Isn't the Lichess system pretty much the Elo system? I was under the impression that it is. If that's the case, I would think the win probabilities would be much the same.
If I'm mistaken, my apologies (and please inform me as to how the Lichess rating system is different, if possible). Thanks.
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Update: So I've done a smidgen of research. Lichess uses the Glicko-2 system, as opposed to the Elo system. The Glicko and Glicko-2 systems are newer and introduce the variable of "rating reliability," designated in the formulas as RD (for Ratings Deviation). From what I'm reading, because the Glicko systems take into account the reliability (RD) of the players' ratings, you can't create a win probability table in the way you can with the Elo system.
Lichess discusses the Glicko-2 system here:
lichess.org/faq#ratingsWikipedia article on Glicko-2 here:
en.wikipedia.org/wiki/Glicko_rating_systemAnd here's a table comparing the two rating systems, with an entry on score probabilities:
www.englishchess.org.uk/wp-content/uploads/2012/04/Elo_vs_Glicko.pdf