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Mathematics, 24.02.2020 22:25 travisvb

You play a game against Bob Hough. You have a very big urn, and at the start of the game, there are twenty balls, two each numbered one through ten. At each turn, you throw out one ball, and Bob dumps in any (finite) number of his choice of balls with smaller (positive integer) labels. For example, if you throw out a ball labeled 2 ten, Bob could dump in a million balls labeled four. But if you throw out a ball labeled one, then Bob can’t do anything. You win if you can empty the urn. Can you win? What is your strategy?

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