Is there a table of win probabilities for Lichess games based upon rating difference?

well gentleman asked how to estimate. Unless RD is small you cannot really estimate. The RD shoudl not event have impact on estimate just variance of the estimate , which is part of formulas for reason of keeping the update simple

ANd I understand the formulas and their inner workins well enough. I dunno how math-abled you are so cannot really compare

as for bettet: Any maximumlikelihood system that takes history of games into account is more accurate. there is for instance
http://universalrating.com/ it is maximu likelihood system withd decaiying history. Source code is not available
Remi Couloum is academic that has done researc on subject and his BayesElo is good https://www.remi-coulom.fr/Bayesian-Elo/ like the Elostat he is comparing his work with

And if you like study the match on these bradley-terry models with maximum likelihood estimation this is nice paper on finding the maximum likelihood estimate for a set of games http://personal.psu.edu/drh20/papers/bt.pdf
Obviously other multivariable minimisation algorithms work as well

as for what is best dunno there is no good comparison of all. There FIDE and Deloitte sponsored competition about decade a go and I can find result but I did articel with situation at some point of competittion
https://en.chessbase.com/post/can-you-out-predict-elo-competition-update
Not full results but for comparison post of the refence algorithms
Chessmetrics Benchmark: #10
Glicko-2 Benchmark: #38
Glicko Benchmark: #39
PCA Benchmark: #66
Elo Benchmark: #82
As you can see Glicko-2 was no where near the top. Mister G had a entry on compeitition best of my memory which was variation of Glicko-2

Problems with good algorithms

1. Take more computing
2. People treat rating as money hence the feel it unfair if the rating changes when they dont play. Which will happpen and makes ratings more accurate

@petri999 Trust me, I'm no mathematician or statistician and I'm sure your abilities exceed mine in both areas by a wide margin. With that said, if I'm understanding you correctly, Glicko-2 came in at #38 out of 162 rating systems. That's top 23%, which isn't bad at all--especially considering that other rating systems require game histories for the players, which would be a resource nightmare for a website like Lichess.

Bottom line: It seems to me that Glicko-2 does a good job and may be the best balance between precision and practicality.

well some of the 162 were made by pro chess players trying twiddle things like K in Elo system with some algorithm. Those were bound fails. But year given the age of G-2 it was not bad. And as goal is to almost as light as Elo it is doing okay

@petri999 Fair enough. By the way, I love your country. Hyvä Suomi! :)