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 Flipping Even-Odd (Posted on 2011-01-28)
A game is played starting with 6 fair coins laid out with heads face up.

Each round consists of flipping all of the coins showing heads.

If an even number of coins is flipped and an even number of heads comes up the player loses.

If an odd number of coins is flipped and an odd number of heads comes up the player loses.

Rounds continue until the player either loses or reaches zero heads.

The player wins by getting to zero heads without losing.

What is the probability of winning this game?

Examples:
6→3→1 would be a loss.
6→3→0 would be a win.
6→0 would be a loss (even→even rule is applied first.)

 No Solution Yet Submitted by Jer No Rating

 Subject Author Date solution detailed by computer Charlie 2011-01-29 15:45:03 computer solution Charlie 2011-01-28 18:15:08 A start (spoiler) Steve Herman 2011-01-28 14:47:28

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