User blog comment:BonesMcGee/Brainstorm: Potential savings in using the hurry hatch trick/@comment-5116140-20120911130813/@comment-5116140-20120911143838

Hi TinyBoy,

The distribution cannot be binomial, since there is no upper limit on how many shakes it might take to get a HH10. If you think it is binomial, you need to state the value for N, corresponding to success on all tries. Is it 10? 100?

The geometric distribution is the only memory-less discrete distribution, and that alone qualifies it is the right one for this problem.

You can of course construct a binomial out of a collection of geometric distributions by asking questions like how many users out of 100 will have success in 10 or fewer attempts. That however does not get to the fundamental data point, which is simply how many attempts did it take to have one success. (rare dino)

You are correct that there is an independence thing going on here. (but it really amounts to memory-less in this case.)

Let n dnote the random variable recording the number of tries (eggs) to get one rare dino. By rare, I just mean HH is not 12.

Let E(n) be the expected number of tries. Then E(n+k | k) = E(n)

That is, if you have k HH12's in a row, this does not change your probability of getting a rare egg in the next n tries. The geometric distribution has''' no memory. '''

It is the same as flipping a fair coin until you get one head. Just because you flipped 10 tails in a row, that does not change the chance the next flip will give a head.