Applying Expected Value

I took my undergraduate probability course this year and wanted to apply the Expected Value calculations to a situation I had recently. I thought this would be easy, after all, EV is an easy calculation. But, as with most math problems, the hard part is figuring where to put what numbers.

I am on the button, pre-flop, folded to me. I have QJclubs and decide to steal from the BB, who is also the small stack. I raise to 300 (3xBB), he goes all-in for $692. After I call, I discover he had ATos.

Knowing his cards, what is the correct way to do an EV calc for calling? Do you use your net gain (the pot minus what you've put in it), or the total pot?

According to an odds calculator, I am 45% to win this situation. Here's what I get.

Fold
EV: 100% chance of losing: 1 * 310 = -310

Call
Win: 45% chance of winning <HOWMUCH>: .45 * ?? = CL
Lose: 55% chance of losing <HOWMUCH>: .55 * -?? = CW

Decision: Call if -310 > CW + CL

Get the question? Is HOWMUCH the total pot after I call ($1524), or is it my net change after calling (1524-702=822)? (Since both calculations suggest calling is correct, this is, obviously, just for my own edification).

Question 2: Of course, OTB, I didn't know what his hand was. And I probably should have figured that he was likely to play back at me in that situation. But having blundered, how would I apply the EV calculation without knowing his cards?

Thanks,
-SD

Anything put in the pot isn't yours anymore. So the calc of calling is:

EV Call = .45($992) + .55(-$392) -> ($446.4) + (-$215.6) = $230.80

EV Fold = $0
(You don't lose anything when you fold, you already contributed the $300 on the previous action)

EV Call > EV Fold, therefore call is correct (in a cash game)

I'm assuming this was a tourny so other factors mater more than making the most +EV decisions, but that's how the EV is done.

When actually at the table you don't really have time to try and calculate EV for different plays exactly.

Just taking a quick look at the odds, his shove makes the pot $992. You have to put in 400 to win 1000, so you're getting 2.5:1.

Those are pretty huge odds, if you have 28% equity then calling is fine. Someone with 6 bb's is shoving such a wide range a call is mandatory. The only hands you're not correct calling against are QQ-AA.

Thanks, Mase. It took me a moment to figure out where you were getting your numbers from.

This looks much better than what I was trying. But what is wrong with the way I was doing it? Was it just a poorer way of doing the same thing, or was it wrong? If wrong, why?

Again, thanks.
-SD

I think your way would reach the same conclusion, just adjust the -310 to 0. That was the only error in your original equation, and a very common one by the way.

Yeah, now that I look at it, you simply laid it out a little differently.
CW = 45% $992 (The $300 you put in + his $692, this should be the current size of the pot)
CL = 55% -$392 (The amount you have to call to stay in)

CW= $446.40
CL = -$215.60

At this point you'd be exactly where I was.

CW+CL = $230.80 which is greater than 0, making the call correct.


When first introduced to EV, the equations were always laid out in the manner I wrote out, and that's really the only reason I do it that way.

One thing I take away from all of your responses - and what I was trying to learn - is that you do not do the calculations net of what you've put in. The pot is not yours, it is out there to be won. What you have put in the pot is not yours anymore, and the calculation should be done assuming you've already lost that money (though it could be won back).

BTW, your numbers for the total pot forgot about blinds and antes. But that was insignificant as you explained your thinking well and the lesson was learned.

Thanks,
SD

Good point about the blinds. I'm glad I could help