Ok, I'm not quite sure what you are doing with your table and I think by the term p-value that you mean the distribution parameter p. Please be more clear about what you are trying to find. p-value has a very specific meaning in statistics. Are you saying that you don't what the population parameter p is, but you ran several experiments and you want to use the results from those experiments to estimate the population parameter p?
I could be wrong, but based on some googling, it doesn't look like there is 1 accepted way of doing it. Probably the most brain-dead way of doing it would be to average all of the values from your experiments (the number of "failures" in each experiment). Then an estimate of p would be , where is the number of successes before you terminate the experiment, and is the average of the 's.
This is based on the fact that is an unbiased estimator of the population mean, which is given by . Unfortunately, the estimator I gave above is not unbiased. But if the number of experiments you run is sufficiently large then it should be pretty good.
In fact, this is what wikipedia has listed as a biased estimator (see here)The unbiased estimator does not work for . So if your then you can compute the for each experiment, and then average those.