Use of Mathematics to Read Hands

When you cannot put a player on a hand but have minimized his most likely hands to a limited number, you take the help of poker mathematics to ascertain the chances of his having certain hands as compared to others. After that you decide what kind of hand you must have in order to continue the play. Use of mathematics is specifically essential in draw poker, where your main hint to what your rival can have is what you know about his opening, calling and raising requirements.

For example, if you think your rival will raise with three 2s or better before the draw, you can take the help of mathematics to ascertain what hand is favored to have him beat. It works out to something like three queens. Of course, then if you have three 3s, it is not worth calling that rival's raise on the chance that he has particularly three 2s. But if you have something such as three 5s or three 6s, the pot odds makes it correct to call because at present you not only draw out on a better hand by making a full house or a four of a kind, but there are few hands your rival could have which you already have beat.

To verify the chances a rival has one or another hand, you may sometimes use a mathematical process based on Bayes' Theorem. After determining upon the type of hands your rival would be betting in a particular situation, you ascertain the possibility of his holding each of those hands. Then you can make a comparison with those possibilities. For example, if in a draw poker you think a specific player will start either with three-of-a-kind or two pair but will open with one pair and will check as a slowplay with a pat hand, then it is 5-to-2 against that player's having trips when he does start. Why it happens so? Commonly, as per the draw poker allocation, a player will be dealt two pair 5 percent of the time and trips 2 percent of the time. Comparing with these two percentages, you arrive at a ratio of 5-to-2. Hence, the player is a 5-to-2 favorite to have two pair.

Suppose, in hold'em a rival places in a big raise before the flop and you read his hand for the kind of player who will raise only with two aces, two kings, or ace, king. The chance that a player gets two aces on the first two cards is 0.45 percent. Even with two kings the chance he will get is also 0.45 percent. Thus, on average he will get 0.9 percent of the time with two aces or with two kings. The chance of getting an ace, king is 1.2 percent. By comparing these two possibilities - i.e. 0.9 and 1.2 percent - you conclude that the chances are 4-to-3 in support of your rival's having ace king rather than two aces or two kings. Obviously, if you know your rival is 4-to-3 favorite to have ace, king is not sufficient to determine his raise with, say, two queens. If he does have ace, king, then you are a small favorite but if he has two aces or two kings, then you are a big underdog. However, the more you know about the probability of a rival's having one hand rather than another when he bets or raises, the easier it is for you to decide whether to fold, call, or raise.

We spoke about a player in seven card stud raising on third street with king showing and we spotted out he might have two kings, but he might also have a small pair or a three-flush or something like J, Q, K. To make it clear, let's assume you know this specific player will raise only with a pair of kings or a three-flush. You have a pair of queens. The chance is about 11 percent before the raise that your rival has another king in the hole to make a pair of kings and it is about 5 percent that he has three of the same suit. This is mathematical possibility depending on the card allocation and it has nothing to do with action that a poker player takes. Hence, when your rival raises, which at present reduces his possible hands depending on what you know about him to either two kings or a three-flush, he is an 11-to-5 favorite to have the two kings and you would certainly fold your two queens. On the other hand, another king showing anywhere on the table basically reduces the mathematical possibility of your rival's having two kings before he raises because there are only two kings instead of three among the unseen cards. The possibility of your rival having two kings is reduced to almost 7 ½ percent. A raise makes it to about 40 percent that your rival has a three-flush instead of two kings. Based on your position, your queens may be strong to verify a call. In this situation, you read your rival's hand not depending on what you know about him, the action he takes, and the exposed card you look, but also depending on the mathematical comparison of his possible hands.

Naturally, it does not take a mathematical expert to understand that another king on the table reduces the chances of a rival's having two kings before he raises, therefore using math to read hands does not need always the exact allocation possibilities represented here. Moreover, you need to complement mathematical conclusions with what you know about a player. For instance, in a small-ante game, some players may not raise with two kings when there is no other king showing in expectation of making a big hand, but they will raise with two kings when there is a king showing to try to win the pot. They consider going for the pot right away clearly because there was other king, which decreases their chances of improving. When you are up against such players, the other king might really increase the possibility of their having two kings after they raise - not depending on mathematics but depending on the action they have taken and what you know about the way they play poker.

Reading Hands in Multi-Way Pots

The other aspect of reading hands and determining how to play your own is the number of players in the pot. Any time someone bets and someone else calls, you are in a more dangerous position than when it is just up to you to call. Generally, a caller in front of you makes it necessary for you to tighten up essentially because you no longer have the extra equity that the bettor may be bluffing. Whether he is bluffing or not, the second player may have something to call. Thus, when your hand is rarely worth a call in a heads-up situation because of the extra chance of catching a bluff, it is not worth an overcall when someone else has called in front of you.

As per such situation we have taken an example when I was playing in a small ante razz game. On the first three cards I had an:

It is a good hand but not a best one. The high card came in and a player called with a 5 showing. I was ready to call or possibly to raise. However, a player in front of me, who was playing tight, raised with a 4 showing. Had the first player with the 5 showing not called the initial bet, I would have called the raiser with my 8, 5, 2 because though the raiser was playing rigid, there would have been a chance he was semi-bluffing. But, however, the raiser raised another low card that had already called, it was almost a surety he had a better hand than I did; and there was also the probability the first caller had a good hand. Hence, based on the small ante, my hand was no longer worth a call.

The same kind of idea must be employed when deciding whether to call a raise cold. As little exception, you require a better hand to call a raise cold than you would need to raise yourself. The easy explanation to this rule can be given an example from draw poker. Suppose, in the game you are playing you determine to raise before the draw with aces up or better. You see your hand and find that you have three 2s. You are ready to raise but instantly the player to your right, who will also raise with aces up or better, place a raise. But, instead of raising, you cannot call now. You must fold because the chances are better that the raiser has you beat.

This concept applies to every game. When you have a minimum or a close minimum raising hand and the player to your right, who has an identical aspect as yours, raises in front of you, then his hand is possibly better than yours and your correct play would be to fold.


Reading hands is a strong tool of poker because it permits you to play correctly more frequent, as per the Fundamental Theorem of Poker. The more better you read your rival hands, the less possible you are to play your hand separately from the way you would play it if you could really see what you rival had. Weak players are difficult to read because there is less style in their play. Good players are easier because there is logic to their play. On the other hand, rigid player are more difficult to read because of their skill to conceal their hands.

The other way to read hands is to put rivals on several of potential hands and reject some of them depending on their play and the cards they chase from one round to the other round, and making an order in which they chase their cards. Secondary and corresponding way is to work backward, observing at a rival's further play in terms of how he played his hand in earlier rounds.

You can read hands by using mathematics and comparing the potential hands based on the Bayes' Theorem. If you think you know a rival will bet only certain hands, you develop a percentage on the basis of the probability of that rival dealing each of those hands. To make it clear, you can split his possible hands between those you can beat and those you cannot beat. The percentage reveals which of the hands he is favored to have.

Consequently, when reading hands you must determine the number of people in the pot. When there is a caller in front of you, the caller and the original bettor cannot bluff both, hence you must play on the assumption that you are up against at least one legitimate hand. When there is a raiser in front of you with the identical aspect as yours, you should have more than your minimum raising hand to call that raiser because you have to figure your minimum raising hand is beat.

In the entire page, it is suggested that an essential principle of reading hands is to know your rivals. It forwards us to the next section, "The Psychology of Poker".