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Why is the Stockfish ELO rating changing?

I'm pretty new to lichess so sorry if this is a stupid question. If I understand this right the lowest Stockfish level (I) equals a rating of 1500 ELO points. Why then do the ELO points for all other levels keep changing? It also seems that sometimes the ELO points of a higher level - let's say level IV are lower than the points of level III.

At this very moment the ELO points are 1500 - 1600 - 1682 - 1620 - 1784 and so on...
ELO is a name, therefore Elo, and lichess uses Glicko 2.

The different AI levels have different amount of time and minimal amount of moves, they are also running on different hardware so they don't always have equal strength.

The rating is calculated in the same way as for players, it changes depending on the rating of the ones challenging it and the result.
Thanks for answering. So lichess uses a rating system called Glicko 2 - I didn't know that. It still seems strange that a higher Stockfish level would have a lower rating. Does that really mean that Stockfish IV is weaker than Stockfish III?
No, it does not. It depends entirely on the people that play it. They should all theoretically be higher than each other.

The fact Stockfish Lv. 3 has a higher rating than Lv. 4 is almost entirely psychological. My guess is that lower-ranked players are afraid to go above level 3 and play and lose to level 3.
If an equivalent number of people with a full range of ratings played every Stockfish level, then there would be an obvious progression, where each level is stronger than the one before it.
yes, just because it wouldn't do well against me doesn't mean it's a bad program or it is getting worse xD
I dont think it works that way.. if I understand it correctly, the stockfish engine is the same in all levels, it hasnt really an ELO rating. The thing is, at every level the engine gets limited in time to move and depth. So the lower de level you choose, the less time to move and less depth of continuation moves stokfish gets. at maximum level you play against his raw strenght.
I thought games against stockfish are unrated?! (at least one I played was)
#7, there is no such thing as 'raw strength' when it comes to engines. It is set to skill 20/20 on the highest level, sure, but the depth and time is still very important. Stockfish is still given only 400ms on level 8 with a depth of 12.

#8, they are unrated for you meaning you don't gain rating if you play against Stockfish. But the rating shown on the levels IS determined by your own rating. So basically, Stockfish gains and loses rating based on your own, but you don't.
#4: nice and clear explanation, to which we could probably add the fact that players don't necessarily take games against the engine very seriously (from using it to create the "chess alphabet" to experimenting with 1.h4, putting one's self in a dubious position on purpose to see how one can deal with it, asking for multiple takebacks or creating tons of games in a short amount of time, etc...) so that overall ratings for the engine can not be considered as 100% sound.

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