs on the button:

[A] AKs calls and plays 3 handed:
.399*12-4 = .788 EV for JJ
.388*12-4 = .656 EV for AKs
.214*12-2 = .568 EV for 87s.
[B] AKs 3-bets, 87s folds, JJ just calls.
.539*14-6 = 1.546 EV for JJ
.461*14-6 = .454 EV for AKs.

So AKs does better by letting 87s into the pot. And he does exactly the same amount better (.656-.454=.202) as he does when he's in the SB (1.656-1.454 = .202). So no, this is not a feature of being in the blind. Whew.

I make the following conclusions: [A] Unlike stud, when the pot is small the best hand has the best of it and nobody else should be raising to drive out the other players (whereas in stud the 2nd best hand should often try to drive out the 3rd best) [B] Being in the blind can and should increase your chances of calling, but does NOT affect your chances of Raising when your clearly have a good hand.

Nice post.

- Louie