Poker Math & Probabilities (Texas Hold'em)

Poker Math & Probabilities (Texas Hold'em)

The following tables provide various probabilities and odds for many of the common events in a game of Texas hold 'em.

Starting Hand Probabilities

AKs (or any specific suited cards) AA (or any specific pair) AA or KK AKs, KQs, QJs, or JTs (suited cards) AK (or any specific non-pair incl. suited) AA, KK, or QQ AA, KK, QQ or JJ Suited cards, jack or better AA, KK, QQ, JJ, or TT Suited cards, 10 or better Suited connectors Connected cards, 10 or better Any pair One or more Aces Two suited cards

Odds

330-to-1 220-to-1 110-to-1 82-to-1 82-to-1 73-to-1 55-to-1 55-to-1 43-to-1 33-to-1 26-to-1 20-to-1 16-to-1

6-to-1 3-to-1

%

0.30% 0.45% 0.90% 1.21% 1.21% 1.36% 1.81% 1.81% 2.26% 3.02% 3.92% 4.83% 6.25% 16.60% 24.00%

Common Pre-Flop Match-Ups

Pair vs. Pair Pair vs. Overcards Pair vs. Suited overcards Pair vs. Undercards Pair vs. Suited undercards Pair vs. Overcard and an undercard Pair vs. Overcard and one of that pair Pair vs. Undercard and one of that pair Two high cards vs. Two undercards High card, low card vs. Two middle cards High card, middle card vs. Second highest, low card High card, same card vs. Same card, low card Same high card, high kicker vs. Same card, low kicker

Example

JJ v 77 55 v AQ 55 v AQs JJ v 75 JJ v 75s 99 v K8 88 v 89 QQ v Q9 KT v 74 J3 v 97 K8 v T6 K9 v 97 AK v A9

Win %

80% v 20% 55% v 45% 50% v 50% 85% v 15% 80% v 20% 70% v 30% 65% v 35% 90% v 10% 65% v 35% 55% v 45% 60% v 40% 70% v 30% 75% v 25%

Note: The math presented above is rounded and doesn't account for all possibilities. The number of clean suits and/or the max number of straight outs also need to be considered.

The Probability that....

Non-pairs will pair at least one card Non-pairs will pair both hold cards A pair will flop a set A pair will flop four of a kind Two suited cards will flop a flush Two suited cards flop a four flush (flush draw) Two suited cards will make a flush by the river

Odds

2-to-1 50-to-1 8-to-1 400-to-1 118-to-1 9-to-1 15-to-1

%

32.00% 2.02% 12.00% 0.25% 0.85% 10.90% 6.50%

You Hold

A Pair Two Pair Inside Straight Overcards Open-ended Straight Four Flush Straight & Flush Draw

Hope to Make

Three of a Kind Full House Straight Pair Straight Flush Straight / Flush or Better

Outs

2 4 4 6 8 9 15

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