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Poker Mathematics Overview

The relative values of Poker hands were determined by a rather complicated mathematical process of counting the actual number of Poker hands in the pack.

Possible Poker Hands In A 52-Card Deck

Straight Flush 40
Four of a Kind 624
Full House 3,744
Flush 5,108
Straight 10,200
Three of a Kind 54,912
Two Pairs 123,552
One Pair 1,098,240
No Pair, less than above 1,302,540
Total 2,598,960

Possible Hands Of Less Value Then One Pair

Ace Counts HighAce Counts LowNumber of Hands
Ace High King High 502,860
King High Queen High 335,580
Queen High Jack High 213,180
Jack High Ten High 127,500
Ten High Nine High 70,680
Nine High Eight High 34,680
Eight High Seven High 14,280
Seven High Six High 4,080
Total   1,302,540

Chances Of Being Dealt Poker Combinations In The Orginal Five Cards

Royal Flush 1 in 649,740
Straight Flush 1 in 64,974
Four of a Kind 1 in 4,165
Full House 1 in 649
Flush 1 in 506
Straight 1 in 255
Three of a Kind 1 in 47
Two Pair 1 in 21
One Pair 1 in 2.5
No Pair 1 in 2

Chances of Improving A Hand On The Draw

Cards Held In HandCards DrawnPossible ImprovementOdds Against Making
One Pair 3 Two Pair 5 to 1
Threes 8 to 1
Full House 97 to 1
Fours 359 to 1
Anything 2.5 to 1
One Pair And An Ace Kicker 2 Aces Up 7.5 to 1
Another Pair 17 to 1
Threes 12 to 1
Full House 119 to 1
Fours 1080 to 1
Anything 3 to 1
Two Pairs 1 Full House 11 to 1
Anything 11 to 1
Threes 2 Full House 15.5 to 1
Fours 22.5 to 1
Anything 8.5 to 1
Threes And One Odd Card 1 Full House 14.67 to 1
Fours 46 to 1
Anything 11 to 1
Four Straight (Open-End) 1 Straight 5 to 1
Four Straight (One End Or Interior) 1 Straight 11 to 1
Four Flush 1 Flush 4.25 to 1
Four Straight Flush (Both Ends Open) 1 Straight Flush 22.5 to 1
Anything 2 to 1
Four Straight Flush (Interior Or End) 1 Straight Flush 46 to 1
Anything 3 to 1
One Ace 4 Pair of Aces 3 to 1
Aces Up 14 to 1

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