另一道概率题,应该是个经典问题 (转载) - 未名空间MITBBS历史存档

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另一道概率题,应该是个经典问题 (转载)

另一道概率题,应该是个经典问题 (转载)# CS - 计算机科学

s*n2005-10-27 07:10

1 楼

【以下文字转载自 EE 讨论区】
发信人: skymoon (海上生明月，天涯共此时), 信区: EE
标题: 另一道概率题,应该是个经典问题
发信站: BBS 未名空间站 (Thu Oct 27 20:36:00 2005), 站内
发信人: skymoon (海上生明月，天涯共此时), 信区: Mathematics
标题: 另一道概率题,应该是个经典问题
发信站: BBS 未名空间站 (Thu Oct 27 20:35:56 2005), 转信
A,B两人掷骰子.骰子的结果是[0,1]上的均匀分布.A先扔,有两次机会,但是结果之和不能
超过1,否则失败.A可以放弃第二次.B后扔,也是相同的规则.问如果A考虑到B的最佳策略,
自己的最佳策略应该是什么?赢的概率呢?

o*12005-10-27 07:10

2 楼

能
,
Ha, this is another one. I thought you just post one question.
Anyway, I didn't have time to do the calculation but idea is straightforward.
1. If eventually A get result X (0<= X <= 1) The chance A could win is X^2.
2. Now A must throw at least once, otherwize he lost anyway. The only possible
strategy is when he should throw the second time based on the result of the
first throw. Let's say the result for the first throw is x, then he has two
choices:
i. Don't throw the second, the c

【在 s*****n 的大作中提到】

: 【以下文字转载自 EE 讨论区】
: 发信人: skymoon (海上生明月，天涯共此时), 信区: EE
: 标题: 另一道概率题,应该是个经典问题
: 发信站: BBS 未名空间站 (Thu Oct 27 20:36:00 2005), 站内
: 发信人: skymoon (海上生明月，天涯共此时), 信区: Mathematics
: 标题: 另一道概率题,应该是个经典问题
: 发信站: BBS 未名空间站 (Thu Oct 27 20:35:56 2005), 转信
: A,B两人掷骰子.骰子的结果是[0,1]上的均匀分布.A先扔,有两次机会,但是结果之和不能
: 超过1,否则失败.A可以放弃第二次.B后扔,也是相同的规则.问如果A考虑到B的最佳策略,
: 自己的最佳策略应该是什么?赢的概率呢?

o*12005-10-27 07:10

3 楼

.
possible
Anyway, I forgot how to solve equation of 3 degree. So I will give an
estimation:
2.ii is actually \integral_{0}^{1-x}(x+y)^{2}dy = 1/3(1-x^3)
So the solution for x^2 = 1/3(1-x^3) would be the answer and it is
obviously between 1/2 - 1/(3^{1/2}).

【在 o*****1 的大作中提到】

:
: 能
: ,
: Ha, this is another one. I thought you just post one question.
: Anyway, I didn't have time to do the calculation but idea is straightforward.
: 1. If eventually A get result X (0<= X <= 1) The chance A could win is X^2.
: 2. Now A must throw at least once, otherwize he lost anyway. The only possible
: strategy is when he should throw the second time based on the result of the
: first throw. Let's say the result for the first throw is x, then he has two
: choices: