Poker Probability - Statistics

by Jordan Jones

September 21, 2009

Besides a hunch or premonition, what else should a poker player rely on when debating whether to hold 'em or fold 'em? Statistics should serve as an outline for winning play – rather than a strict set of rules. Successful poker players are able to merge both intuition and numbers to make consistent well rounded choices. Without getting too in depth, the following will attempt to show some basic poker probability.

• Starting hands - With a standard 52 card deck, there are 1,326 combinations of hands in poker. The odds of being dealt suited hole cards is 3.25 to 1, whereas a pocket pair is 16 to 1. Any specific pair has 220 to 1 odds of being dealt as hole cards (starting off with 2 2 is just as likely as A A). Being dealt any 2 cards with a minimum rank of 10 is 5.90 to 1. Although over cards have a tendency to intimidate us, let this stat be informative not deceptive. While at a table with 5 poker competitors, statistically if you aren’t holding at least a 10, someone else is. The number of possible card combinations being held by opponents is astounding. While at a table with two opponents, the possible amount of hole card combinations is 690,900 – add three more players and the number jumps to over 9 trillion!

• Community cards – With a standard 52 card deck there are 19,600 poker flop combinations. While holding two unsuited cards the odds of flopping a pair are fairly common, 2.1 to 1. The chances of flopping a flush are 118 to 1 while the chances of flopping a straight are 101 to 1. Suppose you have 4/5ths of a flush after the flop. The chances you will make it are 1.86 to 1. Since flush draws can be very tempting, be sure to examine the position you are in as well as your high card. The chances of 3 consecutive cards being flopped are 27.8 to 1, by the turn the odds go to 7.46 to 1, and by the river the figure is 2.99 to 1. Take this into consideration when chasing those straights, especially a low end or inside straight.

• Completed hands – Looking at the odds for completed hands is somewhat misleading, keep in mind many of these poker hands are folded before they gain any notoriety. Making a hand is not always the same as making the winning the hand. Here are the odds for completing a several hands which are commonly met through draws; a full house is 694 to 1, a flush is 509 to 1, a straight 255 to 1, three of a kind 47 to 1.

Now the objective here is not to memorize numbers but rather to grasp a concept. Many casual or simply uneducated poker players are plagued with something known as an optimism bias. To these individuals once they’ve made the draw, they’ve also made the hand – and they play like it. This brings up a concept called pot commitment. Don’t over commit yourself to a pot when it’s unnecessary (e.g. unfavorable odds without a tell in sight). When contemplating your next poker move, determine if the risk you’re taking is worth the amount you could possibly be making.

Bibliography:

Petriv, Mike Hold'em Odds Book Objective Observer Press. 1996

Yao, King Weighing the Odds in Hold 'em Poker Pi Yee Press. 2005

Caro, Mike MCU Library www.poker1.com 2002

Author Copyright © Jordan Jones
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