Something Bothering Me About Pot Odds

Sklansky's Fundamental Theorem of Poker is widely accepted and it makes sense: make fewer bad decisions than your opponents and you win. How do you judge decisions? Well, there are a number of ways but one of the most prominent is pot odds. Pot odds tell you whether you're getting sufficient return on your money given the risks you are taking. Pot odds of course are based on mathematical expectation, in other words: (the chance that you will win X the amount you will win) - (your chance of losing X the amount you lose). If the difference is positive, you are making a good play, according to the standard wisdom.

As you've gathered, however, one of the goals of this blog is to question the standard wisdom and I'm going to question it here. First of all, I've got no problem in general with judging your plays based on pot odds. However, let's dig a little deeper. I want to make two points. First, there are differing degrees of positive expectation: your expectation could be slightly positive or it could be highly positive. Second, the accuracy of probability calculations depends to some degree on the number of trials. What do I mean by this: I mean that when you have an Ace-Six and you're hoping to draw another Ace, the probabilities look like this on the flop (3/50 + 3/49 3/48). This adds up to roughly a little better than a 1 in 6 chance overall of getting the Ace on the flop. Now you might expect that if you look for this draw 6 times, you might reasonably hope to get one Ace but not so. Probabilities are most accurate over large numbers of trials (see law of large numbers). You might hit 3 Aces or you might well hit none at all. Flip a coin ten times and it's highly unlikely you come up with 5 heads and 5 tails.

So what does all this mean? To me, it means this: before applying pot odds robotically, ask yourself how many hands of NLH you're planning on playing a year. If its tens of thousands, then play by the pot odds book. If, however, you're going to play in 3-4 tournaments a year, which the Hold 'Em Scholar is probably looking at right now, then you've got to be careful about playing tournament hands where the odds against your winning are 2 to 1 and the pot odds are 3 to 1. You just don't have that much of an edge in this situation, given the risk. In other words, you probably want to choose situations where the pot odds are more like 4 to 1 when the odds against you are 2 to 1 and you know you aren't going to be playing an NLH tournament every weekend.

Let me give an example of a hand I wouldn't play, that Phil Gordon apparently would. This example comes from Phil's Little Green Book (Gordon, Little Green Book, p. 42). In discussing a sandwich play, Phil says that he'd push in all his chips where the pot odds are roughly 2.5 to 1 and the odds against him are about 1.5 to 1. Mathematically, this is the right move. Pot odds tell you to make it, Sklansky would presumably tell you to make, but I ain't making it in the early to middle rounds of a tournament. Why? Because I'm only playing a limited number of tournament hands a year and the odds are that I'm going home if I make this play. I don't know that I'm going to play enough hands over the course of the year to make this play pay off. You'll have to make your own decisions...