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Problem 227

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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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追赶游戏

“追赶游戏”是一个需要偶数名玩家和两个骰子进行的游戏。

所有玩家在桌子边坐成一圈；游戏开始时，选择两名相对而坐的玩家，每人拿一颗骰子。在每一轮，拥有骰子的两名玩家掷出骰子。
如果玩家掷出点数1，他将骰子交给他左侧的那名玩家；如果他掷出点数6，他将骰子交给他右侧的那名玩家；除此之外的情况，他保留这颗骰子。
当每一轮结束时，如果有一名玩家拿着两颗骰子，游戏结束，这名玩家输掉游戏。

如果有100名玩家参与游戏，游戏进行的期望轮数是多少？

你的答案应当保留10位有效数字。

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