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Why do so many avid poker players tend to shy away from anything that has to do with the mathematics of poker? Then they blame bad luck for another losing session.

Poker Math primarily consists of (1) probabilities, and (2) poker odds. If we can minimize the need to use it, especially the more complicated probabilities, it will make life much easier at the poker table.

Probability is the ratio of the number of favorable events to all possible events. From the probabilities, you can calculate the corresponding odds for or against the preferred event. That idea frightens many poker players.

From a practical standpoint, it is possible to avoid Poker Math until after the flop, and then to make it easier to estimate and apply the probabilities when you have a Drawing Hand after the flop. That’s most of the time.

Use the 4-2 Rule to estimate the probability of completing your Drawing Hand, with a simple multiplication to calculate it; and then convert that probability to your card odds.

Indeed preflop, for starting-hand selection, you need not concern yourself with any aspect of Poker Math. All you need is knowledge of the favored starting-hands. We recommend using the Hold’em Algorithm or a chart/table of preferred starting-hands, found in many poker books. (But don’t limit your selection to Phil Hellmuth’s “Ten Top Starting Hands.”)


Let’s discuss the mathematical concept of probability, applied to the game of poker. During our recent Claude Pepper Seniors’ Poker Class, I explained what “probability” is, and how to use it to calculate the odds for or against something happening.

As a matter of interest, here are the probabilities and related odds of being dealt the following hands:

A-A: Probability is 0.5%. Odds are 220-to-1 against.

Two suited connectors: Probability is 3.5%. Odds are 26-1 against.

Any pair: Probability is 6%. Odds are 16-1 against.

Two connectors: Probability is 14.5%. Odds are 6-1 against.

Any Ace (A-x): Probability is 14.5%. Odds are 6-1 against.

Two suited cards: Probability is 23.5%. Odds are 3.3-to-1 against.

What can we learn from this information?

The higher the odds against it, the more valuable is that starting-hand. (Incidentally, the probability of being dealt an unsuited, unconnected non-pair is about 60%. That’s what you can expect in the hole most of the time.)


With odds of 6-1 against each player, at a full table of nine players, it is highly likely someone holds an Ace in the hole. Many play A-rag from any position. If you start with a big pair (other than pocket Aces), and an Ace falls on the flop, your hand likely has become an underdog, with only two outs. Underdogs usually lose.

Also, it is much more likely you will be dealt two suited cards in the hole than two connectors. That’s why, in the Hold’em Algorithm, connectors are given a much bigger point bonus than two suited holecards. Suited connectors are even rarer, and hence more valuable.

I have taught our seniors poker class how to convert the probabilities to the corresponding odds. Most important, as noted above, you can avoid this exercise preflop by using the Hold’em Algorithm (or equivalent) to quickly decide whether to play that starting-hand. Thereafter, on subsequent betting rounds, you would use Poker Math, but only to estimate the odds to decide whether to continue in that hand – or raise.

Note: Part II, will continue our discussion of “Poker Math – the Easy Way!” Learn the best way to estimate your card odds and pot odds, and how to use this information.

“The Engineer,” a noted author and teacher in Greater Los Angeles, is a member of the Seniors Poker Hall of Fame. Contact George at [email protected].

About the Author

George Epstein

A retired engineer, George Epstein is the author of “The Greatest Book of Poker for Winners!” and “Hold’em or Fold’em? – An Algorithm for Making the Key Decision.” He teaches poker courses and conducts a unique Poker Lab at the Claude Pepper Senior Center under the auspices of the City of Los Angeles Dept. of Recreation and Parks and at West Los Angeles College.

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