pperle
commented
8 years ago @ELynx Thank you very much for your contribution, this means a lot to me. I think the most interesting value would be the standard deviation which simply is:
\sigma = \sqrt{\frac{1-p}{p^{2}}}
where p is the probability
In order to calculate "y% a success is in the first x throws" the formula would look like this:
y=1-(1-p)^x
1-y=(1-p)^x
\log_{1-p}(1-y)=x
where p=probability, x=number of throws and y=success rate.
Example (30% probability to catch the pokémon and we want a success rate of 90%):
\log_{1-0.3}(1-0.9)=6.45570But the standard deviation would be:
\sigma = \sqrt{\frac{1-0.3}{0.3^{2}}} = 2.78887
With given probabilities, you can calculate on what throw Pokemon is likely to be caught. Of course it still can be caught on 1st throw or not caught on 100th, but a good estimate of spent resources is more intuitive than pure probabilities. Here is the math behind Number of trials to first success