ABC of Poker: Pocket Pair Odds

With 52 cards in the deck, 13 ranks and 4 suits, calculating probabilities in Texas Hold'em is unfortunately a little more complicated than the 50/50 chance of landing heads in a single coin flip :) What is more, even if you do get dealt a promising starting hand like a pocket pair, chances are someone at the table will be dealt a higher pair. So what are the odds of this happening?

Pre Flop Drawing Odds

To calculate the probability of being dealt a specific pair, AA for example, you multiply the probabiliies of getting each card:  4/52 x 3/51 = 12/2652 = 1/221 = 0.45%:

1st card: 4 Aces out of 52 cards in the deck, or 4/52 multiplied by

2nd card; 3 Aces out of 51 cards, 3/51

The probability of landing one of the top five pairs: AA, KK, QQ, JJ, TT is 5/221 = 2.26%

Respectively, the probability of getting dealt ANY pocket pair of the 13 possible ones is 13/221, or 5.9%.

Say you do hit those 5.9% and land a pocket pair. How likely is someone else at the table to hold a higher pair?

The Gordon Pair Principle

This simple equation was developed by poker pro, commentator and author @Phil Gordon:

C = (N x R) / 2

Where C = percent chance someone left to act has a bigger pocket pair

N = number of players left to act

R = number of higher ranks than your pocket pair 

Example from the WSOP hand in the above photo where UTG raised with J♥J♣,

N=6 players left to act  R=3 (there are three ranks higher than jacks) 6x3 / 2 = 9%

The formula was developed for situations when you are the first to act and results are not reliable if there have already been one or more raises by the time the action gets to you.

Gordon Pair Principle, more examples

If action had folded to Greg Himmelbrand in HJ with 6♥6♠ in the above hand (which you can watch here) the equation would be: N=4 x R=8 / 2 = 32/2 = 16%. Again, if he were the first to act, the button, with 4♥4♣, would face 10% chance of either the SB or BB holding a higher pair (N=2 R=10 2x10 / 2 = 10)

Probability of facing one or multiple higher pairs pre-flop

Source: http://en.wikipedia.org/wiki/Poker_probability_%28Texas_hold_%27em%29

You will have noted the vulnerability of small pocket pairs, especially in full-ring games, so beware! Position is key and discipline even more so. If you pay to see the flop with a small pair, be prepared to fold unless you get that set!  Queens and Jacks give you great odds pre-flop but should be played with caution thereafter (see overcard probability table below). As for the 'holy grail of poker' - KK and AA - these are the best pre-flop shove hands you can get and raise and re-raise is the way to go in any position!

Pocket Pairs After the Flop

Next on #RKHabc we will consider how to calculate drawing odds based on number of outs after the flop. Meanwhile, here is some information about what you can expect with a PP:

Probability of improving a pocket pair

Every pocket pair's dream is to become a set and chances on the flop are approximately one out of 8 times.

Source: http://www.suntzupoker.com/poker-odds.aspx

Once in about 1,000 hands you might get into a 'set-over-set' situation, with two players starting with pocket pairs and completing three-of-a-kind on the flop or by the river as.in this hand from the RankingHero Last Longer in Unibet Open:

More on pocket pair odds:

Pocket Pair Odds Example - Texas Holdem PokerPocket Pair Odds Examplewww.texasholdem-poker.com

How likely is your pocket pair to hold up

In the event that nobody else was served a pocket pair, you will be concerned about the probablity of overcards coming up on the board and giving an opponent a better hand:

Source: About Online Poker, Nicolae Sfetcu

Coming up: Outs and Odds & the 'Rule of 4 and 2'