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Play or Pass (Posted on 2013-05-28) Difficulty: 3 of 5
A game consists of two players taking turns, each time removing a limited number (1 to k) candies from either of two plates, initially containing m and n candies (m>=n).

The player who removes the last candy (or candies) wins.

The player to make the 1st move is defined by a toss of a fair coin and has the unique option, after counting the candies, either to start playing or to waive his turn and let his rival to begin.

Both players have correctly analyzed the game and play according to the best available strategy.

What is the probability that the player designated to go first decides to waive his turn?

Rem: You may assume that both m and n are 2-digit numbers and k is a one digit number over 4.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: Avoiding the problem | Comment 2 of 4 |
(In reply to Avoiding the problem by Steve Herman)

Steve, find the strategy and then probability for given values 


Then  generalize for a randomly chosen values, using your
own assumption.

  Posted by Ady TZIDON on 2013-05-28 17:49:45
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