# How does Carcassonne (iPad) calculate its Elo rating?

In playing Carcassonne for the iPad I've been very curious how the Elo for a player is calculated, and by what means it is adjusted at the end of a game. I have played games where I have tied with the AI at the end of the game, but the Elo distribution was different. How it is calculated?

-
I don't know the exact calculations, but basically, you get more points for defeating a higher-ranked opponent, and less for beating a lower-ranked opponent. (This happens when you lose too.) So, if you tied the AI, and they had a higher ELO, you'd gain some points, while they'd lose a few. – Nicholas1024 Mar 16 '11 at 22:42

Wikipedia has an extensive article on the Elo rating system.
Also it should be Elo not ELO because it's named after Arpad Elo.

-
Updated; thanks for the answer! – fbrereto Mar 17 '11 at 5:53

Elo is used in chess rankings mostly, but can be used in lots of one-on-one or team-on-team ratings. It can also be used for other things, for instance ranking girls, as seen in the movie The Social Network,

:)

Your ranking at the start of the match forms the basis of the expected outcome of the match. A win could be 1 point, a draw 0.5 points and a loss 0 points. If the system calculates your chance of winning as being 90%, your expected score is 0.9.

Score can be calculated after each match or after a tournament. If your expected score in a four-match tournament was 2.8 (you were among the better players in the tournament), but you only managed to score 2.5 (1 + 1 + 0,5 + 0), then you will lose ranking points.

The bigger the difference between the expected score and the actual score, the more of a rating change you will see. So if a low ranked player beats a high ranked player, he/she will gain more points than if a high ranked player beats a low ranked one.

The actual score you end up with depends on the implementation of the Elo algorithm, and especially on how the K-factor is used. See http://en.wikipedia.org/wiki/Elo_rating_system for details.

-