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A host and 9 guests are seated at a circular table. Your host is feeling generous: she places a gold coin in front of her, and announces that one of you will be taking it home.

Whoever has the coin — beginning with the host — will flip it: if heads, they pass left; tails, they pass right. This continues until everyone has held the coin at least once — at that instant, the game ends, and the person holding the coin takes it home. In other words, the winner is last person to hold the coin for the first time.

In the example below, the coin goes from the host to A to B, then circles between A and B for a while, then goes from B to C. In that hypothetical scenario, it would be impossible for the host, A, B or C to win (but you would still have a chance).

You're sitting immediately to the host's right and the game is about to begin. What's your probability of winning?

Mohit Aneja
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    What have you tried? The result is slightly unexpected, and is easy to explore with a host and $3$ guests – Henry Aug 07 '18 at 07:48
  • I was stuck at this problem for long. I couldn't figure out a way to find it. But one answer in the link attached above suggests that it is equally likely for every player to win (and that too without any computation!). Thanks for helping @Henry – Mohit Aneja Aug 08 '18 at 05:46

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