heads up theory

[randomstumbl]

I'm sure there's some sweet math I don't know to solve this, but I had an idea. The button should bet when he has a 50% or greater chance of being called by a worse hand. So, if we will bet with a 40 he will raise with a 70 and we should reraise with an 85 or higher. He should then reraise with a 93 or higher. We'll reraise with a 97 or higher. He'll reraise with a 99 or higher and we should never lose more than 7 bets. To put in the 8th bet, we have to have the 100 card.

FYI, I'm just taking the total range of hands subtracting out the range I wouldn't have put in the prior bet with and dividing by two. That finds the point at which we're indifferent to raising (or sometimes the marginally profitable point because of rounding).

I don't think checkraising will ever be profitable. I would think we'd have to checkraise with our best hands. That would allow the button to raise more liberally and only put in two bets when we have our best hands. Betting out seems like a dominant strategy.

By betting out and calling we will lose .5 a bet (.4(1)+.3(-1)+.3(-2)=-.5). By checking and calling we'll lose at least half a bet and we won't make as much on our better hands. So, we should bet out with 40 and check/call with 39 or below. Let me know if I've screwed up the math somehow.