Hi.

This thread is related with another one I already posted:

The average number of tries

And Chiro helped me.

Now I have another problem to solve.

Given a space of algorithmic probabilities - see the previous thread - one can calculate the probability of a arbitrary sequence of programs. It came from multiplying each probability of each program.

Well, given that probability P of a sequence of programs, we can say that the average number of sequences one must try to happen the desired sequence above is 1/P.

Now the problems come.

I would like to know how many tries one should expect to happen this desired sequence.

Note that each T tries gives us a T size sequence of programs. In T tries one should expect to get a certain amount of possible (likely) sequences of programs. The problem is to estimate this amount. Making the usual exponentiation ("number of possible programs")^T won´t work. The number of programs are infinite. However, the sum of all probabilities of each program is 1 due to kraft´s inequality.

Solved this estimation, it is easy make it equal to 1/P and find the minimum T that satisfy this equation. Note that average number of tries is different from average number of sequences.

Thanks.