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  #1  
Old 12-28-2005, 10:46 PM
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Default Yahtzee Texas Holdem

There are 9 types of winning hand :

Winning Hands Reference Chart

A Straight beats a Full House and a Flush beats Four Of A Kind. [img]/images/graemlins/wink.gif[/img]

It's holdem with dice. There's 20 dice like in the picture which are 'shuffled' in the bag. You get 2 hole dice then there's a flop, turn & river.

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?


Yahtzee Texas Holdem Review

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  #2  
Old 12-29-2005, 05:53 AM
BruceZ BruceZ is offline
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Default Re: Yahtzee Texas Holdem

Cool, Hold'em Yahtzee.

[ QUOTE ]
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?

[/ QUOTE ]

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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Old 12-29-2005, 10:13 AM
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Default Re: Yahtzee Texas Holdem

that should be C(20,7) not C(20,5) since you get 7 dice to make a hand with shouldn't it?
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Old 12-29-2005, 10:42 AM
BruceZ BruceZ is offline
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Default Re: Yahtzee Texas Holdem

[ QUOTE ]
that should be C(20,7) not C(20,5) since you get 7 dice to make a hand with shouldn't it?

[/ QUOTE ]

You're correct. I was only considering 5 dice hands, as in the original Yahtzee. Since there are 7 dice, there are also a lot more Yahtzee flushes since the other 2 dice can be anything. I made the changes to my original post in red.
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