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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 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 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 Hand | Cards Drawn | Possible Improvement | Odds 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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