Can someone tell me if my logic is correct?
It can be boldly said that if there were only 6 games, the outcome of any one of the teams winning at the end of 6 games played is equal. It will be explained near the end. (Refer to paragraph 5)
We need to calculate the probability that the game will extend till the 6th game. And if the probability of the game extending upto the 6th game is more than (1/2) or 0.5, then it means that team B has gained the upper hand since now they have neutralised team A's initial advantage, hence B is more likely to win.
After calculations using combinatorics, we see that the probability of the game extending upto the 6th game is 0.622, which is clearly more than 0.5. So in more cases than not, the teams will play 6 matches or more.
It can be argued that team B could have lost more than team A at the start of the 6th game. But even if this has occured, it is neutralised once the 6th game has ended since at this point, both teams have played 3 matches at their home turfs. Upto the 6th game, it is equally likely for any one of the teams to have won.
But since there is an existence of a 7th game, which is to the advantage of team B, there is more of a chance for B to win.
The logic used using combinatorics was the probability of game extending upto the 6th match = (probability that team A will lose 2 games out of the first 4 games + probability that A loses one game out of 4 and loses the 5th game)=0.622.