Does the ELO system works like the one in the wiki?

[Realdeo]

Wiki says that BGA's ELO system works like this:

First 30 games ->

K = 60 x (number of players/2)

For the next games ->

K = 40 X (number of players/2)

This game: http://en.boardgamearena.com/#!table?table=20602569 has 6 players so. Perudo recommended size is 6 players.

If K = 180, like the original rule, my elo will be 2070.
If K = 60, my elo will be 1709.
If K = 40, my elo will be 1649.

But my elo in the game turned into 1638 instead.

So I am actually wondering how the Elo system actually work.

[Jest Phulin]

I haven't seen the exact code, but it looks like there should also be an adjustment of a division by (N-1) on the K-factor, where N is the number of players. This accounts for you playing N-1 mini-games (one against each opponent) during this 1 game.

-----Long boring math follows-----
It looks like original Elos were 1530, 1543, 1635, 1630, 1692, and 1514. This gives Ea* to be 0.481, 0.353, 0.359, 0.282, and 0.523 respectively. But, you won, so your new Elo should be 1530 + K(1-Ea). K needs to be modified for more than a 2-player game, so it is. If you stopped here, you would expect an Elo gain of (93+116+115+129+86= 540, after rounding), leading to your result of 2070. But then it looks like K is being modified again, since there are 5 outcomes to this 1 game. If you divide your 540 gained Elo by 5 (for your 5 mini-games -- 1 against each opponent), this gives the 108 Elo gain you see.

*Ea being Qa/(Qa+Qb), Qa being 10^(Ra/400), Qb being 10^(Rb/400), Ra and Rb being the Elo ratings of player A and player B.
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Remember that the Elo system was developed for a specific 2-player game. Any implementation of it for any other game and any other number of players will be "broken."

Also remember that Elo on this site was developed to allow players to more easily find opponents of near their own skill level (with the hopes that near-matches of skill level lead to more fun in playing). Any other use of Elo on BGA leads to discussions of how "unfair" the system is.