I made a bet with a friend and I would like to know if I'm ahead or not. We have a package of 6 games. Each game have a different probability of a team to win.
If it's a tie 3-3, it's a push. If it's 4-2 or 5-1 or 6-0, it's a win (same amount regardless).
Let say my probability for each matchup is :
- 0.5
- 0.5
- 0.34
- 0.45
- 0.72
- 0.65
How can I calculate the probability of a tie and a win ?
Thanks !
For the win percentage, you need to go through all of the combinations of 4-2, 5-1, 6-0, and add up the probabilities. For your data, I come up with your winning chances as 0.390023 (anybody want to check that?). I assumed all games are independent.
Adding up the 0-6, 1-5, and 2-4 cases, I find your chances of losing are 0.288038 Finally, the chance of a 3-3 tie is 0.321939
For larger problems like the 10-game case you mention (or if you just don't want to do the tedious calculations for the smaller problem), you should use simulation.