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.
How does this work? If I know that there's evidence that will convince my future self that finding the coin will make me win, then I update on this, and don't believe you when you say that I'll lose if I find the coin. Vice-versa after the memory wipe.
Tell the person in both states that if he finds the coin an arbitrary dog is going to die and the subject will receive $100. Then just before the subject starts to hide the coin, show the a cute puppy to them. The subject will try to hide the coin very well, and then later, without the memory of the cute puppy, will try to find the coin. Incentives should work out, adjust the animal(child?) and dollar amount to suit the subject.
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!