A Practical Guide To Quantitative Finance Interviews 收录了一些量化面试中的经典题目. 本文介绍的是来自第二章的「Card Game」.

Card Game #

Problem #

A casino offers a card game using a norrnal deck of 52 cards. The rule is that you turn over two cards each time. For each pair, if both are black, they go to the dealer’s pile; if both are red, they go to your pile; if one black and one red, they are discarded. The process is repeated until you two go through all 52 cards. If you have more cards in your pile, you win $100; otherwise (including ties) you get nothing. The casino allows you to negotiate the price you want to pay for the game. How much would you be willing to pay to play this game?

Solution #

由于对称性, 无论过程如何, 最终两堆的卡牌数一定相同 (平局, get nothing). 因此不应该支付任何代价来玩这个游戏.