Hypothetical Freeroll

A no-limit game. You hold 7 [img]/images/graemlins/club.gif[/img]6 [img]/images/graemlins/club.gif[/img] on the button. The flop comes: 3 [img]/images/graemlins/diamond.gif[/img]4 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/spade.gif[/img]. An opponent goes all-in in front of you and accidentally shows 7 [img]/images/graemlins/diamond.gif[/img]6 [img]/images/graemlins/diamond.gif[/img]. In what situations would you call her bet? In what situations would you not?

Mathematical answer preferred. Feel free to generate pre-flop action that would justify either response.

[mudbuddha]

how much of your stack is commited before the all in?

if there is not much, it is game theory question
your results are either losing your stack 1/3 of the time or a tie 2/3 of the time..

if most of your stack is in.. then u might as well call..

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if most of your stack is in.. then u might as well call..

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You are definately behind here; I'd like to know exactly how much. i.e. What pot odds do you need to call this bet?

[mudbuddha]

fair enough.
im interested in finding out the method of calculation since almost every decision here is -ev. seems to me ( my common sense is warped tho)

[AaronBrown]

Assume you can ignore other players, if there's anyone behind you seeing the straight with flush draw will almost certainly cause them to drop without a pair on the board.

Out of the 990 possible boards, 630 tie and 360 lose for you. If there is P is the pot before your opponent's raise, and the smaller of your two stacks is S, by calling you win P/2 630 times and lose S 360 times. That's breakeven if S is 7/8 of P. Any larger bet than that and you should fold.

In practice, one of you will have to be shortstacked to make this a good bet, unless there was really vigorous preflop action.

Would that be 1.875:1 pot odds that you need to "draw" to your split?

[AaronBrown]

That's a little tricky to define. Normally, pot odds are defined for winning the pot. But I'd state it as 1.875:0.875, or 15:7 instead. You need $15 in the pot before you bet for every $7 you put up, meaning $8 in the pot before your opponent bets, to make this breakeven EV.

2.14 : 1

So she's about a 2:1 favourite... quite a deceiving situation!

Thanks Aaron.

You'd need about 2.5to1 pot odds to call.
Example. The pot is $15 he goes all in for $10.
Pot=$25; costs you $10 to call.
He is about 37% to catch his flush.
Out of 100 hands: 37 times you will lose your $10. -$370
Out of 100 hands: 63 times you will win $17.50 from the split pot. $1102.50
Dividing $1102.50 by 100 will give us our average loss or gain after each hand.
$1102.50/100=$11.03. Net gain of $1.03 per hand. +EV

If however, you were only getting 2to1 odds you would lose money.
Example: The pot is $10 and he goes all in for $10.
Pot=$20; costs you $10 to call.
He is about 37% to catch his flush.
Out of 100 hands 37 times you will lose $10. -$370
Out of 100 hands 63 times you will win $15 from the split pot. $945
Dividing $945 by 100 will give us our average loss or gain after each hand.
$945/100=$9.45. Net loss of $0.55 per hand. -EV

[AaronBrown]

Well, you have a 64% chance of tying, which is like a 32% chance of winning. The pot odds are computed as (1-p) where p is your chance of winning. In this case, (1-32%)/32% = 68%/32% = 2.14.