Puzzleup 2018 (7) DICE GAME - 拼圖

題目網址: http://www.puzzleup.com/2018/
http://www.puzzleup.com/2018/puzzle/?7
答題時限: ９月13日７ＰＭ－比賽結束（約12月12日）
加分時限: ９月13日７ＰＭ－９月19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 with a fair 6-sided die. You will throw the die and
as long as the result of the throw is greater than or equal to the previous
throw, you will continue throwing. If the throw is lower than the previous
one, you will stop and get as many points as the sum of all throws,
including the last one. For example, if you get 2, 5, 5, and 3 as a result
of 4 throws, the game will end with 15 points.

What is the expected value of the points you will get at the end of the game?

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

你要玩一個使用公平六面骰的遊戲。一直丟骰子，只要這次丟出來的點數大於或等於上
次丟出來的點數，就可以一直丟下去。如果點數比之前的小，那麼遊戲結束，你的分數
為所有擲出的點數和，包括最後一擲。舉例來說，你丟了2,5,5,3，總共丟了四次，遊
戲結束得分為15。

試問遊戲結束時，你得分的期望值為何？

以最簡分數回答，如 123/4567。

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