The problem seems ill-defined to me in the same sense that Bertrand's paradox is (https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) https://en.wikipe

The problem seems ill-defined to me in the same sense that Bertrand's paradox is (https://en.wikipedia.org/wiki/Bertrand_paradox_(probability) https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)). Your optimal strategy involves maximizing an objective function that depends upon your opponent's strategy. "Assume nothing" about your opponent is an incomplete problem specification, because you must assume something in order to determine which function to maximize. For example, consider that your opponent chooses to redraw any time his number is greater than 0.5. His expected value then becomes less than 0.5, which means that if you choose to redraw any time your own number is below 0.618..., then your strategy is suboptimal. So, we have to assume something about the opponent's strategy. Is it a uniform strategy state space? Is it a state space where both players are superrational?