[defen]

> All that statistics gives you is the probability of having a result at least this extreme with an unbiased coin.

If you subscribe to frequentist statistics and use the null hypothesis of "coin is not biased", yes. But if you're a Bayesian you can compute the probability that the coin bias is greater than a given amount.

[thelema314]

Granted. But in either case, there's no proof - only a probability that you haven't reached an incorrect conclusion. I associate the concept of proof with logical certainty, and no statistical method will give you that.