By Conway, based on Beanstalk by Isbell, is an elegant game. Two moves: 3n+1 and 3n-1, then automatically dividing by 2 until it is odd. Getting to 1 wins. The major open question is whether there are starting numbers from which neither player can force a win.
How far out has it been verified? What is the longest known win? What are some strategies that don't involve a giant look up table? Probably factorization.
Reminiscent of Collatz conjecture.
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