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标题: 二人猜数 [打印本页]

作者: fzy 时间: 2005-9-10 01:36
标题: 二人猜数

难度：++

二人猜数。甲在1到9中选一个奇数，乙在2到8中选一个偶数。如果两数差1，乙胜，否则甲胜。

问两人的最佳策略各是什么？如果两人都采取最佳策略，获胜的概率各是什么？

作者: QL 时间: 2005-9-11 06:14
标题: 回复：二人猜数

This can be formulated as a max-min problem..., is there an simpler approach?

作者: husonghu 时间: 2005-9-11 06:39
标题: [@};-][@};-][>:D<]Nice to you again, QL. .....

Could you give some details about your max-min approach?

作者: 寒潭清 时间: 2005-9-11 09:20
标题: 欢迎QL回来,问好..[@};-][@};-][>:D<]

欢迎QL回来,问好..

作者: QL 时间: 2005-9-11 20:41
标题: 回复：欢迎QL回来,问好..[@};-][@};-][>:D<]

Thanks.

作者: QL 时间: 2005-9-11 20:49
标题: 回复：[@};-][@};-][>:D<]Nice to you again, QL. .....

Assume 甲's strategy is to randomly pick an odder number with probablity p1,p3,...,p9

and 乙's stragetgy is to randomly pick an even number with probability q2,q4,...q8

Then 乙 pick q's so as to maximize

p1*q2+p3*(q2+q4)+....p7*(q6+q8)+p9*q8

and 甲 minimize the resulting formular.

作者: fzy 时间: 2005-9-14 19:51
标题: Answer

The best strategy for A is to choose 1, 5, and 9 with probablity 1/3 each. It can be calculated that A can win at least 2/3 of the time no matter what B does.

The best strategy for B is to choose 2 and 8 with probability 1/3 each, and 4/6 with a combined probability 1/3. It can be calculated that B wins at least 1/3 of the time no matter what A does.

作者: husonghu 时间: 2005-9-15 03:14
标题: Good[@};-][@};-] But a small question for you ....

.....A can win at least 2/3 of the time .....
.....B wins at least 1/3 of the time .....

Are these two statements a little contradicting?

作者: fzy 时间: 2005-9-15 19:29
标题: 回复：Good[@};-][@};-] But a small question for you .

These two statements are not contradicting to each other, since we have >= and <=. Together they guarantee that both strategies are optimal: If applied together, A wins 2/3 of the time, B 1/3, which answers part 2.

原贴：

文章来源: husonghu® 于 2005-9-14 19:14:31
标题：Good But a small question for you ....

.....A can win at least 2/3 of the time .....
.....B wins at least 1/3 of the time .....

Are these two statements a little contradicting?

作者: 野菜花 时间: 2005-9-22 21:07
标题: Thanks a lot for your expensive flower!! [@};-][@}

Thanks a lot for your expensive flower!!

[@}

作者: fzy 时间: 2005-9-22 22:07
标题: 我的花和别人一样钱呀。（莫非别人有discount？[:((]）

我的花和别人一样钱呀。（莫非别人有discount？

）

作者: 野菜花 时间: 2005-9-22 23:11
标题: You sold your posts for less money than they

really worth.

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