Chance of passing series/ being promoted

tjmmachine

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Jul 2, 2017
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Hey guys, not anything I need to know but was just interested.

So I play League of Legends a fair bit and have taken an interest in their ranking system. You need to earn a certain amount of points to get into a 'series' where it's decided if you're to be promoted to the next rank or not. To be promoted in a regular series you have to win 2 out of 3 games. I was wondering (assuming 50% win rate) what is the chance to be promoted (my reasoning drew me to 50% chance to be promoted). However, if you've previously been up for a series and failed you're given an automatic win, so you only have to win 1 game, but they reduce the amount of games to 2, so effectively you have your first game played for you. I initially thought the chance to pass this series would be 75% (again, given 50% win rate) but since as soon as you either win two or lose two games (with the free win counting as a game) would it be 66% instead given that there are only 3 options, those been; W, W->L, L ->L. Also, if you think that the chance to win a full 3 game series is anything but 50% please let me know and why that would be.

Again, not desperate to know, just interested.
 
So I play League of Legends a fair bit and have taken an interest in their ranking system. You need to earn a certain amount of points to get into a 'series' where it's decided if you're to be promoted to the next rank or not. To be promoted in a regular series you have to win 2 out of 3 games. I was wondering (assuming 50% win rate) what is the chance to be promoted (my reasoning drew me to 50% chance to be promoted). However, if you've previously been up for a series and failed you're given an automatic win, so you only have to win 1 game, but they reduce the amount of games to 2, so effectively you have your first game played for you. I initially thought the chance to pass this series would be 75% (again, given 50% win rate) but since as soon as you either win two or lose two games (with the free win counting as a game) would it be 66% instead given that there are only 3 options, those been; W, W->L, L ->L. Also, if you think that the chance to win a full 3 game series is anything but 50% please let me know and why that would be.
Who is "they"? What are the (mathematical) specifics of "a certain amount of points"? "It's decided" how, and by whom? How certain is the "50% win rate"? Is this rate to be assumed for all games, or does one's win rate go up after having played a particular game once, or twice?

Please reply with the mathematical specifics and precise conditions under which the probabilities are to be computed. When you reply, please include a clear listing of your thoughts and efforts so far. Thank you! ;)
 
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