I would like to know how the rating of a player is calculated and how a puzzle with a pre-defined rating is paired with that player. If someone could tell me, I would be very thankful!
I believe lichess uses the Glicko rating system ("glicko 2") as described here: https://en.wikipedia.org/wiki/Glicko_rating_system .
A puzzle can be given a rating the same way a player can. If you get it wrong, the puzzle wins and if you get it right, the puzzle loses. I'm not sure how they pick which puzzle you get next, but it's probably some random process that avoids duplicates. Perhaps others can comment on that.
Spoiler alert: It's complicated.
Just observing your own games, you should figure patterns of how the ratings change depending on the rating difference between players (and assuming they have the minimum deviation of 45-50)
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