fair cards

二人扑克游戏

一副牌扣在桌上，庄家按顺序将牌一张张翻开。你可以在任何时候叫停（除非牌已翻完）
。叫停之后再翻开下一张牌，如果花色为红，则你赢。

你的最佳策略是什么？


Solution 1.

when you have seen n cards, suppose you have probability f(n) (this depends
on the n cards that already delt) to win if you stop right now. You can
check that f(n) is a martingale. So your startegy will not change your
probability to win, which is 1/2.

Solution 2 (heard from a friend).
The problem is equivalent to (in terms of probability): once you call stop,
you open the LAST card, instead of the NEXT card, to determine if you win or
lose.

So the problem is changed to always opening the last card, which is
independent of where you call stop. So it is still 1/2.