红黑配对发牌游戏的价值
Card Game
题目详情
赌场用一副 52 张牌提供游戏：你每次翻两张牌：
- 两张都黑：归庄家；
- 两张都红：归你；
- 一红一黑：两张都丢弃。
最后如果你那堆牌比庄家那堆多，你赢 100 美元，否则（含平局）赢 0。你可以谈判入场费。问：这游戏值多少钱？
A casino offers a card game using a standard deck of 52 cards. You turn over pairs of cards:
- If both cards are black, they go to the dealer’s pile;
- If both cards are red, they go to your pile;
- If one is black and one is red, both cards are discarded.
At the end, if your pile has more cards than the dealer’s pile, you win $100; otherwise (including a tie), you get nothing. You can negotiate how much you pay to play. How much is this game worth?
解析
这游戏价值是 。
无论过程如何，你那堆的红牌数量总是等于庄家那堆的黑牌数量；每次丢弃也是“一红一黑”成对丢弃，不改变平衡。
因此你永远不可能让自己那堆严格多于庄家那堆，胜率为 0，合理入场费为 0。
Original Explanation
It is worth $0. No matter how the cards come out, the number of red cards in your pile will always equal the number of black cards in the dealer’s pile. Each time you discard, it is one black plus one red, which never affects the balance of leftover black and red cards. So you cannot end with strictly more cards than the dealer.