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Math can play a key role in making the decisions in poker most likely to win the chips for you.

There are two types of hands you might hold: Made Hands – could win without further improvement; and Drawing Hands – generally must improve to become the winner.

For preflop, the only made hands are A-A, K-K, and Q-Q. Based on the math of poker, what’s the best way to play these hands? For purposes of discussion, let’s focus on the pocket aces.

Your A-A is about an 80% favorite vs. a player with a smaller pair or any other drawing hand with which an opponent is likely to pay to see the flop. With two such opponents, your chance (or probability) of winning drops to about 80% x 80% or 64%.

With four opponents, your chance of winning falls further to about 40%. (We got this estimate of the probability of winning simply by multiplying 80% times 80% for every additional opponent who stays to see the flop.)


We can easily convert the probability to odds by subtracting the final estimate of the probability of winning from 100%. Thus, with four opponents calling to see the flop, the probability of losing is: 100% – 40% = 60%. And, the odds are: 60%-to-40%, or 3-to-2 against you.

Significance: For every five such hands, on average, you will lose three and win two. Your hand is said to be a 3-to-2 underdog. (Note: the probability of winning must be over 50% to be a favorite.)


In a limit game, the apparent response would seem to be you should always raise with A-A to force out players behind you – to reduce the size of the playing field. Not always! Sure, if you ended up playing against just one opponent, you will win 80% (4 out of 5) of those hands.

Trouble is – unless it’s a no-limit game and you can get your opponent to play most of his chips – with just one opponent, you win a very small pot, especially after the dealer rakes it. If you go through the math to calculate the most profitable situation, it’s best to play against 3-4 players. Then there is a respectable pot for you (hopefully) to win.

Poker math shows that the optimum situation with A-A on the hole, is to play against 3-4 opponents – no more, no less.


Epecially in a limit game, during the preflop round of betting, if you are in an early position, consider the likelihood that most, if not all, of your opponents might fold to your early-position raise. Then your A-A will go for naught.

Consider that you will be dealt A-A only once out of 221 hands (on average); the odds are 220-1 against it. With 33 hands dealt per hour, on average, it will take almost seven hours to receive another such hand. It would be a shame to waste it.

If it’s a loose table, and you don’t have an image as a tight player, the raise may still keep a few opponents in the hand. Unless you are certain of that, it would be wise to just call the big blind from an early position with your pocket aces.

On the other hand, from a middle or late position, if three opponents have already called to see the flop, then your raise is a smart decision. Very likely, the opponents positioned behind you will fold to your raise, while those who had already “invested” to see the flop will call your raise to defend their prior bet.

That raise will have served to reduce the size of the playing field down to three or four (if one of the blinds elects to call) and get more chips into the pot you have a good chance of winning. That’s the ideal situation for you.

To add icing to the poker cake, you also have bought yourself the virtual button – last to declare for the rest of this hand. You will be able to see what all your opponents do before it’s your turn to declare. The edge is all with you! Good luck!

“The Engineer” is a noted author and teacher in West Los Angeles, who was recently elected to the Seniors’ Poker Hall of Fame. E-mail him 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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