EV of a shove - my attempt

[caddie444]

I'm going to attempt to calculate the EV of shoving the nut flush draw in the following situation:

PokerStars No-Limit Hold'em, $0.25 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

MP1 ($28)
MP2 ($31.50)
Hero (CO) ($27.35)
Button ($40.60)
SB ($27.60)
BB ($33.35)
UTG ($33.30)
UTG+1 ($25)

Preflop: Hero is CO with ,
4 folds, Hero bets $0.75, Button raises to $1.75, 2 folds, Hero calls $1

Flop: ($3.85) , , (2 players)
Hero checks, Button bets $3.25, Hero raises to $25.60 (All-In)


(Please don't comment on accuracy of ranges just yet, this is merely meant to be a procedural exercise for me)

EV for this play:

Villain's range for 3B'ing pre and cbetting flop:

99+, AQs+, KQspades, AQo+ = 30(pairs) + 12(AK) + 12(AQ) +1(KQspades) = 55 combos

Villan's calling range after I shove flop:

99+ KQspades = 30(pairs) + 1(KQspades) = 31 combos

So he folds (55-31)/55 ----> 24/55 or 44% of the time

My equity vs his calling a shove range is 39%

1. 44% of the time when he folds I profit $7.10 (Whats in the pot) EV= (.44 x $7.10) = $3.12

2. 56% of the time he calls and I either win or lose:

a) win = (.56 x .39)($55.05) = $12.02

b) lose = (.56 x .61)($55.05) = -$18.81

EV of shove = $3.12 + $12.02 - $18.81 = -$3.67

I just did this intuitively so pls point out any errors if you see any

[daviddem]

Let me redo this for you:

- Villain's range after his cbet: 99+,AQs+,KsQs,AQo+
Combos: 99(3),TT(6),JJ(3),QQ(6),KK(6),AA(3),AQ(12),AK(12), KsQs(1) = 52 combos
Note that there are only 3 combos for 99 because there is a 9 on the board. AA and JJ also have 3 combos each because you hold one A and one J. AK has 12 (3 aces times 4 kings because you are holding one ace), and so does AQ, and obviously KsQs has only one.

- Villain calls your shove with: 99+,KsQs
Combos: 99(3),TT(6),JJ(3),QQ(6),KK(6),AA(3),KsQs(1) = 28 combos

So he folds (52-28)/52 = 46.1% of the time, in which case your profit will be 3.85+3.25 = 7.10

Your equity with AsJs against 99+,KsQs on a 9s5s5h board is 38.8%:

Text results appended to pokerstove.txt

  27,720  games     0.005 secs     5,544,000  games/sec

Board: 9s 5s 5h
Dead:  

equity  win  tie  pots won  pots tied    
Hand 0:     38.777%      38.76%     00.02%              10743             6.00   { AsJs }
Hand 1:     61.223%      61.20%     00.02%              16965             6.00   { 99+, KsQs }

So when he calls, 38.8% of the time you win and your profit on your 25.60 shove investment will be 3.85 + his 25.60 = 29.45 and 61.2% of the time you loose and your loss will be what you invested in the shove: 25.60

EV(he folds) = 0.461*7.10 = 3.2731
EV(he calls) = 0.539*(0.388*29.45 - 0.612*25.60) = -2.2857
Total EV = $0.9874

Note: if you want to do this perfectly, you also have to remove the rake from your profits! Let's say about $0.4 if he folds and $3 if he calls. Your EV becomes $0.175 !!

[spoonitnow]

So he folds (55-31)/55 ----> 24/55 or 44% of the time

My equity vs his calling a shove range is 39%

1. 44% of the time when he folds I profit $7.10 (Whats in the pot) EV= (.44 x $7.10) = $3.12

2. 56% of the time he calls and I either win or lose:

a) win = (.56 x .39)($55.05) = $12.02

b) lose = (.56 x .61)($55.05) = -$18.81

EV of shove = $3.12 + $12.02 - $18.81 = -$3.67

I just did this intuitively so pls point out any errors if you see any

Something in the bold is wrong and I'm pretty busy at the moment and woke up late so I'm not going to go through and figure out what it is exactly, but basically you're not winning and losing the same amount in these scenarios. When you lose, you're losing what you shoved, and when you win, you're winning the size of the pot right before you shoved plus the amount he called.

[caddie444]

Ok thanks guys, I now understand the flaw in my approach to figuring out the EV of my win/loss when he calls, you both explained it very well. This has been real helpful for me, I think I'll try posting another one later on, and I'm definitely psyched to mess around with the EV of shoving in different situations.

[spoonitnow]

Ok thanks guys, I now understand the flaw in my approach to figuring out the EV of my win/loss when he calls, you both explained it very well. This has been real helpful for me, I think I'll try posting another one later on, and I'm definitely psyched to mess around with the EV of shoving in different situations.

Message me on AIM and I'll show you how to do this faster without needing equations.

[daviddem]

Message me on AIM and I'll show you how to do this faster without needing equations.

Spoon, if you have time, I would like to see how you figure out whether the shove is +EV without equations. We can always compare pot odds with estimated equity to analyze the situation when we are called, but I would not know how to mentally estimate the fold equity while in play without working out the combos in his range.

Good if you post it here so all can benefit!

[spoonitnow]

Spoon, if you have time, I would like to see how you figure out whether the shove is +EV without equations. We can always compare pot odds with estimated equity to analyze the situation when we are called, but I would not know how to mentally estimate the fold equity while in play without working out the combos in his range.

Good if you post it here so all can benefit!

Come to IRC and message me, my AIM is broken. There's a sticky in the community forum on how to get there.

[caddie444]

Come to IRC and message me, my AIM is broken. There's a sticky in the community forum on how to get there.

Pretty interested so will try and do this sometime this week