The point being, there’s a lot more winning non-zero answers than zero answers.
Yes, but what are the odds of you getting the right non-zero answer, given that everyone else is trying to do the same thing? You seem to be forgetting that it’s worse to lose than to share a win.
if the average is less than 3⁄4 then the zeros will still win
It depends where in the range of 0-average the guess is.
But of course I see what you mean; I meant between 0 and (average * 3⁄4), sorry.
EDIT: (average 3⁄4 + average 3⁄8) is the upper bound, unless I forgot something or you’re not allowed to go over.
EDIT 2: The point being, there’s a lot more winning non-zero answers than zero answers.
Sure, but what are the odds of you getting the right one. If they’re too low, then you could still better of with zero.
If I rank a tie and a loss the same, then I’m don’t risk anything by guessing a non-0 value for the chance of winning outright.
Yes, but what are the odds of you getting the right non-zero answer, given that everyone else is trying to do the same thing? You seem to be forgetting that it’s worse to lose than to share a win.