CardSharp

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. The reason this example is so important is that the potential for set farming arises every hand, and is thus a fundamental part of the fabric of NL holdem.

Stacks are 100BB deep. The action goes as follows: You have pocket aces on the button and raise to 3BB. The SB folds. The BB calls. What is your target pot size?

Now first, we have to make sure this is a legitimate application of the payoff rule. The starting pot was definitely small. BET=3BB. ES=100BB. Now, is villain on a draw? The answer is certainly yes, since we hold the nuts and yet any possible hand could hold is in fact drawing to beat us. So what’s P(draw) – is probability of outdrawing us on the next street? The answer is, we don’t know for sure. If he’s got a pair, it’s about 12%. If he’s got a suited connector or something, it’s slightly worse. So, what number do you use?

Payoff Rule Clarification #1:

When an opponent could be on one of a number of possible draws, it’s generally best to gear your play towards the most likely, and/or the worst case scenario from your perspective. Only ignore the worst case scenario if it requires very specific cards from your opponent (say, one specific combination of hole cards) that you have no reason to believe he might hold.

In this case, a pair drawing to a set is both the most likely and the worst case scenario, so it’s obviously what we have to deal with. That means P(draw)=0.12 and now we have all the parameters to apply the payoff rule. ideally, we would like to have been able to bet P(draw) * ESS, or 12BB preflop. If we had done that, we could put all the money in with no concern whatsoever that our opponent might be able to profitably set farm (or run any worse draw) against us. But instead, we only bet 3BB. There were good reasons for this – in the vast majority of games 12BB would have killed our action. So we took what we thought we could get – 3BB. But now we’ve got a problem – we only bet 1/4 of what we would have liked to bet. According to the payoff rule, this means we don’t want to get more than 1/4 of our stacks, or 25BB total, in by the river. Now we have to figure out how to make that happen.

First, notice what happens if a pot sized bet goes in on all three remaining streets. Ignoring the 1/2BB in the pot, the first bet would be 6BB. The 2nd would be 18BB and the third would be 54BB. Of course that last bet is way over the total amount of money we wanted to go in. But the 3BB preflop plus the next two pot sized bets add up to 27BB, which is very close to our target. So one way to achieve our goal is to remove one street of betting. Which leads to this general principle:

Payoff Rule Clarification #2:

When you hold a top pair/overpair hand after the flop, it’s usually advantageous to eliminate a round of betting.

Now, this is easier said than done as we’ll learn in a bit. But it should be clear that allowing a pot sized bet to go in on each remaining street is not desirable.

Of course, another method of keeping the pot small is to make smaller bets – 3 bets of 1/2 pot would keep you under the desired limit for example. However, this method doesn’t work as well as you might think for one simple reason: your opponent tends not to cooperate. Opponents who flop a big hand have a tendency to adopt a very specific line – initially they slow play and let the preflop raiser continuation bet. Then, either on the turn or the river, they check-raise. The problem with betting every round is that you ensure they always have the opportunuty to get their check-raise in

The most popular method of pot control, if you’re the player in position, is generally to eliminate the turn betting by simply checking behind on the turn. Then if your opponent leads the river, you call. If they check again, you bet small as they likely don’t have much of a hand. There are a lot of alternatives, but this is a standard play that every player should know and regularly execute. We’ll discuss why this works so well, some alternatives, and the effects of position on potsize control in the next article.