EV / Fold Equity Calculation

[FinalTable12]

Final Table at a Brick & Mortar Casino. The blinds are 8,000 and 16,000 with 2,000 ante. Everyone folds to the button who make it $40,000. Small blind folds. I'm in the big blind with 124,000 with A [img]/images/graemlins/spade.gif[/img] 7 [img]/images/graemlins/diamond.gif[/img].

Assume I go all-in. The pot size would be 196,000. It would cost the button to call another $100,000. Assuming that I have a 30% chance of winning if he calls. What percentage of the time must he fold to make the all-in the right play? Please also explain how you would calculate this.

Thanks for the help. This is my first post.

[jay_shark]

EV in fold equity call it A :

196000X

Ev if villian calls and you win call it B:

8000+16000+ 8000 in antes +140000 = 172000

That is , you'll win 172000 , 30 % of the time when villian calls 1-x % of time .

172000(0.3)(1-x)

Ev when villian calls and you lose call it C:

124000*0.7(1-x)

Now solve for A+B-C>0

you should get x>15% .

[FinalTable12]

Jay,

Thanks for the response. I don't quite understand how you calculated situation B. The blinds are 8,000 and 16,000 with a 2,000 antes (9 players) = 40,000 in chips. Button raises 40,000 that makes it 80,000 in the pot prior to my action. If I go all in for the additional 124,000 and the button calls, the pot would be 80,000 + 124,000 + 100,000 (button already has a raise in) = 304,000. Not quite sure how you got the 172,000 number.

Sorry if I didn't clarify everything in the original post. The X number seems real low to me.

[jay_shark]

The only way the pot size can be 196000 once you push all in is if there are 8k in antes or 4 players .

16k+8k +2k*4 +124000 +40k =196k

In any case , if there are 9 players then there are 18k in antes + (16k+8k) in blinds and 124k+40k =206k

fold equity :

206000X

B) 182000(0.3)(1-x) ...182k=16k+8K+2k*9 +140k

c) 124000(0.7)(1-x)

Now just simplify and solve for x.

x>13.5% .

This should make sense because even if the button raised to 140k , then it would cost you 124k which is pot odds of 182k:124k which means you only need to win 40 % of the time to show a profit .

Let me know if I screwed up with the arithmetic but this is the right idea .

[AaronBrown]

I'm going to use the following numbers:

Pot before any betting: $18k antes + $8k SB + 16k BB = $42k
Button makes it $40k, $82k in the pot, $24k to you to call
If you put in $124k, the pot has $206k, if button calls, there's $306k in the pot.

If these aren't correct, you can substitute.

Right now there's $82k in the pot and you're deciding whether to call, fold or go all-in. If you fold, you get zero (the fact that you contributed $18k is irrelevant, that's the pot's money now). If you call, it depends on what happens in the hand. I'd call you roughly even (that's a rough guess, obviously it depends on the player and the table), so I figure your EV is $53k in pot equity after you call (the pot is $106k, half figures to be yours) minus the $24k to call, for $29k. You might figure more or less.

If you go all-in, one of three things can happen. (1) He folds and you make $82k, the amount in the pot now. (2) He calls and loses and you make $182k, the amount in the pot now, plus the 100k he calls with. (3) He calls and wins, you lose the $124k it costs you to go all-in.

Using Jay_Shark's formula, your EV is:

82*X + 182*0.3*(1-X) - 124*0.7*(1-X)
= 114.2*X - 32.2

If X = 28% this is zero, meaning you need more than a 28% chance of folding to make going all-in better than folding. But you'd need X > 54% to make all-in better than calling.

[jay_shark]

What Aaron said .

82k is the right fold equity and NOT what I had . B and c numbers are correct .

I had a gut feeling I had an arithmetic error as always :P