Surprised there's not a specific mention of learning by doing, which means probability of success is not static, when this is _just_ under the surface of the content of this post. They did kind of hint at this with the "Each attempt... a little better than the last."

I didn't read the article, I don't think these kind has any value, but if you are here.. :)

i think it is rather binary, so

P_overall_success = 1 - (1 - P_success) ^ #attempts

and expected number of first success:

n = 1 / P_success

I don't see "cost" mentioned anywhere there.