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Three d20 betting game

You are sitting at table and there happen to be three, fair, twenty-sided dice. Your friend offers you a wager: She says she will roll two of the dice, and you can roll one. If your number lies between her two numbers you win, if not, you lose. (In the event of a tie, you also lose). Should you take this bet? What are your chances of winning the game?
What is the probability that one dice rolls between two others?
Answer and calculation below: