Are you sure about this? I would say that the more "Godlike" (basically less limited to using "small numbers") your adversary becomes, the further away from your pick the median of the distribution is likely to be, and therefore the less effective your pick becomes.
But then I suppose the standard deviation could also increase with this, which perhaps cancels this out (to some extent? Completely?) I suppose it depends on the subjective nature of increasingly advanced adversaries and how they choose to play the game. But certainly they could play it so that it vanishes to zero in the limit - by increasing the range of the possible median point but also keeping the standard deviation low.
For example, all beings use a normal distribution for the main distribution. But they pick the mean of the distribution randomly first using a separate sub-distribution, and always use a standard deviation of 1 for the main distribution. The sub-distribution is just a uniform distribution between -x and x with x corresponding to the being number. So:
Being 1 uses a sub-distribution that is a uniform distribution between -1 and 1 to pick the mean for their main distribution (which is a normal distribution with standard deviation 1).
Being 2 uses a sub-distribution that is a uniform distribution between -2 and 2 to pick the mean for their main distribution (which is a normal distribution with standard deviation 1, not 2).
Being 3 uses a sub-distribution that is a uniform distribution between -3 and 3 to pick the mean for their main distribution (which is a normal distribution with standard deviation 1).
And so on. The higher up the beings you go, the less effective the picking strategy becomes, with it being useless in the limit.
Obviously you can't have this case where your probability becomes exactly 0.5, but you can get arbitrarily close to it.