The Two Dice Wager

A gambler presents you with an even-money wager. You will roll two dice, and if the highest number on either die is one, two, three or four, then you win. If the highest number on either die is five or six, then she wins. Should you take the bet?


Two Dice

See Answer
You may be tempted to take the bet because you can calculate that your odds of winning with one die are 4 out of 6, or 2/3. What happens now that two dice are involved?

Instead of six possibilities, there are now 36. You can make a simple grid to see your odds of winning, with the six possible results for the first die forming the columns, and the six possible results for the second die forming the rows. As you can see, your odds of winning are 16 out of 36, or 4/9, so you should not take the bet.

Two Dice Probabilities


2 thoughts on “The Two Dice Wager”

    1. This puzzle is certainly trickier than it seems. The way the wager is phrased, if there is a 5 or a 6 on either die, the gambler wins. With two dice, the gambler will win about 5 out of 9 rolls. If you don’t believe it, you can test it with real dice.

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