This week’s post is a puzzle. It is not even a relatively new puzzle… but I think it’s a good one, because the problem, and more precisely one of its several solutions, have an interesting relationship to some slightly more practical situations that I have been asked about recently. (As a teaser, I recall being involved at least once in such a “practical” situation, that nearly escalated to physical confrontation. It is strange the things that people feel strongly about.)
Before going into more detail, though, it has been suggested– correctly, I think– that I tend to spoil possibly interesting problems by including solutions in the same post. To remedy that, following is just the statement of the problem. Discussion is welcome in the comments; I will continue next week with my view of the problem and how I think it applies elsewhere.
Consider a standard, shuffled poker deck of 52 playing cards, of which 26 are red and 26 are black. I place the deck face down on a table. I will draw a card, one at a time, from the top of the pile and place it face up on the table for you to see whether it is red or black. At some point before drawing the last card in the deck, you must say, “Stop.” If the next card that I turn over is red, you win one dollar. If it is black, you lose one dollar.
What is the optimal strategy for playing this game, and what is the probability of winning?