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 Backgammon

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22. Iunie 2005, 13:48:09
AbigailII 
Subiectul: Re: win and lose against the same player
Modificat de AbigailII (22. Iunie 2005, 13:50:08)
Hrqls: shouldnt a win + a loss equal out to a draw

No. A win followed by a loss is slightly worse than two draws, while a loss followed by a win is slightly better. It's easiest to see when you have two players with equal rating, and an equal number of games played. Assume their current ratings to be R. Then a win will give an increase of r points, a loss will give a decrease of r points, will a draw doesn't change the ratings. So, after drawing the first game, it's still r points change for a win/loss, and no difference with a draw. With two draws, both players still have rating R. But what if player A wins the first game? Then her rating will be R + r, while player B's rating will be R - r. So, the expected change in rating for player A for the second game will be an increase of p for a win, a decrease of s for a loss, and a decrease of q for a draw, with 0 < q, p < r < s. So, if player A wins, then loses, his rating will be R + r - s < R. And player B, who first loses, then wins, will end up with a rating higher than R.

A win and a loss will be equivalent to two draws only if the rating is calculated after the entire match - but not if you calculate ratings after each result (which is what happens on Brainking).

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