### Brain Teasers

# Kebab Palace Casino

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability

Just to be different, the "Kebab Palace Casino" in Madadia has dice with 20 sides.

The "house" rolls two 20-sided dice and the "player" rolls one 20-sided die. If the player rolls a number on his die between the two numbers the house rolled, then the player wins. Otherwise, the house wins (including ties).

What is the player's probability of winning?

The "house" rolls two 20-sided dice and the "player" rolls one 20-sided die. If the player rolls a number on his die between the two numbers the house rolled, then the player wins. Otherwise, the house wins (including ties).

What is the player's probability of winning?

### Answer

It is easily seen that if any two of the three dice agree that the house wins. The probability that this does not happen is 19*18/(20*20).If the three numbers are different, the probability of winning is 1/3.

So the chance of winning is 19*18/(20*20*3) = 3*19/200 = 57/200.

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