A poker calculation

To make up 0.25 small bets per hand in IO, we need to know that BB will on average pay off that much [B]when we win (36.7% of the time), net of the times she wins and we have to pay her off (31.34% of the time).[/B] Note that I'm ignoring the button's involvement because he's already in the hand. Technically he plays a role in converting scoops into fractional pots, but this is getting way too complex already.

If we average X excess bets when we scoop her and lose Y bets when she scoops us, we break even when:

0.37 X - 0.31 Y = 0.25 small bets (the amount of preflop equity we sacrifice by not knocking her out).

0.37 X = 0.25 bets + 0.31 Y bets
X = 0.67 + 0.84 Y