Not too long ago, I wrote about the payoff rule:
The Payoff Rule For Big Bet Poker
Situation: The pot was small, you are on a made hand, and you believe your opponent was on a draw. On the last street you bet your made hand for some amount (BET) that charged the draw to see the next card. The draw had probability P(draw) of hitting. There was ESS money behind in the smaller of your two stacks at the start of the previous street.
Now, the draw hits and you have to decide how to proceed. If BET > P(draw) * ESS, you should aways be willing to get money in and pay off the draw, up to and including wagering your entire stack. If BET < P(draw)*ESS, you should try to limit the percentage of your remaining stack that goes in on future streets based on the fraction of how much smaller BET is than P(draw) * ESS. In other words, apply pot control. If you can’t accomplish that, you need to fold some percentage of the time on future streets such that you pay off no more than that amount on average.
The payoff rule is not an absolute thing - the more money that was in the pot to start, the more willing you should be to pay off. If your opponent may have a made hand you beat instead of a draw, you should pay of more. If your opponent may have a made hand that beats you, you should pay off less.
Now, we originally derived this rule in the context of set farming. I’d like to re-visit that example, and see how the pot control works in practice.
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