by kingjames01
As I've said, I think as stated the problem is ill-defined.I'm going to restate the problem in different words and tell me if you think I need to tweak anything.
Suppose that we have a card game played between 2 opponents using asymmetric factions, C and R.
Now suppose that we ask have a statistically large pool of contestants to complete a statistically large number of games.
After doing so we conclude that the game is balanced such that any 2 randomly chosen equally skilled players, can sit down and play in a series of matches and expect to win 50% of the time as faction C and 50% of the time as faction R against each other.
First, we should consider what happens if we introduce a super player X into the player pool. Whenever X is matched up with a random player from the pool for a series of matches, X's win percentage is statistically different than the norm.
Let the probability for player X to win a match if X is playing as C or R be represented by X_C and X_R, respectively.
Can we find a general solution to describe this scenario if we know that:
1) the game is balanced and
2) player X's overall win percentage?