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SB folds x percent, BB folds y percent, our bet size is b in big blinds
Both players fold: x*y percent of the time (or just xy for short)
If we're not taking into account anything post-flop and assume we just lose the hand right then if the blinds don't fold:
EV of Stealing = (1.5)(xy) + (-b)(1-xy)
We want the EV of stealing to be zero:
(1.5)(xy) + (-b)(1-xy) = 0
1.5xy - b + bxy = 0
-b + bxy = -1.5xy
b(-1 + xy) = -1.5xy
b = -1.5xy/(-1 + xy)
Example: SB folds 75 percent, BB folds 60 percent
xy is 0.75 * 0.60 = 0.45
b = -1.5xy/(-1 + xy)
b = -1.5(0.45)/(-1 + 0.45)
b = -0.675/(-0.55)
b = 1.227
If you want to understand the math of this a little bit better, I wrote an entire series that teaches you how to do EV calculations using only basic addition and multiplication. The first part of the series is here.
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