Poker Math is not Common Core ; Poker Variance Works

poker math

Don’t avoid using poker math

by George Epstein
Poker, Texas Hold’em Betting tips: Know the probability of what the next card could be.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


Allow poker variance to work

 by Irene Edith
Allow poker variance to workIn life, we all experience “ups” and “downs” – good days and bad days; good health and illness; family celebrations and disputes. We have learned to accept it.

Don’t let the bad experiences get the best of you. Roll with the punches. Meanwhile, look ahead to the “ups.” Be patient. So, too, it is in playing poker.

When luck is with you, you are on an “up.” You win lots of chips; hope it keeps up. But, sooner or later, your luck is bound to turn against you – bad! That’s “variance.” A math expert would describe it as a measure of the spread of a statistical distribution about its average or mean value. Sometimes it is referred to as “variability.”

Variance is a fact of life at the poker table – a matter of chance or luck. It is unpredictable; you have no control of it. While you are playing Texas hold’em, you cannot control the hole cards that are dealt to you, nor the community cards the dealer lays out on the board. But, there is a way skill can help you.

Handling Varince

Remember, when you sit down at the table, you would like to go home a winner – more money in your pocket than when you arrived at the casino. Considering your share of the house rake and inherent variance, that’s not easily done.

A reasonable goal might be to double your buy-in. The best way is to use “money management.” Michael Wiesenberg’s Official Dictionary of Poker defines money management as “playing in such a way as to minimize your losses and maximize your wins.”

Poor money management is losing your buy-in and then losing even more in an attempt to get even. To avoid this occurrence, before you have lost it all, ask yourself an important question: “Is this table too aggressive (lots of raising), especially before the flop, or too tight (only one or two players staying to see the flop almost every hand)?”

Change to a “better” table. For me, that is a loose – passive game: three or more opponents usually calling to see the flop, with only occasional raises preflop. Most of your playable starting hands will be drawing hands that must improve to win the pot.

For such starting hands, it is best to see the flop at minimum cost (just call the Big Blind) and in a multi-way pot (three or more opponents staying to see the flop) so you can win a decent pot if/when you connect. Remember, the odds are usually against your drawing hand becoming the best hand in that game.

Most aggravating is when you finally catch some good hands – you are on an “up” – and soon find yourself well ahead. But it’s much too early to quit for the evening. Besides, you would like to win even more. (A little greed?) What’s more, you still haven’t reached your goal for the session.

Face reality

Sooner or later, variance will “ordain” that someone else will be the lucky guy – not you. So, let’s consider another form of money management.

It is often the case, you will find yourself ahead at some point during that session. Here’s the idea: Set aside a portion of your winnings – at least equal to the minimum buy-in – enough to play several hands.

Just move those chips a bit to the right. Let’s call that your “play money.” Add the rest of your winnings to your buy-in, a bit to the left. That’s your “money in the bank.” Now continue in the game using only your “play money.” Perhaps you lose a hand, and then win a decent-size pot. Add part of that pot to your “money in the bank” and the rest to your “play money.”

It’s so much fun to watch both stacks grow big – as you overcome variance.

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