Hello math people,
I am trying to find the answer to a probability question that’s been boggling me for a while now.
Lets say that you participate in a competitive game (it is a zero-sum game with a clear winner and loser after each match).
- The competitive scene is divided in leagues.
- Each won match AWARDS you a token and each lost match LOSES you one.
- After you have accumulated exactly 10 tokens you climb to the next league.
My question is: provided you know what your win-rate is at said game, how can you assess intelligibly what number of games you expect to play to beat a whole league?
I know that a 100% win-rate equates to ten games to pass the league.
I also know that you are expected to beat the league at some point with a 50% win-rate. (Losing a game at zero tokens downgrades you to the league below with 9 tokens. There is an infinity of leagues above and below you.)
Clear question: provided a winrate between 0,5 and 1, when do I expect to have had ten more wins than losses?
Thank you all in advance, I don’t have the required background to process this question.
Best wishes!
I am trying to find the answer to a probability question that’s been boggling me for a while now.
Lets say that you participate in a competitive game (it is a zero-sum game with a clear winner and loser after each match).
- The competitive scene is divided in leagues.
- Each won match AWARDS you a token and each lost match LOSES you one.
- After you have accumulated exactly 10 tokens you climb to the next league.
My question is: provided you know what your win-rate is at said game, how can you assess intelligibly what number of games you expect to play to beat a whole league?
I know that a 100% win-rate equates to ten games to pass the league.
I also know that you are expected to beat the league at some point with a 50% win-rate. (Losing a game at zero tokens downgrades you to the league below with 9 tokens. There is an infinity of leagues above and below you.)
Clear question: provided a winrate between 0,5 and 1, when do I expect to have had ten more wins than losses?
Thank you all in advance, I don’t have the required background to process this question.
Best wishes!