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Hi All. Hope you are all well in the current circumstances. I've been trying to learn more about probability during the lock down and this is a problem I have been stuck on for a while.
In an example tournament, lets say there's 10 players (A through J) who all play each other once. There's 3 possible outcomes for each player for each match; a win, a loss and a tie. A win is worth 2 points, a tie is worth 1, and a loss is worth 0. At the end of the tournament, the teams are ranked 1st to 10th on the basis of how many points they've earned.
If the probability of each outcome for each game for each player is known, as shown below for example for player A, could it be used to calculate the probability that they would win the tournament? Or finish second, or finish in the top half, etc.
| Game | Probability Player A Win | Probability Opponent Win | Probability Draw |
|---|---|---|---|
| A v B | 72% | 8% | 20% |
| A v C | 65% | 13% | 22% |
| A v D | 50% | 28% | 22% |
| A v E | 84% | 14% | 2% |
| A v F | 77% | 10% | 13% |
| A v G | 91% | 5% | 4% |
| A v H | 78% | 7% | 15% |
| A v I | 69% | 8% | 23% |
| A v J | 80% | 1% | 19% |
Any help would be greatly appreciated!
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