Pocket aces no guarantee in hold’em

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In a horse race, every horse is rated based on its chance of coming in first in competition with the other horses in that race.

The lower the odds against the horse, the more likely it will finish first.

So a 4-1 shot is a big favorite over a 20-1 longshot. This is reflected in the payoff.

The more horses at the starting line, the less likely the favorite will cross the finish line in first place. So it is in the game of poker.

Your hand may be the favorite before the flop against each of your opponents; but, the more opponents staying to see the flop, the less likely  you will be the winner at the showdown.

Let’s say you got lucky and were dealt pocket Aces. (The odds are 220-1 against it; but it does happen!) It is the best possible starting hand. It’s favored over each and every opponent’s starting hand.

The probability of winning against any opponent is about 80% (possibly slightly higher).

Probability is simply the likelihood or chance a given event will occur. Often, we express it as a percentage: What percent of the time will that event occur?

Multiplication Rule

This rule applies to the situation when we want to know the probability of two or more events occurring at the same time, knowing the probability of each event by itself. In this case, what is the probability your A-A will win against more than one opponent?

From this probability, we can quickly estimate the odds for or against you. With your pocket Aces, let’s assume three opponents stay to see the flop with you, even after you raise preflop.

Then, using the Multiplication Rule, the probability you will win against all three of them is 80% x 80% x 80% = 51.2%. You are a slight favorite (over 50% probability) to win that pot. If four or more opponents stay in, then you become a probable loser (less than 50%).

What are the odds?

By definition, odds are the number of successes you expect to get for every failure, on average. They can easily be calculated from probabilities.

In this case, if you win 80% of the time against each opponent, then you will lose 20% of the time (100% – 80% = 20%) to each. So, the odds are 80-to-20, which reduces to 4-to-1 in favor of your A-A to win the hand against each individual player.

More opponents

But, what is the probability and the corresponding odds if several opponents stay to see the flop? According to probability law, we multiply each opponent’s probability to determine how likely your A-A is to beat all of the players who saw the flop with you. So, if four or more opponents stay to see the flop, pocket Aces has less than 50% chance of winning the pot.

According to the Rule of Multiplication, if four opponents stay to see the flop. the probability of A-A winning at the showdown is about 80% x 80% x 80% x 80% = 41%. Anything less than 50% is an underdog and not favored to win. This is reflected in the odds: Since 100% – 41% = 59%; then the odds are 59/41 = 1.4-to-1 against you.

Loser’s Lament

You may have heard a loser say, “I can never win with pocket Aces.” Usually, it’s because he played against so many opponents that his pocket Aces no longer were favored – and thus became a longshot. That means his pocket Aces would lose more often than hold up.

Considering both probability and pot size, with pocket Aces, the optimum usually is playing against two or three, but never more than four opponents.

“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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