# Drawing a Diamond

A gambler has a proposition for you.

In this scenario, let’s say you are always willing to take a bet on 50-50 odds or better, but you will never take a bet when the odds are against you.

First the gambler separates the four aces, shuffles them, and deals you one card from the stack of four. “Would you be willing to bet that you have a diamond?” he asks. “Of course not,” you say. “There is only a 1 in 4 chance, or 25 percent.” The gambler then deals you a second card from the three remaining aces. “How about with your odds doubled?” he asks. “OK,” you say. “Now the odds are 50 percent, and I will take a bet with 50-50 odds.”

The gambler then replaces the aces in the deck, shuffles the full deck of 52 cards, and then deals you a single card. “I assume you still will not bet that you have a diamond,” he says. “That’s right,” you say. “It’s still a 25 percent chance.” The gambler then deals you a second card. “How about with your odds doubled? You’ll take this bet, correct?”

Is the gambler right about your chances? Should you take the bet?