Odds and Probabilities in Texas Hold em

One part of Texas Hold'em strategy that you need to know and understand concerns probabilities and odds. Texas Hold'em poker is a game of skill, but it contains an element of chance, and therefore you need to know the likelihood of certain outcomes. Probabilities are expressed in terms of poker odds.

Comparing pot odds and winning odds

One term you must know if you are to succeed in Texas Hold em is pot odds. Pot odds stand for the amount in the pot versus the amount that you must pay in order to compete for the pot. For instance, if you have to call $10 to win a $40 pot, the pot odds are 400 to 100, or 4 to 1 (the same thing). If your chances of winning the pot are better than 4 to 1, you’d be correct to call. If they are worse, you should probably fold.

(We say ‘probably’ because in real life, other factors enter the equation as well.)
So how can you tell your winning odds? Let’s look at an example. Suppose you have two spades and the board shows two more spades. There’s a single card left to come, which means that the odds against you making your flush are about 4 to 1. Why is that? Well, here goes. Since you can see four spades, among the cards that you have not seen there are nine spades left. You have seen a total of six cards: the two in your hand and the four on the board, so there are 46 unseen cards, 37 of which are not spades. If we assume that improving your hand to a flush will win you the pot, which is a rather good assumption most of the time, your odds of winning are 37 to 9, which is roughly the same as 4 to 1.
If you have four cards in a sequence, there are eight cards that will complete your straight. For example, if you have 5-6-7-8, there are four fours and four nines. This gives the odds 38 to 8, which is the same as 4.5 to 1. With this hand, pot odds of 4 to 1 are not enough. Calling with those pot odds is a losing play in the long run.

Good to know probabilities

When you play poker, it helps to know a few probabilities by heart. Here is a list for the most common cases in Texas Hold em:
If you have flopped four suited cards (a four flush), the odds for completing the flush with two cards to come are about 2 to 1. With one card to come, the odds are about 4 to 1, as explained above.
As we also saw, the odds of making a straight from an open-ended straight draw are about 4.5 to 1 against with one card to come. With two cards to come they are about 2.5 to 1, that is, on the flop.
If you hold a pocket pair before the flop, the odds against you hitting three of a kind on the flop are about 8 to 1 while the odds of hitting three of a kind by the river are 4 to 1 against. The odds of improving a flopped set to a full house on the river are 2 to 1 against, more or less.

Facing the harsh reality

As is often the case, the reality is not that simple. Things are usually complicated by other aspects. For example, you cannot be sure to win even if you hit you flush or straight. Someone may hit a full house to beat your flush; someone may hit a flush to beat your straight, and so on. In a real poker game, there’s also the phenomenon of implied odds. That is, the additional money you may win or lose on later streets, for example, if you make your hand on the turn, of if you don’t. Calculating implied odds is as much an art as a science, given that the probable behavior of your opponents must be estimated.