I'm currently experimenting with some bookmaker odds regarding football matches. We can estimate the given probability of winning the game from the odds. For example, if the odds for the win are 1.5 and we take into consideration that the bookmaker's margin is 6%, then the probability should be around 62.89%.
Assume we have three teams: Team A, Team B, and Team C. In the recent past, Team A played versus Team C, and Team B played versus Team C. Both Team A and Team B hosted the game. The next game for Team A will be versus Team B. For the sake of simplicity, let's assume that for each of the matches a given team came out (or will play) with exactly the same line-up.
From the odds, we have estimated that:
The probability that Team A will win with Team C was X.
The probability that Team B will win with Team C was Y.
To remove the home field advantage let's assume that Team A will play Team B on neutral ground.
Can we estimate what is the probability of winning by Team A and what is the probability of winning by Team B based on the previous predictions?
What will be the impact if we assume that one of the teams will be the host?