"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.
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK