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Erik's Open Problem: Nim for Money:
Suppose we have a new version of the game of Nim (which we will play with coins, instead of nimheaps of stones), where at the end of the game, the winning player will get to take home all the coins they collected from the piles, while the losing player takes nothing. What is the winning strategy for the winner to both win and take the maximum possible number of coins? What is the best strategy for the Nim loser to make the winner take the fewest coins?
Conjecture 1: The winning player always has a strategy that allows him to get at least half of the coins
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