翻牌喊红：最优胜率

You are playing the following game with a well shuffled deck of 52 cards facing down: at times $n = 1,2,\ldots ,52$ , you turn over a new card and observe its color. Just once in this game, right before turning over a card, you must say "The next card is Red!" You win the game if the next card turned over is indeed red, and lose otherwise. Let $R_{n}$ be the number of red cards remaining face down after the $n$ th card has been turned over. Show that $X_{n} = \frac{R_{n}}{52 - n}$ , $0 \leq n < 52$ , is a martingale. Show that there is no strategy that guarantees winning with probability higher than $\frac{1}{2}$ .