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Roll the Die Higher (Posted on 2005-04-07) Difficulty: 3 of 5
Two players alternate throwing a six-sided die. The first player who fails to roll a higher number than the preceding roll loses. What is the probability that the first player wins?

What if the die is n-sided?

See The Solution Submitted by Charlie    
Rating: 3.8571 (7 votes)

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re(2): Solution w/o expl. and a question | Comment 5 of 13 |
(In reply to re: Solution w/o expl. and a question by Richard)

This is wrong: the sum is NOT to infinity, but to n=6. Also, you forgot the (1-5/6) that divides [1-(5/6)]^n. The answer is (6^6-5^6)/6^6.
  Posted by Federico Kereki on 2005-04-07 20:54:37

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