42. Consider the following game. A deck of cards is shuffled and its cards are turned face up one at a time. At any time you can elect to say "next," and if the next card is the ace of spades, then you win, and if not, then you lose.

Of course, if the ace of spades appears before you say "next," then you lose.

Also, if there is only one card remaining, the ace of spades hasn't yet appeared, and you have never said "next," then you are a winner (since you will say

"next"). Argue that no matter what strategy you employ for deciding when to say "next," your probability of winning is ${1}\over{52}$.

HINT: Argue that for any of the (51)! orderings of the cards different from the ace of spades, there is, for each strategy, exactly one ordering of the full deck that results in a win.