I’ll commit to my ignorance here, before you give the solution. I don’t think it’s possible to get better than 50%, unless ROB has a known and flawed algorithm for choosing. I see some similarity to https://en.wikipedia.org/wiki/Two_envelopes_problem, which makes the point that there is no uniform distribution over an infinite set.
But there’s a lot of wiggle room in “better than 50%”—if you mean 50% + epsilon over hugely many trials, you can probably argue that there is some bound that you can infer with some chance of correctness, and if that happens to be one of the numbers, you know which direction to guess. If you mean “measurably better than 50%”, or “better than 50% for every A and B”, then no.
One possible method for ROB: pick a number in the middle-third of a large but finite set of integers. Flip a coin to add or subtract one. Those two adjacent integers are what gets sent to TABI.
edit: and it didn’t take long for dxu to show me how I’m wrong. reason for my error:
I mistakenly focused on the coin flip and the labeling of A and B, rather than the underlying fact that we one number MUST be larger than the other—we don’t care which is A and which is B, we care which is bigger.
I’ll commit to my ignorance here, before you give the solution. I don’t think it’s possible to get better than 50%, unless ROB has a known and flawed algorithm for choosing. I see some similarity to https://en.wikipedia.org/wiki/Two_envelopes_problem, which makes the point that there is no uniform distribution over an infinite set.
But there’s a lot of wiggle room in “better than 50%”—if you mean 50% + epsilon over hugely many trials, you can probably argue that there is some bound that you can infer with some chance of correctness, and if that happens to be one of the numbers, you know which direction to guess. If you mean “measurably better than 50%”, or “better than 50% for every A and B”, then no.
One possible method for ROB: pick a number in the middle-third of a large but finite set of integers. Flip a coin to add or subtract one. Those two adjacent integers are what gets sent to TABI.
edit: and it didn’t take long for dxu to show me how I’m wrong. reason for my error:
I mistakenly focused on the coin flip and the labeling of A and B, rather than the underlying fact that we one number MUST be larger than the other—we don’t care which is A and which is B, we care which is bigger.
Please spoiler your edit