题目227：追逐游戏

欧拉计划

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.

题目：

"追逐游戏" 是一个偶数玩家参与，用两个骰子来玩的游戏。

玩家围绕桌子坐成一圈；游戏开始时面对面的两个玩家各拿一个骰子。每一回合，拥有骰子的两个玩家各掷一回。
如果一个玩家掷出１，他要把骰子传递给左边与他相邻的人，如果一个玩家掷出 ６，他要把骰子传递给右边与他相邻的人。其它情况，玩家保留骰子到下一回合。

玩家们掷过骰子并且传递之后，一个玩家拥有两个骰子时游戏结束；这个玩家就输了。

在一个有 100 名玩家的追逐游戏中，游戏持续回合数的期望值是多少?

给出你的答案并保留 10 位有效数字。