Pick any cumulative probability function P(x) such that a > b ==> P(a)

P(b). Now if the number shown is y, guess "low" with probability

P(y) and "high" with probability 1-P(y). This strategy yields a probability of > 1/2 of winning since the probability of being correct is 1/2*( (1-P(a)) + P(b) ) = 1/2 + (P(b)-P(a)), which is > 1/2 by assumption.

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