Texas Hold'em Strategy: learn odds and probabilities

Sunday, 30 January 2011

Every single decision you make at the poker table is in some way related to odds and probabilities. Whether you are deciding to bet, call, fold, raise, or even bluff, odds and probabilities are an integral part of the decision-making process. Expert players understand the simple math behind every decision they make – now you can too.

Starting Hands Odds & Probabilities

Odds/probability of being dealt Pocket Aces	220 to 1 (or 0.45% chance)
Odds/probability of being dealt either Pocket Aces or Pocket Kings	110 to 1 (or 0.90% chance)
Odds/probability of being dealt any Pocket Pair	16 to 1 (or 5.88% chance)
Odds/probability of being dealt suited Ace-King	331 to 1 (or 0.30% chance)
Odds/probability of being dealt offsuit Ace-King	110 to 1 (or 0.90% chance)
Odds/probability of being dealt Ace-King (either suited or offsuit)	82 to 1 (or 1.20% chance)
Odds/probability of being dealt any two suited cards	3.3 to 1 (or 23.3% chance)
Odds/probability of being dealt Pocket Aces, Pocket Kings or Ace-King	46 to 1 (or 2.13% chance)

Odds/Probabilities when holding Pocket Pairs

Odds/probability of flopping a set or better	8.5 to 1 (or 10.5% chance)
Odds/probability of flopping a set	7.5 to 1 (or 11.8% chance)
Odds/probability of flopping a full house	136 to 1 (or 0.73% chance)
Odds/probability of flopping quads	407 to 1 (or 0.25% chance)
Odds/probability of making a set or better by the river	4.2 to 1 (or 19.2% chance)

Odds/Probabilities when holding two Suited Cards

Odds/probability of flopping a flush	118 to 1 (or 0.84% chance)
Odds/probability of flopping a flush draw	8.1 to 1 (or 11.0% chance)
Odds/probability of flopping a backdoor flush draw	1.4 to 1 (or 41.7% chance)
Odds/probability of making a flush by the river	15 to 1 (or 6.25% chance)

Odds/Probabilities when holding two Unsuited Cards

Odds/probability of flopping a flush draw	88 to 1 (or 1.12% chance)
Odds/probability of flopping a backdoor flush draw	6.8 to 1 (or 12.8% chance)
Odds/probability of making a flush by the river	53 to 1 (or 1.85% chance)

Odds/Probabilities when holding two Non-pair Cards

Odds/probability of flopping at least a pair (using one of your pocket cards) from two non-pair cards	2.1 to 1 (or 32.3% chance)
Odds/probability of flopping a pair (using one of your pocket cards) from two non-pair cards	2.5 to 1 (or 28.6% chance)
Odds/probability of flopping two pair (using both of your pocket cards) from two non-pair cards	49 to 1 (or 2.00% chance)
Odds/probability of flopping any two pair from two non-pair cards	24 to 1 (or 4.00% chance)
Odds/probability of flopping a set (using one of your pocket cards) from two non-pair cards	73 to 1 (or 1.35% chance)
Odds/probability of flopping a full house (using both of your pocket cards) from two non-pair cards	1087 to 1 (or 0.09% chance)
Odds of flopping quads (using one of your pocket cards) from two non-pair cards	9799 to 1 (or 0.01% chance)

Odds/Probabilities of the Flop

Odds/probability of the board showing three of a kind on the flop	424 to 1 (or 0.24% chance)
Odds/probability of the board showing a pair on the flop	5 to 1 (or 16.7% chance)
Odds/probability of the board having three suited cards on the flop	18 to 1 (or 5.26% chance)
Odds/probability of the board having two suited cards on the flop	0.8 to 1 (or 55.6% chance)
Odds/probability of having a rainbow board on the flop	1.5 to 1 (or 40.0% chance)
Odds/probability of the board showing three cards in sequence on the flop	28 to 1 (or 3.45% chance)
Odds/probability of the board showing two cards in sequence on the flop	1.5 to 1 (or 40.0% chance)
Odds/probability of the board showing no card in sequence on the flop	0.8 to 1 (or 55.6% chance)
Odds/probability of making a full house or better from a set on the turn card	5.7 to 1 (or 14.9% chance)
Odds/probability of making a full house from two pair on the turn card	11 to 1 (or 8.33% chance)
Odds/probability of making a flush from a four-flush on the turn card	4.2 to 1 (or 19.2% chance)
Odds/probability of making a straight from an open-ended straight draw on the turn card	4.9 to 1 (or 16.9% chance)
Odds/probability of making a straight from a gutshot straight draw on the turn card	11 to 1 (or 8.33% chance)
Odds/probability of making a pair from two overcards on the turn card	6.8 to 1 (or 12.8% chance)

Odds & probabilities at the Turn

Odds/probability of making a full house or better from a set on the river card	3.6 to 1 (or 21.7% chance)
Odds/probability of making a full house from two pair on the river card	11 to 1 (or 8.33% chance)
Odds/probability of making a flush from a four-flush on the river card	4.1 to 1 (or 19.6% chance)
Odds/probability of hitting an open-ended straight draw on the river card	4.8 to 1 (or 17.2% chance)
Odds/probability of hitting a gutshot straight draw on the river card	11 to 1 (or 8.33% chance)
Odds/probability of hitting a pair from two overcards on the river card	6.7 to 1 (or 13.0% chance)

Odds & Probabilities from Flop to River

Odds/probability of making a full house or better by the river from a set on the flop	2 to 1 (or 33.3% chance)
Odds/probability of making a full house or better by the river from two pair on the flop	5.1 to 1 (or 16.4% chance)
Odds/probability of making a flush by the river from a four-flush on the flop	1.9 to 1 (or 34.5% chance)
Odds/probability of making a backdoor flush by the river	23 to 1 (or 4.17% chance)
Odds/probability of making a straight by the river from an open-ended straight draw on the flop	2.2 to 1 (or 31.3% chance)
Odd/probability of making a straight by the river from a gutshot straight draw on the flop	5.1 to 1 (or 16.4% chance)
Odds/probability of making a pair or better by the river from two overcards on the flop	3.2 to 1 (or 23.8% chance)

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