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Old 12-29-2005, 05:53 AM
BruceZ BruceZ is offline
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Join Date: Sep 2002
Posts: 1,636
Default Re: Yahtzee Texas Holdem

Cool, Hold'em Yahtzee.

You auto win the game if you get a 'Yahtzee Flush'. Five dice of the same number and suit. Can anyone work out the odds of getting one?

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number of flush Yahtzees = 4 colors * 6 numbers <font color="red">* C(15,2) other 2 dice * 6^2 numbers for other 2 dice</font>

total combinations = C(20,<font color="red">7</font>) dice * 6^<font color="red">7</font> number combinations

6*4*C(15,2)*6^2 / [C(20,7)*6^7] =~ 239,204-to-1.

This would include cases where the flush Yahtzee is on the board, which wouldn't be an automatic win. To exclude these cases, multiply the above probability by the fraction of flush Yahtzees which are not on the board [C(7,2)-1]/C(7,2) to get 251,164-to-1.
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