Re: game with a not too obvious solution
If II generates his numbers randomly, and given that the tails are infinite, I cant think of any probability function that will have an EV other than 0. No matter how large or small the first number he picks is, there is still a "50/50" chance that the next number will be greater or smaller. If II can have a strategy where even he cant predict the relationship between the two numbers, how can I do better than 0 EV?
If the tails were finite but very large then a f(x) like you are proposing might work.
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