My question was about likelihood. If I present you with exactly two coins, visually indistinguishable, but you know that one is very heavily weighted and one

My question was about likelihood. If I present you with exactly two coins, visually indistinguishable, but you know that one is very heavily weighted and one is unweighted coin. Then by repeatedly flipping them, you could reach incredible confidence (99.9999%) within a few minutes regarding which is which. Rather than a "proof" you should think about the payoff if you then had to bet about which was which and then it was revealed. If one landed heads 105 times and tails 3 times in your quick test, there is a conceivable universe in which that was the fair coin. But you would not accept 200:1 payoff to bet that that is the fair coin. You are much more confident than 200:1 that it is the weighted coin.