Analyze This Hand

/ When someone seeks advice on playing a particular poker hand, many so called experts love to give the simple answer “it depends.” Basically what they mean is that the right answer, the best play, depends on the tendencies of your opponents. Well “Duh,” no kidding. Except that they hide behind this answer to disguise the fact that they might still get it wrong even if they knew those tendencies.

It is not so simple to come up with the right poker play even if you know exactly how the others are playing. It takes the ability to properly apply both math and logic, an important poker talent that many poker writers secretly know they lack. So they fall back on the “it depends” answer.

The thing is that the relevant parameters that the answer depends on are often known — either because they are specified in the original question or because the situation is such that almost all opponents will play the same way. When that happens one should be able to come up with the indisputable best play. The fact that most writers can’t, doesn’t mean you can’t. Here is an example.

The game is limit hold ’em. It is probably a tournament because you have such a short stack, but the answer would be the same for a side game. The stakes are $100-$200 with a $50 and $100 blind. All fold to the button who makes it $200. The small blind folds. You started this hand with $300 and have $200 after putting in the blind. Your hand is

What do you do?
Before answering this question, we do have to agree on some assumptions. Assumptions that would accurately describe the vast majority of opponents. Number one is that they will raise with a lot of hands. That is a standard play in this spot. Second we assume that a reraise before the flop will always be called. Obviously. He’s getting $550-to-$100 odds on that all-in reraise. Third we assume that if you call before the flop and check on the flop he will usually bet. I am sure you agree that almost all opponents will play this way. So let’s start the analysis.

First, let’s see if you should possibly throw the away. You are getting 3½-to-1 on his raise which would make this an easy call. The problem is that extra $100 in your stack. Might that change things?

If you shove it in before the flop the real odds you are getting are no longer $350-to-$100. They have gone down to $450-to-$200 or 2½-to-1. Is it worth taking those odds with ?
Well of course it is. If he would raise with anything, your hand would actually be a slight favorite. But even if he was throwing bad hands away, there is no way his remaining hands would beat you anywhere near the 69 percent or so needed to make it right to fold.
This means that we have established that folding cannot be right. We showed that reraising shows a profit (if the big blind is counted as no longer yours). That beats folding and breaking even

In fact, I believe most players would reraise in this spot. But there are alternatives. You could merely call before the flop. And then depending on what came, you could bet, check and call, or check and fold. Let’s look at these alternatives.

First notice that if you always check and called you would essentially be in the same position as you would have been had you raised before the flop. Given the fact that your check will almost always elicit a bet, playing that way results in a showdown for the $650 pot. Just like your reraise would. So this strategy gains nothing over the all-in raise.

But what about checking and sometimes folding? Oh yeah? When would you do that? You would be getting $550-to-$100 on his flop bet and you have an ace. Between the times you catch an ace and the times ace high wins unimproved, your chances would always total more than the necessary 15 percent to win the pot.

So checking and folding is out. And checking and always calling is no better than reraising preflop. What about calling before the flop and betting out on the flop? The problem of course with this play is that it allows your opponent to save a bet when he flops nothing. Moving in before the flop prevents this. But wait. What odds is he getting on your flop bet? Again it is $550-to-$100. Suppose the flop is

and he has

Your bet has caused him to fold a bet with six outs! He is less than a 5½-to-1 dog so he costs himself money by folding. Money (actually EV [expectd value]) that you gained. Had you reraised you would have won an extra $100 most of the time to be sure. But that isn’t enough to make up for the risk of losing the pot on the turn or the river.

It is true that there are not too many flops that your bet will make him “incorrectly” fold. But so what. It is simply getting extra equity with everything else being equal. Unless you flop aces or better your bet on the flop will always be one that you want him not to call (except for some of the rare times he has a deuce).

And what about those times you do flop aces? Check it of course. He will bet it for you even probably with hands that he would have folded had you bet.
The above analysis is almost ironclad. If you had trouble following it you need to reread it as many times as necessary until you do. It involves important poker principles that you need to know (plus it tips you off to a key tournament play). You call before the flop and then come out betting unless you flop aces or better. And it doesn’t depend.

David Sklansky