Puzzle #16: Turning Red
You shuffle a normal deck of cards face down and then begin to flip over cards from the top of the deck, one at a time, placing them face up on a table. At any time (but only once), you can choose to stop, and if the next card is red, then you win. If you never stop, then by default you’re forced to choose the last card (again, you win if it’s red). Is there a strategy that maximizes your chance of winning this game? If so, what is it? If not, why not? You must shuffle the cards thoroughly and are not allowed to cheat in any way (like by marking cards). You may only observe the cards that you flip and choose when to stop.
Find the solution at the bottom of this page.
