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OT - Yahtzee Problem

Posted By: Bob Koca
Date: Saturday, 17 December 2011, at 1:45 a.m.

In Response To: OT - Yahtzee Problem (David Rennie)

The chance of a small straight on one roll of 5 dice is not too hard:

Look at the 6^5 = 7776 sequeces of possible dice. How many give a small straight?

12345, 12346, 23456, all give the small straight. Multiplying by 5! = 120 possible orderings we have 360 ways so far.

1234 and a 5th value from {1,2,3,4}

or 2345 and a 5th value from {2,3,4,5}

or 3456 and a 5th value from {3,4,5,6} also all give a small straight. That is 12 ways and each can be ordered 60 ways so 720 more.

Total of 1080 ways. 1080/776 is approximately 13.9%

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