How games of chess will it take for me to beat my friend 50 times? (Hypothetical)

Question

I have an 86% win rate against my friend in chess.

How games of chess will it take for me to beat my friend 50 times?

 

What is the algorithm used to solve this?

Answer 1

 

 

If you are interested in the number of trials it takes to achieve a certain number of successes, at which point you stop the trials, you use a negative binomial distribution.

 

f(n,x,p) = (^n-1_n-x) p²(1-p)^n-x

 

which has an expectation of

 

x/p

 

In this case, the number of trials needed will be

 

50/0.86 = 58.139

 

Since you can't play a partial game of chess, you must say that it will take 59 games to beat your friend 50 times at chess.