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标题: A Card Game [打印本页]

作者: sean9991 时间: 2005-2-1 01:35
标题: A Card Game

You have 52 playing cards (26 red, 26 black). You draw cards one by one. A red card pays you $1. A black one fines you $1. You can stop any time you want. Cards are not return to the deck after being drawn. What is the optimal strategy in terms of maximizing expected payoff?

作者: QL 时间: 2005-2-2 05:18
标题: 回复：A Card Game

In general, let's assume there are r red cards and b black cards, and the expected earning

using the optimal strategy is e(r,b), then we have:

e(r,b) = e(r-1,b)*r/(r+b) + e(r,b-1)*b/(r+b)

with boundary condition:

e(r,0) = r; e(0,b)=0

Then we can calculate e(r,b), and stop the game when e(r,b)<=0, where r and b are the

number of cards remaining in the deck.

作者: 独木桥 时间: 2005-2-2 08:56
标题: 回复：回复：A Card Game

Good try. But I think the equation shoud be

e(r,b) = max{[e(r-1,b)+1]*r/(r+b) + [e(r,b-1)-1]*b/(r+b),0}

作者: QL 时间: 2005-2-2 17:21
标题: 回复：回复：回复：A Card Game

I think you are right.

作者: sean9991 时间: 2005-2-4 00:19
标题: 回复：回复：回复：A Card Game

It's a good answer. But can you figure out what should be the optimal strategy?

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