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Probability Tables

“The odds of getting a royal fizzbin are astronomical. Spock, what are the odds of getting a royal fizzbin?” Captain James T Kirk

Odds are a fairly serious business. We don’t want to lose our sense of humor but we also don’t want to lose our shirt.

It’s a good idea to go into every battle prepared. And believe me, Poker can be a battle. The following charts will help you in those situations where a gut feeling just isn’t going to be enough.

The Odds Of Being Dealt These Hands Using 5 Cards

Hand 3 Cards  5 Cards  7 Cards
Royal Flush 1 Chance In 649,739 Hands Dealt
Straight Flush 1 Chance In 72,192 Hands Dealt
Four of a Kind 1 Chance In 4,164 Hands Dealt
Full House 1 Chance In 693 Hands Dealt
Flush 1 Chance In 508 Hands Dealt
Straight 1 Chance In 254 Hands Dealt
Three of a Kind 1 Chance In 46 Hands Dealt
Two Pair 1 Chance In 20 Hands Dealt
One Pair 1 Chance In 4 Hands Dealt
No Pair 1 Chance In 2 Hands Dealt

The standard poker hands are ranked based on the probability of their being dealt pat in 5 cards from a full 52-card deck. The following table lists the hands in order of increasing frequency, and shows how many ways each hand can be dealt in 3, 5, and 7 cards.

 
Hand 3 Cards   5 Cards   7 Cards
Straight Flush 48 40 41,584
Four of a Kind 0 624 224,848
Full House 0 3,744 3,473,184
Flush 1,096 5,108 4,047,644
Straight 720 10,200 6,180,020
Three of a Kind 52 54,912 6,461,620
Two Pair 0 123,552 31,433,400
One Pair 3,744 1,098,240 58,627,800
High Card 16,440 1,302,540 23,294,460
TOTALS 22,100 2,598,960 133,784,560
 
The above charts at best can only serve as a rough guideline. Many factors are to be considered when establishing the “true odds”, including the number of players at a table and the game being played.
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