Probabilities boost results in Texas hold'em poker

Jul 30, 2013 3:00 AM

In a recent issue, we explained that Probability is the likelihood (chance) a certain thing will happen. Knowing the probabilities, you can estimate the card odds against making your hand.

We showed how to use this, along with old-fashioned logic, to be a bigger/better winner when you hold pocket Aces. Let’s look at two much more common situations.

Small pair in the hole: Holding a small pair preflop, you are a huge underdog against an opponent with a bigger pair (4-to-1 against you); about even-money or slight favorite versus a player holding two overcards and a 2-to-1 favorite over an opponent with one overcard to your pair.

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Let’s say you were dealt 4-4. There are 10 possible overpairs (A-A down to 5-5). At a full table of nine players, the probability one of your eight opponents has a bigger pair is approximately 30%. (Ref. Texas Hold’em Poker Textbook, Tom Green;

Still much higher is the probability any opponents staying to see the flop have one or two overcards to your pocket 4s. All in all, the more opponents staying to see the flop, the less likely your small pair will hold up. Logic and probability tell us that, unless you are playing against a single opponent – who does not have a higher pair in the hole – you are most likely to lose with your pocket 4s.

In a no-limit game, a huge preflop bet/raise might get you heads-up. In that case, probability tells us your lone remaining opponent most likely does not have a pair in the hole, and so you usually are a favorite to win that hand.

In a limit game, unless it is a very tight table, you are almost certain to get a few callers if you raise from a middle/late position. Possibly, you might get heads-up by raising from an early position – but then you can hardly win many chips.

Bottom line: For the most part, you are better off playing your pocket 4s, hoping to catch a set on the flop. But the probability of flopping a third 4 is only about 11%. You will hit it only 1 in 9 times.

The odds are much against you – about 8-to-1. Logic suggests you invest as little as possible – no raises against you – to see the flop with at least three opponents. (That’s the essence of the Hold’em Caveat concept) Otherwise, it’s just another marginal drawing hand that is best folded.

In fact, the Hold’em Algorithm would have you fold that hand without question in any early or middle position.

J-10 offsuit in the hole: Now that’s a hand the Hold’em Algorithm would encourage you to stay to see the flop from any position. Lots of possibilities. You are an underdog against any opponent with a pair in the hole; likewise, you are about a 1.8-to-1 underdog against an opponent with two overcards, and about 1.4-to-1 underdog to a single overcard. But your J-10 is too good a hand to just fold without seeing the flop.

Still, it’s just a drawing hand that has to improve to become a winner. Recognizing the flop of three cards will permit you to see over 70% of your final hand, it is reasonable to take a shot at the flop. Besides, it’s not likely an opponent has a higher pair in the hole.

This is where the Hold’em Caveat comes in: Call to see the flop if there are no raises and it’s a multi-way pot with three or more opponents staying to see the flop. But you can’t be sure of that if you are in an early or middle position.

In that case, hopefully you have selected a loose-passive table at which to play. That would be a tough decision at an aggressive table with lots of raising likely. Yes, probability and logic are great partners.

“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].

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