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Poker Odds & Probabilities

Odds & Probabilities


Hand No. of Ways Odds in 5 cards
Royal Flush 4 1 in 649,740
Straight Flush 36 1 in 72,193.33
4 of a Kind 624 1 in 4,165
Full House 3,744 1 in 694.16
Flush 5,108 1 in 508.80
Straight 10,200 1 in 254.80
3 of a Kind 54,912 1 in 47.32
Two Pairs 123,552 1 in 21.03
One Pair 1,098,240 1 in 2.36
No Pair 1,302,540 1 in 1.99

Chances of competing your hand when drawing one card

Four cards to a Flush 1 - 4.5
Straight open at both ends 1 - 5
Straight open at one end 1 - 11
Straight open on inside 1 - 11
Straight open at both ends 1 - 5
Straight Flush open at both ends 1 - 23
Straight Flush open at one end 1 - 46
Straight Flush open on inside 1 - 46

Low Hands Deals Per Pat Hand Hands Possible
Ace High + 5 502,880
King High + 8 335,580
Queen High + 12 213,180
Jack High + 20 127,500
Ten High + 37 70,360
Nine High + 36 71,860
Eight High + 70 35,840
Seven High + 170 15,360
Six High ++ 500 5,120
Five High ++ 2,500 1,024
+ = No straights or flushes. Ace is high.
++ = Including straights and flushes. Ace is low.

There are 2,598,960 various poker hands in a pack of fifty-two-card deck. If one player is dealt 100,000 hands in one lifetime, he will never hold more than 4% of all the possible hands.

Below is an estimation table of the number of pat (on the first five cards) hands that a single player can get in a whole lifetime.

Hands Approx. In One Lifetime
Royal Flush 0.15
Straight Flush 1.4
4 of a Kind 25
Full House 170
Flush 200
Straight 400
3 of a Kind 2,000
Two Pair 5,000
One Pair 40,00
No Pair 50,000

Investment Odds are the anticipated returns on money that is bet. These odds are approximated by the impending size of the pot and the probability of winning, which equals into the Investment Odds.

Investment Odds are important for making correct betting and playing decisions and when Investment Odds are greater than 1.0 the play is positive and should be made. The willpower to understand Investment Odds is not a mathematical dilemma. Working out the Investment Odds is the judgment resulting by meeting together and objectively weighing up the facts of the game, players and the circumstances.

  Five Card Stud Six Card Stud Seven Card Stud
Hand Combs Probs Combs Probs Combs Probs
Royal Flush 4 0.00000154 188 0.000009 4,324 0.00003232
Straight Flush 36 0.00001385 1656 0.000081 37,260 0.00027851
4 of a Kind 624 0.00024010 14664 0.000720 224,848 0.00168067
Full House 3,744 0.00144058 165984 0.008153 3,473,184 0.02596102
Flush 5,108 0.00196540 205792 0.010108 4,047,644 0.03025494
Straight 10,200 0.00392465 361620 0.017763 6,180,020 0.04619382
3 of a Kind 54,912 0.02112845 732160 0.035963 6,461,620 0.04829870
Two Pair 123,552 0.04753902 2532816 0.124411 31,433,400 0.23495536
One Pair 1,098,240 0.42256903 6612900 0.324822 58,627,800 0.43822546
No Pair 1,302,540 0.501177394     23,294,460 0.17411920

Edge Odds specify the relative functioning of a player in a game. The odds are calculated by the average winnings or losses of a player, currency X 100% = Edge Odds percentage. The more games analized the better the results are. Below is a performance evaluation of players based on a seven-man game.

Grading Edge Odds Without Bad Player Edge Odds With Good Player
Good Player Not Applicable 25 - 65
Sound Player 10 - 25 05 - 20
Average Player 00 - 15 (-5) - 10
Weak Player (-10) - 05 (-15) - 00
Poor Player (-20) - (-5) (-65) - (-10)

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