# Bet, bet, bet!

Take yourself back in time to California, the Gold Rush, 1849. You’re prospecting for gold. You’ve had a pretty good run of luck. So you decide it’s time to clean up and go into the big city to celebrate. You stumble out of one of the saloons, having spent most of your money on women and wine — and you’re about to squander the rest — when you hear someone call out to you.

From the inky shadows emerges a well-dressed gentleman who proposes a game of chance. He says, “I have this little silk bag. In it are three cards. One of them is green on both sides. Another one is red on both sides. And the third is red on one side and green on the other.

“I’m going to allow you to inspect the bag and put the cards inside. Without looking, I will let you pull one of the cards and place it on this little table in front of me without revealing what’s on the bottom of the card.”

You reach into the bag, deftly pull out one card, and put it on the table. You see a red face. The con man says, “I’ll bet you even money that the other side of the card is also red.” Should you take the bet?

### 3 guesses to Bet, bet, bet!

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• det

probability of my win: 1/3
never play gamble with strangers : P

• So you’re saying he should NOT take the bet, right?
If so, you’re correct!

No, you should not take the bet. When the game started, before anyone did anything, there were equal chances of getting either red or green because there were three green faces and three red faces. But now you know that card you turned over isn’t the “green, green” card. So, there is really only one green face left. And there are two red faces left! So the chances of winning are two to one in favor of red? Believe or not. You can believe it because what you’re dealing with is not cards– you’re dealing with the sides. When you see the red side up, you could be seeing one or the other face of the red/red card. That’s what most people don’t grasp.
You’re today’s winner!

• det

yes he should not take the bet, unless he likes the risk; the con man has 66,66% chance to win