> Each successive heads we observe increases the (conditional) probability of the coin being skewed towards favoring heads. [This is contrasted to the *actual* probability of getting heads, which stays constant at p. We have to be careful about which probability space we're looking at things from -- this depends on how much information about the experimental conditions we have.]

OK then, here's my (probably badly flawed) way of looking at the problem.

I know the coin's skewed, but I don't know which way, so I think it's 50/50 that I'll get a head. I do get a head. In my simple way, that corresponds to 100% probability that I'll get a head on the second coin-toss. However, I have to balance that with my original 50% estimate. The easiest way to do that is to average the two out, which comes to 75% probability. So, before the second toss I'm 75% sure that I'll get a head. I toss the coin for the second time and get a head. Using the same logic as before, my reckoning of the outcome for the third toss is now 75 + 12.5 = 87.5% in favour of heads. Taking this onwards...

After the third toss, probability = 87.5 + 6.25 = 93.75%

After the fourth toss, probability = 93.75 + 3.125 = 96.875

After the fifth toss, probability = 96.875 + 1.5625 (?) = oh 'eck, this can't possibly be right. It's converging on 100%, I can see that, but the maths is getting too hard for me. Any better ideas?

Si-"Only did 1 unit of stats, and that was last year"-gi