Big draw vs. shorty. Your play?

[joewatch]

I know if I check here, Villain will go all in with his likely overpair. But if I pot it, Villain will likely fold. What's the most EV? Check-call, or pot it?

PokerStars Pot-Limit Omaha High, $1.00 BB (8 handed) converter

Hero ($138.65)
CO ($36)
Button ($93.80)
SB ($126.70)
BB ($39)
UTG ($90.45)
UTG+1 ($196.95)
MP1 ($73.50)

Preflop: Hero is MP2 with A[img]/images/graemlins/heart.gif[/img], K[img]/images/graemlins/spade.gif[/img], Q[img]/images/graemlins/heart.gif[/img], Q[img]/images/graemlins/spade.gif[/img].
<font color="#666666">3 folds</font>, <font color="#CC3333">Hero raises to $3</font>, <font color="#CC3333">CO raises to $10.5</font>, <font color="#666666">1 fold</font>, SB calls $10, <font color="#666666">1 fold</font>, Hero calls $7.50.

Flop: ($32.50) T[img]/images/graemlins/heart.gif[/img], 7[img]/images/graemlins/club.gif[/img], J[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(3 players)</font>
SB checks, <font color="#CC3333">Hero ???

[beset7]

set him AI

[joewatch]

<font color="white"> I guess this is just a simple maths problem:


pokenum -o ah ks qh qs - ad ac kh kc -- th 7c jh
Omaha Hi: 820 enumerated boards containing 7c Jh Th
cards win %win lose %lose tie %tie EV
Ks Qs Ah Qh 421 51.34 360 43.90 39 4.76 0.537
Ac Kc Ad Kh 360 43.90 421 51.34 39 4.76 0.463

EV if I pot it = $32.50
EV if I check -call = $57.50 x 0.537 - $25 x 0.463 = $19.40

So it looks like potting it to induce a fold is the best move by far.

</font>

[Tilt]

Hey Joe, NH.

Suppose we give him credit credit for a really strong overpair...

pokenum -o ah ks qh qs - ac ad 4c 4d -- th 7c jh
Omaha Hi: 820 enumerated boards containing 7c Jh Th
cards win %win lose %lose tie %tie EV
Ks Qs Ah Qh 500 60.98 320 39.02 0 0.00 0.610
Ac 4c Ad 4d 320 39.02 500 60.98 0 0.00 0.390

Now lets suppose we are sure that SB is check/folding. Then the question is simple. Do you like 100% of 32.50 more than you like 61% of $83.50? The answer is clearly yes.

Now suppose we think SB is check raising a set, like this one:

pokenum -o ah ks qh qs - ac ad 4c 4d - ts td 5s 5c -- th 7c jh
Omaha Hi: 666 enumerated boards containing 7c Jh Th
cards win %win lose %lose tie %tie EV
Ks Qs Ah Qh 327 49.10 339 50.90 0 0.00 0.491
Ac 4c Ad 4d 31 4.65 635 95.35 0 0.00 0.047
Ts 5s 5c Td 308 46.25 358 53.75 0 0.00 0.462

So even in that case you are substantially +EV. The answer is clearly to check and get all-in (unless you don't like variance, in which case you don't like PLO). I don't think the villain can have a side card combo that really changes the result.

[RoundTower]

You did the maths wrong. Firstly, I do like 61% of 83.50 more than I like 100% of 32.50. But your EV from check-calling is not 61% of 83.50, because 39% of the time you will lose your bet. Basically it is correct to bet if he would be making a mistake by folding. Since he is getting more than adequate pot odds to call, he will be making a mistake to call.

Incidentally this is why you should generally call with your overpair in this situation as the short stack. The player who puts you all in almost certainly has a draw and would like to see you go away.

I assume it is the short stack you are up against here, not the SB with $126.70 as specified in the OP. What I said is correct if the player has enough for one pot sized bet or less.

[joewatch]

Thanks for your analysis Tilt - but I have to mention that your calc is way off.


[ QUOTE ]
Now lets suppose we are sure that SB is check/folding. Then the question is simple. Do you like 100% of 32.50 more than you like 61% of $83.50? The answer is clearly yes.


[/ QUOTE ]

In the $83.50, you put in $25 of the pot. You also didn't subtract the -EV for $25 that you would lose.

In your second example, expected return of check-call is 0.49 x $83.50 - 0.51 x $25 = $28.

The thought of calculating expected return with the side pot vs. the SB hurts my head. [img]/images/graemlins/smirk.gif[/img]

[Tilt]

[ QUOTE ]
Thanks for your analysis Tilt - but I have to mention that your calc is way off.

[/ QUOTE ]

Uh, yep. [img]/images/graemlins/blush.gif[/img] God I'm an idiot. No wonder I make so many stupid calls.

[ QUOTE ]
In the $83.50, you put in $25 of the pot. You also didn't subtract the -EV for $25 that you would lose.

In your second example, expected return of check-call is 0.49 x $83.50 - 0.51 x $25 = $28.

[/ QUOTE ]

Yeah, but I got the 100% of 32.50 right!

[ QUOTE ]
The thought of calculating expected return with the side pot vs. the SB hurts my head. [img]/images/graemlins/smirk.gif[/img]

[/ QUOTE ]

Its almost a coinflip there. I think you should bet and take your 32.50. Unless you like flipping coins.