Three-card monte math which may surprise you
Let's say you're playing a friendly game of three-card monte with a pal. You know the game, you try to pick one winning card out of three offered face down. You pick one. At which point the dealer turns over one of the unpicked cards showing you a loser and offers you the chance to switch your choice between the two remaining face down cards. Should you do it?
Most people would imagine a switch doesn't matter, figuring the odds are 50-50 either way. It might surprise you to know if you switch you improve your chances of winning. Given this scenario, the answer is, yes, you should always switch.
Don't believe it? Consider this: From the start there are three possibilities, you either selected the winner, you selected one of the two losers, or you selected the other loser.
Scenario one: You selected the winner. The dealer turns over one of the two losers and asks you if you want to switch your choice. You switch your choice from the winner to a loser. You lose.
Scenario two: You selected the first of two losers. The dealer turns over the remaining loser and asks if you want to switch your choice. You switch your choice from the loser to the winner. You win.
Scenario three: You selected the second of two losers. The dealer turns over the remaining loser and asks if you want to switch your choice. You switch your choice from the loser to the winner. You win.
As you see, by switching you improve your odds of winning from one in three to two out of three. That's because two out of three times the dealer in turning over a card has a constrained choice, he can only turn over a loser. Since two out of three times you chose a loser, the two remaining cards are a winner and a loser. Therefore, the dealer will turn over the loser and the unchosen, unturned card will be the winner two times out of three. Switch and you win.
Of course, no three-card monte street dealer will offer you that choice. I can't calulate the odds on winning such a game. It's a scam. The odds on getting a good deal on swamp land are… Well, you can guess.
How many more ways than one there are to skin a cat is anybody's guess. I don't even want to think about it.
© Terry Colon, 2006