If Mikhail spends 100 days proving the theorem, and fails, that acts as evidence the theorem is false, so the optimal strategy changes.
Indeed this is always the optimal strategy. Attempt to prove it true till the chance of it being true is less than 50%, then switch.
Under this method you should start off by spending 122 days trying to prove it true, then continuously alternating, so testing the oracle doesn’t cost you anything at all.
Ha! Well done. I spent a week making sure my math was right and never thought of this. I agree that updating the truth probability is a better model of this situation, and I can confirm your numbers.
I suppose we could also update each day’s success chance, with some kind of prior balancing updating truth probability vs. success probability. Though by that point we are likely no longer “simplifying”.
If Mikhail spends 100 days proving the theorem, and fails, that acts as evidence the theorem is false, so the optimal strategy changes.
Indeed this is always the optimal strategy. Attempt to prove it true till the chance of it being true is less than 50%, then switch.
Under this method you should start off by spending 122 days trying to prove it true, then continuously alternating, so testing the oracle doesn’t cost you anything at all.
Ha! Well done. I spent a week making sure my math was right and never thought of this. I agree that updating the truth probability is a better model of this situation, and I can confirm your numbers.
I suppose we could also update each day’s success chance, with some kind of prior balancing updating truth probability vs. success probability. Though by that point we are likely no longer “simplifying”.