We are in the BB and contemplating an all in 3bet over a button open. Some assumptions...

• opponent will fold 65% of the time to our 3bet all in
• the pot before our shove is 12,200
• our all in shove is our stack of 56,000
• we estimate that if our all in shove is called, we will win 35% of the time
• total pot if opponent calls our shove is 120,200

Is the EV of the shove calculated like this...?

• EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 120,200 - 0.65 * 56,000]

Or is it calculated like this...?

• EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 120,200 - 56,000]

Thanks!
Greg

Neither, for several reasons, one of which is an addition error.

If villain opened and you raised with a shove, his call amount will be your raise less his opening bet. If villain checked or you are the opening bettor the shove EV is as follows:

EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 68,200 - 0.65 * 56,000 = 3,544,50

or

EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 124,200 - 56,000] = 3,544.50

I should be more clear... the complete details of the hand...

• blinds 800/1,600 with 200 ante, 9-handed
• opponent raises to 4,000, he covers us
• one flat caller of the 4,000, we know he will fold to a shove 100% of the time
• pot after opponent open = 800 + 1,600+ (9*200) + 4,000 + 4,000 = 12,200 which is what we can win if opener folds to our shove
• we are in big blind and considering a shove of 56,000
• opponent has to call 56,000 - 4,000 = 52,000
• pot when we are called = 12,200 + 56,000 + 52,000 = 120,200
• opening opponent will fold 65% of the time to our shove
• flat caller will fold 100% of the time to our shove
• if opening opponent calls, we estimate we will win the 120,200 pot 35% of the time and lose our 56,000 shove 65% of the time

so I keep coming up with this...
EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 120,200 - 0.65 * 56,000]

Pot is 12,200 after villain bets.
If villain folds to your shove of 56,000, you win that pot. Prob. = 0.65

If villain calls and you win, you gain the pot + his bet + his call = 120,200. Prob = 0.35*0.35

If villain calls and you lose, you lose your shove of 56,000. Prob = 0.35*0,65

Add it all up and you show the right equation in your last posting
EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 120,200 - 0.65 * 56,000]

Yes, it's important to show all the details. In your original post, you did not state that villain had bet 4000 and that's why I assumed no bet on his part.

got it.... thanks. My 1st post should've been more clear.

This all stems from this 3 betting article by Jonathan Little.
http://jonathanlittlepoker.com/3bettingallinpreflop/
The scenario is the same as in the article and I got to thinking about it and I thought it looked wrong.

He's been pretty gracious in an email exchange with me (I do subscribe to his Pokercoaching.com site tho) where I dispute how he did the EV analysis. However, he insists that he is doing it correctly.... and who am I to dispute it (he doesn't insinuate that, but I naturally feel it as I don't have his record for sure)

If you get a chance, check it out and tell me what you think.

Thanks,
Greg

Boy, I messed up this line.
"If villain calls and you win, you gain the pot + his bet + his call = 120,200." The 120K is wrong!

Pot + His Bet + His Call = 8200+4000+52000 = 64200

Then EV = 0.65 * 12,200 + 0.35 * [ 0.35 * 64,200 - 0.65 * 56,000]
or
EV = .65 * 12,200 + 0.35 * [ 0.35 * 120,200 - 56,000],

which is what JL has.

Edit: I see statman has corrected his analysis during my drafting this.

I think there is some mistake.

I believe if you are going to use the EV equation that accounts for the frequency we loose, then the amount you win is not the entire pot including your bet.

So the equation would be:

.35*64,200-.65*56000 = 22,470 - 36,400 = -13,930

This is equivalent to the following equation:

.35*120,200 - 56,000 = 42,070 - 56000 = -13,930.

We can see using regular arthimetic and multiplication rules to transform one into the other:

.35*(120200 - 56000) - .65*56000 =
.35*120200 - .35*56000 - .65*56000 = .35*120200 - 56000

So his formulation is correct and a minor tweak to your formulation and it would be correct as well, and would yield the same results.

ah... I see the error in my ways now! Thanks!!