I formulated a little problem. Care to solve it?
You are given the following information:
Your task is to hide a coin in your house (or any familiar finite environment).
After you've hidden the coin your memory will be erased and restored to a state just before you receiving this information.
Then you will be told about the task (i.e that you have hidden a coin), and asked to try to find the coin.
If you find it you'll lose, but you will be convinced that if you find it you win.
So now you're faced with finding an optimal strategy to minimize the probability of finding the coin within a finite time-frame.
Bear in mind that any chain of reasoning leading up to a decision of location can be generated by you while trying to find the coin.
You might come to the conclusion that there cant exist an optimal strategy other than randomizing. But if you randomize, then you have the risk of placing the coin at a location where it can be easily found, like on a table or on the floor. You could eliminate those risky locations by excluding them as alternatives in your randomization process, but that would mean including a chain of reasoning!
The FINDER should hear the same story as the HIDER, with the only change that "win = find a coin". The finder should also know that the hider received a false information that "win = not find a coin". The finder should also know that the hider received an information that the finder will receive a false information what "win = find a coin", et cetera. (It seems like an infinite chain of information, but both hider and finder only need to receive a finite pattern describing it.)
Now we have a meta-problem: After such explanations, wouldn't both hider and finder suspect that they are given a false information? If yes, should they both expect probability 50% of being lied to? Or is there some asymetry, for example that rewarding "not find a coin" could make more sense to an outside spectator (which makes the rules) than rewarding "find a coin"? A perfectly rational spectator should prevent hider and finder from guessing which one of them is being lied to. But if the chance of both being right or wrong is exactly 50%, why should they even try?
All those are complications that needn't arise with a slightly different formulation. Just imagine that we're talking about someone who for fun decides to put such a challenge to their future self.
Anyway, we can postulate a person who hides something as best as they can, then they erase their own memory, then they decide to locate what they previously hid. Both hider version and searcher version try to do the best they can, because that's the maximum amount of fun for both of them. (The searcher will reintegrate the hider portion of their memories afterwards)