EV spreadsheet I made accounting for FE, PE, and Bet Size

[snelgrave]

Hey all,

I’ve been thinking about how to approach determining EV accounting fold equity and bet size, and I was hoping for a little feedback on a chart I’ve created.

Simple situation – Heads up situation: Hero bets and he knows Villain will only call or fold. Using my back of envelope math I determined that Hero’s expected value is:

EV = Fe*P + (1-Fe)*[(2*B + P)Eq – B)]

Where EV = Expected Value, Fe = Fold Equity, B = Bet Size, P = Pot Size, Eq = Pot Equity.

If we assume a pot size of 1 the equation simplifies to

EV = Fe + (1-Fe)*[(2*B + 1)Eq – B)]

And EV and B wind up being a percentage of the pot.

Since I don’t have a good graphing calculator program for my Mac, I created a spreadsheet in Excel with Fold Equity and Pot Equity in units of 10%. It’s uploaded to Google docs. You find a copy of it at http://spreadsheets.google.com/pub?k...hIA&gid=0.

I apologize that some of the formatting didn’t upload (like the color coding), but it’s still pretty clean.

I have found out that I need to seriously rethink the amount I bet in a variety of situations. Making a ¾ pot bet because that is “standard” can be throwing money away, and, yes Virginia, there is a place for very small (even only ¼ pot sized) bets.

Comments and criticism welcome. Cheers.

[snelgrave]

Republished at http://spreadsheets.google.com/pub?k...Bs4TtIAtX-bhIA

[elitegimp]

I might be misinterpretting something, but is "Pot Equity" the same as "the chance that you win going to showdown"? If so, shouldn't your equation read

EV = Fe*P + (1-Fe)*[(2*B + P)Eq – (1-Eq)B)]

where bolded my additional term? Also, it seems weird that you are counting your bet as +EV when you win (i.e. the (2*B+P) term) and when you lose (the -B term). I think the former should be (B+P)Eq instead, but again it might all stem from me misunderstanding the Pot Equity term.

And all this is based on your original post, not the google spreadsheet (:

[snelgrave]

Pot equity is the percentage of the pot a hand will win in showdown over an infinite number of iterations. It mostly consists of wins, but also includes the share if the hand is a tie. Pot equity is easily found out with the program Pokerstove.

So the first part of the equation (Fe*P) seems pretty self-explanatory – either one picks up the pot with a bet, or one doesn’t. The bets size is irrelevant beyond how much fold equity it generates since one gets that bet immediately back.

Second part, assume a calling station opponent with zero fold equity, one is left with

EV = (2*B + P)Eq – B.

You and your opponent both put in a bet (2*B) which is added to the pot (P). Your share of the pot is simply your equity in this pot. However for the play to be +EV, your share of the pot must be greater than the “start-up” cost of playing (-B). This cost will be the same no matter what your equity is, so adding (1-Eq)B will skew the results toward a false inflation of EV.

Example:

It’s the turn and you have a stack of $100 and a pot of $10. You make a bet of $10 which is called by an opponent with his last $10 (never mind fold equity). You know you have 75% equity in the pot.

Stack Initial = $100, Pot = $10
Stack after bet = $90, Pot = $30
Your share = .75*$30 = $22.5
Stack Final = Stack after bet + your share = $112.5
EV = Stack Final – Stack Initial = $112.5 - $100 = +$12.5

So comparing our 2 equations

EV 1 = (2*B + P) Eq – B = (2*10 + 10)*.75 – 10 = +12.5
EV 2 = (2*B + P)Eq – (1-Eq)B = (2*10 + 10)*.75 – (1-.75)10 = +20

[elitegimp]

Oh, I see what I was doing! Letting p = "percentage of times you win" (what I think of as Equity, which may or may not be correct), then the EV would be

EV = (P+B)*p - (1-p)*B

because you either win the pot and your opponent's bet, or lose your bet (depending on who wins). However, simple algebra lets us do this:

EV = (P+B)*p - B + B*p
EV = (P+B+B)*p - B
EV = (P+2*B)*p - B

so your formula is exactly like mine (:

Using your example: the pot is $10, and you have 75% chance of winning. You bet $10, so your EV would be

EV = ($10 [in the pot] + $10 [from your opponent])*.75 [you win] + (-$10 [from your stack])*.25 [you lose] = $15 - $2.50 = $12.50

Sorry for all the confusion, thanks for clarifying!