颜色消除
Color Elimination
题目详情
Jane 邀请你玩如下游戏。起始时有一副标准 52 张扑克牌，你们轮流各抽两张牌，Jane 先抽。如果两张都是黑牌，Jane 保留它们；如果两张都是红牌，你保留它们；如果一红一黑，则这两张牌被弃掉。整副牌处理完后，你和 Jane 把各自保留的牌合并、洗牌，然后继续重复这个过程，直到某一种颜色被消除为止。如果最后还有红牌剩余，你赢得 $100。问玩这个游戏的公平价格是多少？
Jane offers to play the following game with you. Starting with a standard deck of 52 cards, you take turns drawing two cards. Jane goes first. If the two cards are black, Jane keeps them. If the cards are red, you keep them. If there is one red and one black card, the cards are discarded. When you have gone through the deck, you and Jane combine your cards, shuffle them, and resume, playing until one of the colors is eliminated. If there are red cards remaining, you win $100. What is a fair price to pay to play this game?
解析
这是一个“陷阱题”。牌总是按对被处理，而一红一黑的牌对会被一起弃掉，因此被弃掉的红牌数和黑牌数始终相等。这样一来，只有当整副牌都被消除时，红色和黑色才会被“消除”，而那时不会有红牌剩下。
因此，你不可能赢得这 \boxed{0 \ \text{dollars}}$。
Original Explanation
This is a trick question. The cards are always discarded by pair (red, black) so the number of discarded red cards and discarded black cards is always equal. Thus the red and black colors will be eliminated only when the whole deck is eliminated, and there will be no red cards remaining. Therefore, there is no way to win the $100, so the fair price is