Poker Odds

There are many sites that provide information about poker odds, but none provides a comprehensive single source for basic odds knowledge in Texas Hold 'Em. So here is an attempt at compiling a reference list for what I feel are the most essential probabilities. I recommend memorizing all of these because knowing them off the top of your head gives you an edge in any game.


Pot Odds

Calculating pot odds is a necessary step in determining whether you are justified in playing a hand that may be an underdog at the moment but stands a chance of improving to the best hand. Pot odds are defined as "the ratio of the current size of the pot to the bet that you must call." Put simply, you want the probability of making your hand to be higher than the percentage of money you must invest in the pot.

The best way to quickly compute pot odds is to memorize outs expressed as a ratio. I'm constantly surprised at the number of players who refuse to remember this set of numbers that can be worth so much money at the tables.

Outs | Break-Even Pot Odds with one card to come
1 | 45:1
2 | 22:1
3 | 14.3:1
4 | 10.5:1
5 | 8.2:1
6 | 6.7:1
7 | 5.6:1
8 | 4.75:1
9 | 4.1:1

Another common way to estimate your probability of making a hand is by what Phil Gordon calls "The Rule of Four" and "The Rule of Two."

I have found a quick and easy way of figuring out how often I will draw to a winning hand after the flop.
First I count my "outs," or the cards that will give me a winning hand. For example, let's say I have Tc 9d and I put my opponent on A-K ... The flop comes Ac Td 7s. My opponent is in front, of course, having flopped a pair of aces, but there are five cards -- the two remaining tens and the three nines -- that will put me in front. In other words, I have five outs.
I can calculate the approximate odds of catching one of my cards on the turn or the river by multiplying the number of outs I have by four. In this case:
5 X 4 = 20 %
According to this "Rule of Four," I have about a 20 % chance of catching a winning card on the turn or the river. The actual odds turn out to be 21.2 %, a tiny difference that is irrelevant for most purposes.
With only the river card to come, the "Rule of Four" becomes the "Rule of Two." (Meaning you multiply your outs by two instead of four)

Preflop Odds

Higher pair vs. lower pair: 4.5:1
Pair vs. two higher cards: 55 percent to 45 percent
Pair vs. two lower cards: 5:1
Pair vs. a higher and lower card: 5:2, or about 70 percent to 30 percent
Domination (AK vs. AQ): 5:2, or about 70 percent to 30 percent
Two higher cards vs. two lower cards (AQ vs. 86): 5:3, or about 60 percent to 40 percent
One higher card vs. one lower card (A5 vs. KT): About 55 percent to 45 percent

Odds of being dealt a specific hand

AA: 220:1, or 0.45 percent
Any pair: 16:1, or 5.88 percent
AK suited or offsuit: 82:1, or 1.2 percent
Suited connectors: 46.4:1, or 2.11 percent


Odds of flopping ...

A set from a pocket pair: 7.5:1, or about 12 percent
A flush draw with two suited cards: 8.1:1, or 11 percent
A pair from any two non-paired cards: 2.1:1, or about 33 percent
Two pair from any two non-paired cards, using both of your hole cards: 49:1, or 2 percent

Sources:
"Phil Gordon's Little Green Book," by Phil Gordon
"Harrington on Hold 'em: Expert Strategy for No-Limit Tournaments, Volume 1: Strategic Play," by Dan Harrington
"Small Stakes Hold 'em: WinningBig with Expert Play," by Ed Miller, David Sklansky and Mason Malmuth
Bodog poker, as published by FilmZone.com
Mike Caro University
Two Dimes