HM Quickie 8 Button Steal With Zero Equity
We’ll consider here a button steal to win the pot with a zero equity hand by having both blinds fold to a button open-raise. In that case we assume the win amount is 1.5bb, the typical sum of the forced blind bets. Let fe be the probability both blinds fold and let Bet be the button bet amount. Then the EV equation is
EV = fe*1.5 - (1-fe)*Bet
For determining the maximum bet size to break even (EV=0) given fe is estimated, we have
Bet < 1.5*fe/(1-fe)
For determining the required fold equity (both blinds fold), we have
fe > Bet/(1.5+Bet)
Since fe is for both players folding, the simplest approach is to assume each player folds with probability fe^0.5. Obviously, other combinations of individual fold equities will give the desired combined fe.
The following table provides some results:
Note that the individual fold equities have to be fairly high for all cases even when the button is short-stacked and his bet is only 1bb.
Example: If each player will fold 80% of the time, they both will fold with probability equal to 64%. In that case hero’s breakeven bet size with pure air should be no greater than 2.67bb.
Example: If hero goes all-in with a bet of 5bb, to break even the combined blind fold equity should be at least equal to 77%.
We should note that these results are probably a bit conservative since it is rare for a pre-flop hand to have zero equity. However, that is countered by the fact that, except for an all-in bet, there will be future betting and poor hands do not often realize their low equity since they often cause the player to fold prior to the river. A future post will deal with the case of button’s bluff hand having some equity. We should also note that fold equity is typically partially dependent on bet size, which we have not considered here but will in future posts