Calculating the EV of shoving

Lacks declaration of the variables used.

Originally Posted by jackvance

Lacks declaration of the variables used.

This thread is a continuation of a discussion that started here:
http://www.flopturnriver.com/pokerfo...46#post2171746

Here is the pertinent bit:

F is the number of combos that Villain folds divided by the total number of combos Villain currently holds.
E is the equity (found using equilab or something similar) of Hero's hand vs. Villain's calling range.
P is the amount of the pot (including any bet Hero may be facing)
S is the amount that is currently in Villain's stack (or Hero's stack, if Villain has more chips).

Originally Posted by MadMojoMonkey

F is the number of combos that Villain folds divided by the total number of combos Villain currently holds.
E is the equity (found using equilab or something similar) of Hero's hand vs. Villain's calling range.
P is the amount of the pot (including any bet Hero may be facing)
S is the amount that is currently in Villain's stack (or Hero's stack, if Villain has more chips).

Hi. This is my first post and I am flashing back to reading an essay in front of class in the eighth grade. Please be more gentle than they were.

I have a question about the difference between an EV calc of a bet vs a raise. In other words, what happens to the money that we have to put into the pot just to call the action we are facing? In the calculation done based on the OP, there is .75 that is never included.

Looking at the post above, P should include any bet Hero may be facing. But, that seems to mess up the F*P fold equity by including an amount that is not really part of what we win when the villain folds.

It would seem like it has to be included somewhere in our pot equity calc. For instance, if we are assuming that we never folding so it is not an additional risk, shouldn't it be included in the E*(P + S)? On the other hand, since folding is technically always an option, should it be part of (1 - E)*S, because that is what we are risking...and that is really what that portion of the calculation is about.

I hope I have made some sense. I am really curious about this because as the size of the bet we are facing increases, the larger impact it would seem to make on the final EV calc.

Thanks so much for any help...and more importantly, thanks so much for all the great posts I have been reading the last few weeks!

Originally Posted by boutron

Hi. This is my first post and I am flashing back to reading an essay in front of class in the eighth grade. Please be more gentle than they were.

No prob.

Originally Posted by boutron

I have a question about the difference between an EV calc of a bet vs a raise. In other words, what happens to the money that we have to put into the pot just to call the action we are facing?

A bet is just a special name for the first raise. Conversely, a raise is just a special name for a bet that isn't first. The math is identical.
Please be aware that the math in this thread is about the EV of a shove, not a call.

Don't confuse this specific equation as good for evaluating calls. The difference is that in this equation, the action is closed. There can be no future bets, and the equities at this moment are the only equities that matter.

Originally Posted by boutron

In the calculation done based on the OP, there is .75 that is never included.

Please quote the bit you're referencing.

Originally Posted by boutron

Looking at the post above, P should include any bet Hero may be facing. But, that seems to mess up the F*P fold equity by including an amount that is not really part of what we win when the villain folds.

P represents the amount Hero wins when Villain folds. This is the amount of the pot, any bets Villain has made, and any bets Hero made earlier on this round of betting.
E.g. there's 10 in the pot before the first bet, Hero bets 5, Villain raises to 20. The value of P that Hero should use in doing the EV of a shove calculation is 10 + 5 + 20 = 35. P is the total money in the pot at that moment.

Originally Posted by boutron

It would seem like it has to be included somewhere in our pot equity calc. For instance, if we are assuming that we never folding so it is not an additional risk, shouldn't it be included in the E*(P + S)? On the other hand, since folding is technically always an option, should it be part of (1 - E)*S, because that is what we are risking...and that is really what that portion of the calculation is about.

WE ASSUME WE ARE SHOVING!!!

Other than that, it sounds like you're talking about a specific post in this thread, but you didn't quote it, so I don't know which of the many posts in the thread to which you refer.

Please quote the post you are referencing and I'll try to give an answer.

Originally Posted by boutron

I hope I have made some sense. I am really curious about this because as the size of the bet we are facing increases, the larger impact it would seem to make on the final EV calc.

The equation is the same, whatever numbers you plug into it. If you have no fold equity, then F=0. If you have a pure bluff, with no equity when you get called, then E=0. The math still shows you whether it's a +EV shove. The math does not tell you if it's the most +EV line to take, only the EV of your proposed line (shoving).

Originally Posted by boutron

Thanks so much for any help...and more importantly, thanks so much for all the great posts I have been reading the last few weeks!

Welcome to the forum.

From the OP:
Size of pot before hero shove is $1.30 (0.25 BU raise, 0.05 SB, 1.00 BB 3bet)
Villain has to call $9 if I shove.

From the first replay, which you then explained thoroughly in the next reply:
F*P + (1-F)[E*(P+S) - (1-E)*S]

0.87*1.30 + (1-0.87)[0.42*(1.30+9.00) - (1-0.42)*9.00]

1.13 + 0.13*[0.42*10.30 - 0.58*9.00]
1.13 + 0.13*[4.326 - 5.22]
1.13 + 0.13*-0.894
1.13 - 0.11622 = 1.01378

Thanks so much for the response. I don't think I explained my question very well. When I refer to the difference between bet and raise, I am referring to the fact that a raise includes the amount that I have to call from the action that I am facing. In the example above, that is .75. The Hero is putting 9.75 in the pot when he shoves, of which only $9 is the raise. Only the $9 shows up anywhere in the math.

So, what happens, in the equation, to that .75. I am glad you answered, MMM, because in your variable explanation, you have:
P is the amount of the pot (including any bet Hero may be facing)

So, my question is what is happening to the bet the Hero is facing in the calculation? It's hard to imagine it is completely insignificant, especially if it is very large.

OT, just a quick background, as I hope to dive fully into these forums, I spent many hours in the cardrooms of Gardena in the late 80's, starting at the Normandie Club. After grad school, I supported myself for nearly a year playing 10/20 at the Bicycle Club. Then, the real world intervened and I pretty much forgot about the game. Recently, a family situation has me moving to an area with live poker and I thought I might brush up. OMG! What a shock! This is not your father's poker game.

Anyway, I am putting my energy into learning NL online, as that is the main action where I will be going. Between the highly empirical approach to the game, plus the difference in limit vs no-limit, it has been quite a brain shock. Luckily, this and other sites have made it SO much easier. In MY day, you had to special order Sklansky or SuperSystem from the Gambler's Book Club in Vegas.

Thanks again!