Puzzleup 2017 (14) Dice Game - 拼圖

題目網址: http://www.puzzleup.com/2017/
http://www.puzzleup.com/2017/puzzle/?14
答題時限: 11月９日７ＰＭ－比賽結束（約12月27日）
加分時限: 11月９日７ＰＭ－11月14日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。　
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆DICE GAME

You will play a game of chance with your friend by throwing a dice repeatedly.

* Whenever 4 even numbers appear in a row, you will win.
* Whenever 4 odd numbers appear in a row, your friend will win.
* Whenever 5 even numbers appear (may not be in a row), your friend will win.
* If first and third condition occur at the same time, first condititon has
the priority.

What is your probability of winning the game?

(Enter your answer as a reduced fraction. Example: 123/4567)

你和你的朋友玩一個遊戲, 重覆投擲一個骰子。

* 如果連續出現四個偶數, 你贏。
* 如果連續出現四個奇數, 你的朋友贏。
* 如果出現過五個偶數 (不一定連續), 你的朋友贏。
* 若第一和第三個條件同時滿足, 第一個條件優先。

試問你贏的機率為何?

(以最簡分數回答，如 123/4567。)

--
'You've sort of made up for it tonight,' said Harry. 'Getting the
sword. Finishing the Horcrux. Saving my life.'
'That makes me sound a lot cooler then I was,' Ron mumbled.
'Stuff like that always sounds cooler then it really was,' said
Harry. 'I've been trying to tell you that for years.'
-- Harry Potter and the Deathly Hollows, P.308

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