- #1
Fullhawking
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Useing a common deck of cards, you are dealt a hand of 7 cards. Whis is the probability that all the different suits are present in your hand?
FrankEE2 said:...
The total number of unique 7 card hands that can be made from only 39 cards (3 suites present) would be combine(39,7), or 15,380,937. Since any of the 4 suites could be absent you would multiply that number by 4 to get 61,523,748.
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The probability of getting all suits in a 7-card hand is approximately 0.00000000198 or 1 in 504,000.
The probability is calculated by taking the number of possible hands with all suits accounted for (4 suits x 13 ranks x 12 ranks x 11 ranks x 10 ranks x 9 ranks x 8 ranks = 504,000) and dividing it by the total number of possible 7-card hands (52 cards x 51 cards x 50 cards x 49 cards x 48 cards x 47 cards x 46 cards = 133,784,560).
No, the order of the cards does not affect the probability. As long as the hand contains all 4 suits, it is considered a successful outcome.
The probability of getting all suits in a 7-card hand in a game of poker is the same as the general probability stated earlier (approximately 0.00000000198 or 1 in 504,000). However, this probability may vary depending on the specific rules and variations of the game being played.
The probability of all suits in a 7-card hand is relatively low compared to other probabilities in poker, such as getting a royal flush (1 in 649,740) or a straight flush (1 in 72,192). However, it is still considered a rare occurrence in the game.