poker probablity, math and odds

Poker Probability and Odds In Texas Holdem

In order to master poker, one must understand how poker probability works – and the odds of getting dealt or making specific poker hands in Texas Hold ’em Poker games, as well as being comfortable with the Hold’em poker hand rankings.

If you have ever wondered what are the odds of getting dealt a specific hand in Texas Hold ’em poker games, or hitting a royal flush or 4 of a kind, refer to the poker odds charts below which contain some interesting poker statistics & odds which poker players should be familiar with.

Percentage probability of making specific hands in 5-card Texas Hold ’em
Hand Combinations % Odds
Royal flush
T J Q K A
4 0.0001539077 649737:1
Straight flush
2 3 4 5 6
36 0.0013851695 72193.5:1
Four-of-a-kind
6 6 6 6 X x
624 0.0240096038 4163.99:1
Full house
9 9 6 3 3
3744 0.144057623 693.17:1
Flush
8 A 9 T K
5108 0.1965401545 507.8:1
Straight
4 5 6 7 8
10200 0.3924646782 253.8:1
Three-of-a-kind
2 2 2 9 7
54912 2.1128451381 46.3:1
Two pair
K K Q Q 3
123552 4.7539015606 20:1
Pair
K K 4 9 3
1098240 42.2569027611 1.366:1
High card
A 7 8 9 6
1202540 50.1177394035 0.995:1

Getting dealt a “big pair” like Aces in poker is not as common as one might think, in fact you can expect to get dealt K K or A A less than one time every 200 hands.

Percentage probability of being dealt specific hands in Texas Hold ’em
Starting hands % Probability Odds
A specific pocket pair (e.g , K K ) 0.453 219.75:1
Pocket pair Q x Q x or above 1.36 72.53:1
Pocket pair J x J x or above 1.81 54.25:1
Pocket pair T x T x or above 2.24 43.24:1
Any pocket pair ( 2 x 2 x +) 5.88 16:1
A specific non-paired hand (e.g A K x , K T ) 1.21 82.64:1
Two specific suited cards (e.g A Q , A K ) 0.302 330.12:1
Suited cards (e.g 9 2 ) 23.53 3.25:1
Suited connectors (e.g. 7 8 ) 3.92 24.5:1
Suited cards Ten or better 3.02 32.11:1
Connected cards (e.g 7 8 ) 15.7 5.37:1
Connected cards Ten or better (e.g T J ) 4.83 19.7:1
Any two Cards Q+ (e.g A Q , K Q ) 4.98 19.08:1
Any Two Cards J+ (e.g A Q , A J , K J ) 9.05 10.04:1
Any Two Broadway cards ( A T , A Q , K Q ) 14.3 5.99:1

Position & Action Also Affect Poker Opening Hand Ranges

Good starting hands in poker depend not only on the hand-strength of your two dealt hole-cards, but also on your seat at the table, and any action in front of you.

e.g If it folds to you on the button in a full-ring game, A 3 x is usually a standard raise (you are in position, holding an ace, with a wheel draw, and some fold-equity), whereas if you are in first position (“under the gun”) at a full-ring table (9 or 10 players), then it could be prudent to fold.