Math or Psychology?

The uninitiated often hold one of two views about poker. They either think that “it’s all math” or that “it’s all bluffing.” The math school will often ask questions like: “Isn’t it hard to calculate the odds?” The bluffing school will often ask: “How do you keep a poker face? I always give away my hand.” Whereas neither school is correct, these two extremes are an excellent illustration of the dual nature of poker. The truth is that poker as a mix of math and psychology – a mix of science and art. In poker, math defines the most profitable play you can make in a given situation if you know all the variables. But poker is not exclusively a game of math because you do not know all the variables – you do not know, for instance, your opponents’ cards or whether the players to act behind you will call, raise, or fold. Thus, in poker, psychology is the skill of accurately guessing at the information you do not know for a fact.

Poker books and literature are, generally, an attempt at an approximate balance of math and psychology. The writers are often attempting to teach you a strategy that will make you into a profitable player. For instance, when a poker writer instructs you to play K-J offsuit in late position in a hold’em game if there is no raise, what he or she is saying is: “Based upon certain psychological assumptions that I am making because of my research and experience, I believe that K-Jo is a mathematically profitable hand when you can enter the pot in late position for a single bet.” In other words, a lot of poker literature makes a lot of assumptions about your opponents – specifically about their starting hands and style of play. At low-limits these assumptions are close enough to dead-on that there are many poker books which will teach you the basics quickly and accurately. The books are, however, approximations.

How Does It Work In The Heat Of Combat?

Let me give you an extreme example that will illustrate the interplay of math and psychology. It is the World Series of Poker Championship – the game, of course, is no-limit hold’em. You can bet all of your chips in a single wager if you like. You have played well for five days and been lucky when you needed to be. Now there are only two players left – you and your opponent Phil Hellmuth. You each have the same number of chips. Phil offers to make a deal but you are feeling cocky and say: “No way. Put ’em in the air.” Phil is the button (the small-blind when heads up) and he shoves all-in. You look at your hole cards and discover A-T offsuit. Do you call? Do you want to play A-To for all your chips and the WSOP Championship on the line?

This is, of course, a hypothetical question. Speaking for myself, I can assure you that if I ever do wind up in a heads-up duel with Phil Hellmuth at the final table at the WSOP Championship I will not be able to say: “No way. Put ‘em in the air.” All I am likely to manage is: “Mommy, help me.” Nonetheless, this question serves to illustrate the relationship of math and psychology to poker. Is this a math question or a psychology question? If Phil has a random hand (he has shoved all-in without looking at his cards) then A-To is a 62.722 percent favorite to win. You call. Unfortunately, it is not that simple. It is not a pure math question because Phil does not have a random hand. He has looked at his cards. He has chosen to push all-in with the cards that he has (this assumes that there are some cards he will not push all-in with). You are not up against a random hand; you are up against a hand that Phil thinks is worth an all-in bet in this situation.

Now to make a determination of whether or not you should call you must take a guess at the possible hands Phil holds – the range of hands with which he will make this all-in bet with. What cards would Phil hold to make a huge all-in play with? There is the psychology part of poker. You think about a few things you know. First, Phil is one of the finest players in the world – he is not making some ridiculous amateur mistake by pushing all-in. Furthermore, he has played very few hands this aggressively over the last hour. And finally, you know that Phil wants to regain the WSOP more than anything. It seems very doubtful that he is risking all of his chips on a marginal hand. You conclude therefore that Phil has A-A or K-K. Against that range of hands, A-To will win just 16.2 percent of the time. You fold.

The Best Players Do Both

Admittedly, this example is extreme. The point, however, remains valid. To become a truly skilled poker fox you will have to be very good at both the math and the psychology of poker. You probably know opponents who are good at one or the other. There are players who can rattle off odds and statistics but rarely go home winners because they simply cannot turn their knowledge into a winning style Then, there are players who understand their opponents but insist on gambling with inferior cards and thus, they cannot win.

To become a great player you will have to go beyond the existing poker literature. You will have to understand psychology and math. You will have to know how your opponents are thinking and feeling at every moment. You must have a handle on the kinds of cards they are apt to play and how they will play them. Will this opponent tenaciously hold onto top pair no matter how much aggression you show? Will this opponent routinely fold second pair? In short, you will have to “put your opponents in a box.” The psychological tools you employ will define the parameters of that box. The best players – the world class players – are able to very accurately put their opponents into very small boxes.
Once you have a good handle on your opponents you will need to understand the math of poker well enough to know the best play to make. Should you raise, call, or fold? The answer will depend upon knowing all of the variables for the specific situation you find yourself in. Using psychology you have defined the variables. Math will tell you the right play to make.

In my next column I shall explain the steps that I go through to define the variables. It is not as difficult as it seems. Then, in the concluding column I shall show you how to sort out the math for the situation as you have defined it and make the best play.