MATHEMATICS OF POKER
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
|
Royal Flush |
4 |
|
Straight Flush |
36 |
|
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 High |
Ace Counts Low |
Number 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 Original 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 Hand |
Cards Drawn |
Possible Improvement |
Odds Against Making |
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|
One Pair |
3 |
|
|
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|
One Pair And An Ace Kicker |
2 |
|
|
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|
Two Pairs |
1 |
|
|
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|
Threes |
2 |
|
|
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|
Threes And One Odd Card |
1 |
|
|
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|
Four Straight (Open-End) |
1 |
Straight |
5 to 1 |
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|
Four Straight (One End Or Interior) |
1 |
Straight |
11 to 1 |
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|
Four Flush |
1 |
Flush |
4.25 to 1 |
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|
Four Straight Flush (Both Ends Open) |
1 |
|
|
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|
Four Straight Flush (Interior Or End) |
1 |
|
|
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|
One Ace |
4 |
|
|
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