[didgeoridoo]

0.753?

A the beginning, there's a 1/1000 chance that you pick a double-headed, and a 999/1000 chance you pick a fair coin.

A fair coin would act the way you've observed 1/1024 times. A double-headed coin would act that way 100% of the time.

(This is where I get fuzzy): Given what you've observed, there is a (1000+1024)/1024 = 0.506 chance that the coin is double-headed. There is a 0.494 chance that it's fair.

A double-headed coin would come up heads next 100% of the time. A fair coin would come up heads 50% of the time. So, 0.506 x 1 + 0.494 x 0.5 = 0.753.

How far off am I?

[thejteam]

Your .506 is right but the arithmetic problem that you set equal to it is wrong. I think you meant to type 1024/(1024+1000). (BTW, it should be 1024/(1024+999) ).

[didgeoridoo]

Close enough for beta. We'll refine after user testing. (Guess my specialty!)