Problem 227

The Chase

"*The Chase*" is a game played with two dice and an even number of players.

The players sit around a table; the game begins with two opposite
players having one die each. On each turn, the two players with a die
roll it.

If a player rolls a 1, he passes the die to his neighbour on the left;
if he rolls a 6, he passes the die to his neighbour on the right;
otherwise, he keeps the die for the next turn.

The game ends when one player has both dice after they have been rolled and passed; that player has then lost.

In a game with 100 players, what is the expected number of turns the game lasts?

Give your answer rounded to ten significant digits.

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These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
**