Is there rating formula like ELO but for bughouse chess?
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Yes, you take the same formula and do absolutely the same calculations. Elo formula has very little to do with chess (except of it is used to calculate rating in chess). You can take any event that has win/lose/draw and apply elo formula to calculate the rating.
In bughouse you play in a team of two, so you will end up with a rating for a team.
Salvador Dali
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Well, this works if you want to have "team elo" but what if each player wants it's own elo? – Santropedro Jul 30 '17 at 02:37
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I was on a train and some high school kid I overheard mentioning his Elo which turned out to be some online game. Elo I think is used in any two-sided game and literally has nothing to do with chess. The games that it works for just must have wins counted as 1, draws as a half and loss as 0. Bughouse if the team remains fixed. I think it is used in boxing except perhaps modified to count different kinds of wins differently for different kinds of outcomes. – releseabe Jul 26 '23 at 14:34
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Providing that teams are not fixed, Elo (and Glicko too) does not fit your needs, because it's designed for 1-on-1 matches only.
You need something that manages both team performance and players' rating, as TrueSkill or rankade, our free-to-use rating system. Here's a comparison between aforementioned ranking systems.
Tomaso Neri
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1*A team is a ratable unit of measurement* providing it's fixed. If not (and usually bughouse chess is played by extemporaneous teams, not in weekly organized swiss system tournaments, I think), Elo doesn't work, so you need something else - as TrueSkill or rankade - to have rankings from matches results. – Tomaso Neri Aug 25 '16 at 06:31
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1(Previous comment was added just to reply to a comment that afterwards was deleted) – Tomaso Neri Sep 14 '16 at 19:37