5bet shove math
Posted by Charles St-Pierre
Posted by
Charles St-Pierre
posted in
Mid Stakes
5bet shove math
Im trying to find an optimal % of 4bet bluffing in a specific situation, but im uncertain about certain things regarding the math of 5bet shoves.
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Hero open raise 3bb
Villain 3bet to 9bb
Hero 4bet to 21bb
At this point, if Villain folds to my 4bet, the hand result in a loss of 9bb for him (His 3bet). Thus, do I need to make the EV of his 5bet shove bluffs -9bb in order to make him indifferent between folding or 5bet shoving versus my 4bet ?
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Also, is this formula correct for calculating his 5bet shove EV ?
Notes:
1) No ante, Both players not in blinds positions, 100BB effective
2) Villain hand equity = 31%
3) Villain 5bet shove FE = 32.5%
4) Sizings as describe earlier
Formula:
(FE*POT) + (1-FE)*((EQUITY*WINNINGS) + (1-EQUITY*LOSSES)) = EV
(.325*31.5) + (.675)*((.31*110.5) + (.69*-91)) = -9.023625bb
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Thanks to those who choose to help.
Loading 6 Comments...
This is almost correct. If you want to set the EV of him 3-betting to 9x and subsequently folding to -9x for him, then the EV of him winning an all-in must be +101.5 and the EV of him losing must be -100.
Alternatively, you can consider his 9x raise as a sunk cost for him, then the left hand side is correct, but you must set the right hand side to 0bb. Since folding will result in him "losing 0bb".
Both methods should give the same answer, which is a nice property to have when you want to check the correctness of your calclations!
stumbled across this when trying to do some of these.
can someone please explain to me why (equity * winnings) is not (.31 * 201.5) if we win 31% of the full pot when called? thanks :)
Because you never win 201.5BB when 100BB deep, and for consistency all results are in the unit of BB's won.
I tried to do one of these calcs myself. Can anyone help me if I did it correct?
This particular villain I played 4bets 14.4% and has a 4bet range of 8.2. If I assume a stackoff range of JJ+/AQs+ I should have 59.8% FE and 30% equity with A3s
He opened CO to 2.5bb I 3bet to 8bb he 4bet to 18bb I shoved for 101.5bb with A3s
(FE*POT) + (1-FE)*((EQUITY*WINNINGS) + (1-EQUITY*LOSSES)) = EV
(.598*27.5) + (.412)*((.30*103) - (.70*-93.5)) =
16.445 + (.412)*(30.9-65.45)
16.445 + (.412)*(-34.55)
16.445 + -14.234 = + 2.2bb
EVshoving +2.2bb
EVfolding -8bb
If I did it right, does it mean that shoving is 10.2bb better then folding? Or a shove just wins me 2.2bb and the EV of folding is 0?
Some minor mistakes:
(.598*27.5) + (.412)*((.30*103) + (.70*-93.5)) =EV
You mixed the signs in front of the last term (it´s + instead of -), though your calculation was right again. :)
Then you worked with slightly wrong figures, if I´m not wrong myself. Assuming you were considering your position as SB, the pot you win in case Villain folds is 27, not 27.5, it´s 1bb from the BB plus 8bb from your 3bet (it´s dead money, doesn´t belong to you anymore) and 18bb from the 4bet, so 1+8+18 = 27. If you sit in the BB, the pot is 26.5.
Next number is the amount you´re winning when you win after 5-betting. It´s not 103, but 109. It´s 1bb from the BB, 8bb from your 3bet and 100bb from Villain´s stack, so 1+8+100 = 109.
Lastly you don´t invest 93.5, but 92, your 3bet is gone.
That gives:
EV = (.598*27) + (.412)*((.30*109) + (.70*-92))
EV = 3.09
That means, the EV of shoving is 3.09bb, the EV of folding is 0, so shoving has higher EV.
Can anybody recommend a book for all this info. Sounds great but a dont understand a thing.
Looks alot like the Matrix numbers.
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