Little math problem(s) February 2019

[pier4r]

And another little one.

There are Alice and Barbara that play a game.
Barbara wins alice 60% of the times.

They want to organize a tournament, but they would like to avoid to rely on luck. Therefore they want to make a match be long enough to determine the better player with a certain accuracy.

They know that between players that have 50% chances of win in a games (or close to that) the game would be very long, therefore they decide to pick another case as reference.

They decide to make a tournament with a match composed of "Best of N" games, where N is the number of games needed to ensure that at least 90% of the times a player with 60% chances of winning a game against their opponent will win.

Which N is that?

What is N when the better player has 65% chances of winning a game?
What is N when the better player has 70% chances of winning a game?