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Server Time: 9/6/2008 9:58:25 AM PACIFIC |
 10 Card hand - 4 pairs, 2 four-of-a-kinds - An Apology and Corrections, johnph77, 9. Jul 2003 03:52 | ||
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| I recently responded to a question regarding the probabilities, odds and occurances of getting 4 pairs and 2 four-of-a-kinds in a 10-card hand dealt from a 52-card deck in this forum. However, I used the wrong logic in arriving at those formulas and possibilities and, for this, I owe that gentleman an apology. I also apologize for any inconvenience derived in the use of those figures. Following are the (hopefully) corrected figures and formulas. Total possibilities of 10 cards from a 52-card deck: Formula: (52!-42!)/(10!) = 15820024220 possibilities 2 four-of-a-kinds: You will only be dealt a 4-card hand at random. The first card will be dealt from a 52-card deck. The three matching cards will then be withdrawn from the deck and set aside. The second card will be dealt from a 48-card deck. The three matching cards will then be withdrawn from the deck and set aside. The third and fourth cards will be dealt from a 44-card deck. The six cards set aside will be used to fill the remaining cards in the 10-card hand, giving you two 4-of-a-kinds and two random cards. Formula: (52*48*44*43)/(4!) = 196768 possibilities Odds: 1::80399.375 Probability: 0.0000124379 4 pairs: You will only be dealt a 6-card hand at random. The first card will be dealt from a 52-card deck. The three matching cards will then be withdrawn from the deck and set aside. The second card will be dealt from a 48-card deck. The three matching cards will then be withdrawn from the deck and set aside. The third card will be dealt from a 44-card deck. The three matching cards will then be withdrawn from the deck and set aside. The fourth card will be dealt from a 40-card deck. The three matching cards will then be withdrawn from the deck and set aside. The fifth and sixth cards will be dealt from a 36-card deck. The seventh card will be dealt from one of the three matching cards removed after the first card was dealt. The eighth card will be dealt from one of the three matching cards removed after the second card was dealt. The ninth card will be dealt from one of the three matching cards removed after the third card was dealt. The tenth card will be dealt from one of the three matching cards removed after the fourth card was dealt. Formula: (52*48*44*40*36*35*3*3*3*3)/(6!) = 622702080 possibilities Odds: 1::25.4054462 Probability: 0.03936164 | ||
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