This might be “optimal given your state of knowledge about ROB” but it isn’t “guaranteed to succeed more than 1⁄2 of the time”. For example:
My prior is that Rob always picks a positive and a negative number.
Actually Rob always picks two positive numbers.
Thus when we play the game I always observe a positive number, guess that it is the larger number and have a 0.5 probability of winning. 0.5 is not greater than 0.5
This might be “optimal given your state of knowledge about ROB” but it isn’t “guaranteed to succeed more than 1⁄2 of the time”. For example:
My prior is that Rob always picks a positive and a negative number.
Actually Rob always picks two positive numbers.
Thus when we play the game I always observe a positive number, guess that it is the larger number and have a 0.5 probability of winning. 0.5 is not greater than 0.5
Right, I should have chosen a more Bayesian way to say it, like ‘suceeds with probability greater than 1/2’.