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Q: 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 are the probabilities of the player
winning?


A: 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) <code> 3'''19/200 </code> 57/200.
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