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Summary

Posted By: Johan Segers
Date: Wednesday, 7 September 2011, at 8:06 p.m.

In Response To: Live variance reduction tournament (Johan Segers)

This has been a long and interesting discussion. Thank you very much. In summary:

1. MWC, rather than error rate, is the proper scale to express the magnitude of a player's cumulated errors over a match. MWC Error Total is the most accurate way of measuring a player's skill: even if it may suffer from a small bias coming from the bot's evaluation function, its variance should be small.

2. Tournaments where a player is rewarded with the difference of his own and his opponent's MWC error total constitute the most accurate way of ranking players based on their skill while still retaining a form of direct interaction. However, the format risks to tend to reward bot-like plays while it does not directly rewards winning a match.

3. Variance reduction (luck adjusted result = actual result - amount of luck) enjoys the following properties: - It is unbiased. - It might reduce the luck factor sufficiently to make backgammon tournaments for money legally possible in countries where this is currently problematic. At least in Norway, a tournament based on error rate passed the test. - Some element of luck still remains, but this is not perceived as a problem by the players (if desired, the remaining amount of luck can even be augmented by downweighting the 'amount of luck' term in the above formula). - It benefits the stronger players (which can be perceived as an advantage or a drawback). - Aggregating the results of a number of bots (using the mean or the median) robustifies the outcomes against a particular bot's imperfections.

4. In addition, the variance can be further decreased by smoothing out the prize money more evenly among the participants, as opposed to rewarding a handful of players with almost all of the money. In combination with variance reduction, the better players are almost guaranteed to take some money home.

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