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EV Math

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Smuft   Canada. Aug 03 2016 18:27. Posts 627
Making a spreadsheet to help choose between bet/calling a shove or checking

For visualization purposes (BB to act)


Assumptions made:

Besides the normal assumptions about ranges and equity, we'll also be using "R" for realized equity to help approximate the value of some lines. ie. when we check and get called, there are many different rivers and calculating what we think will happen on each of them is too time consuming so instead we just approximate and say on average we realize X % of our equity


Variables needed:

- equity vs calling range
- equity vs shoving range
- equity vs XB range
- equity vs betting range

- call %
- shove %
- fold %
- XB %
- bet %

- pot
- stack size
- bet size

- R vs calling range
- R vs XB range
- R vs betting range


EV formula for each exit:

(B = Bet, R = Raise, C = Call, X = check, |XD = check down*)
*|XD is where R is used


(BRC):

equity vs shoving range * (pot + stack size) - ((1 - equity vs shoving range) * stack size)


(BC|XD):

(equity vs calling range * R vs calling range) * (pot + bet size) - ((1 - (equity vs calling range * R vs calling range) * bet size)


(BF):

pot


(XX|XD):

(equity vs XB range * R vs XB range) * pot


(XC|XD):

(equity vs betting range * R vs betting range) * (pot + bet size) - ((1 - (equity vs betting range * R vs betting range) * (bet size)


------


Overall EV Bet:

(shove % * BRC EV) + (call % * BC EV) + (fold % * BF EV)


Overall EV Check:

(XB % * XX EV) + (XC % * XC EV)

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 Last edit: 08/08/2016 23:03

Smuft   Canada. Aug 03 2016 18:32. Posts 627

doing some brute force math again, I like to post these as a kind of "peer review" to weed out any errors before I start using them for real analysis


Baalim   Mexico. Aug 06 2016 07:51. Posts 33001

This should be a thread you will get more imput and it will be easier to follow

Ex-PokerStars Team Pro Online 

flounder44   United States. Aug 07 2016 16:45. Posts 916

teal durr


Smuft   Canada. Aug 08 2016 23:00. Posts 627

CORRECTIONS

(BRC):

equity vs shoving range * (pot + stack size) - ((1 - equity vs shoving range) * stack size)

removed "stack size" from the winning side of the equation

(BC|XD):

(equity vs calling range * R vs calling range) * (pot + bet size) - ((1 - (equity vs calling range * R vs calling range) * bet size)

removed "bet size" from winning side of equation

(XX|XD):

(equity vs XB range * R vs XB range) * pot

removed losing side of equation (I'm not risking anything besides there are no bets)

(XC|XD):

(equity vs betting range * R vs betting range) * (pot + bet size) - ((1 - (equity vs betting range * R vs betting range) * (bet size)

removed "bet size" from winning side of equation
removed "bet size" and "pot size" from losing side of equation (quite sure those don't belong there)

---

updated OP to reflect changes

 Last edit: 08/08/2016 23:04

Smuft   Canada. Aug 13 2016 06:18. Posts 627

condensed hero equity and R into a single variable "effective equity" to simplify formulas

resulting spreadsheet looks like: http://i.imgur.com/5hjdJFP.png

color coding cells that belong to different lines seems to make things a bit more intuitive


 



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