On 13/01/2011 02:27 PM, Invisible wrote:

> Suppose the probability of a catch is unconditionally P. How does the
> length of a typical series of consecutive catches vary as a function of P?

Apparently catching or dropping the diabolo can be regarded as a 
Bernoulli trail, and thus performing an open orbit is a kind of 
Bernoulli process. In particular, the number of failures before a 
success is achieved (or, conversely, the number of successes before the 
first failure) follows a geometric distribution.

Specifically, if the probability of catching the diabolo is P, then the 
probability of *not* catching it must be 1-P. Apparently the probability 
of K successes followed by one failure is

   Prob K = P^K * (1-P)

Thus, each series of catches of length K+1 is a factor of P less 
probable than a series of length K.

All of this of course assumes that the trails are *independent*, which 
they manifestly are not...

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