Let me make a simpler form of this problem. Suppose I flip a fair coin a thousand times, and it just happens to land on heads every time. How do I find out that this is a fair coin, and that I don't actually have a trick coin that always lands on heads? The answer is that I can't. Any algorithm that tells me that it's fair is going to fail in the much more likely circumstance that I have a coin that always lands on heads. The best I can do is show that I have 1000 bits of evidence in favor of a trick coin, update my priors accordingly, and use this information when betting.

The good news is that you will only get a coin that lands on heads a thousand times about 00.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000933% of the time, so you won't be this wrong by chance very often. In general, you can calculate how likely you are to be wrong, and hedge your bets accordingly.