In poker playing pocket Aces – not a sure thing
July 09, 2013 3:00 AM
by George Epstein
Probability is simply the likelihood – or chance – a certain thing will happen. On a scale of 0 to 1, a value of 0 means it will never happen. Not even once!
And 1 means it will happen every time without fail – 100%, for sure (like the sun rising every morning). With a probability of ½, the event will occur half the time in the long run – like tossing a coin, heads or tails. Probability also can be expressed as a percentage or a decimal.
In my recent poker class for the Claude Pepper Seniors Poker Group, one session was devoted to “Poker Math Made Easy.” By way of introduction, I explained that combinations-and-permutations can be used to calculate poker odds. That’s OK if you want to teach mathematics or display your math wizardry. But it is much too complicated for almost every poker player – and unnecessary if your primary goal is to win more often and more money.
Consider preflop betting: Let’s start with the best possible hole cards: Pocket Aces! On average, in the long run, you can expect to be dealt A-A only one out of 221 hands – a probability of less than 0.5%. Rare! Surely, you want to make the most of it.
Probability suggests your A-A is a huge favorite over any other hand dealt. (That’s no surprise.) You are about an 80% or higher favorite over each opponent. As Tom Green points out in my favorite poker-math book (Ref. Texas Hold’em Poker Textbook; www.PokerTextbook.info), if there is more than one opponent seeing the flop, we use the AND Rule.
If you are against two opponents, each with a smaller pocket pair, then the probability of outlasting each of them is about 80%; but you have to beat both of them at the same time. Then, according to Green’s AND Rule, the probability of beating both is 80% x 80%, which equals 64%.
Now add a third opponent holding a somewhat weaker hand than these, over whom you are favored by 85%. Then the probability of winning the pot against all three is 80% x 80% x 85% = 54%. You are still a favorite to win, but by just a slim margin.
Indeed, if more than four opponents see the flop, don’t be surprised to lose the pot. Then you might turn to your sympathetic neighbor and moan, “I always lose with pocket Aces.”
The next day, you could complain to your buddies about how “a stupid guy stayed in with a pair of 4s, chased all the way to the river, and then caught a third 4 to make a small set, beating my pocket Aces. Cost me lots of chips. It shoulda been my hand.”
Sure, the 4-4 was a big underdog with odds against him of about 4-to-1 before the flop. But if you let too many underdogs stay to see the flop, you are bound to lose more often.
Some logic: As noted above, your pocket Aces is a favorite as long as you see the flop with three or fewer opponents. The fewer opponents staying in with you, the more likely your A-A will take the pot. But your goal is to win chips – as many as possible, not just to count the number of hands you won during the session.
In a limit game where the bet size is restricted, the optimum is to play against three or four opponents. Two or fewer opponents gives you a better chance of winning, but the pots are bound to be much smaller. More than four opponents can build bigger pots, but you are more likely to lose.
For optimum results, I suggest to my students to use their betting/raising to achieve a goal of three or four – but never more than four opponents staying to see the flop.
On the other hand, in a no-limit game you might do very well against a single opponent if he has a huge stack of chips and is a loose/aggressive player.
“The Engineer,” a noted author and teacher in Greater Los Angeles, is a member of the Seniors Poker Hall of Fame. Contact George at GeorgeEpstein@GamingToday.com.