This guide gives the probability of player $A$ winning a game against player $B$, using their Elo ratings $R_A$, $R_B$:
$$P(A) = \frac{1}{1+10^m}$$
where
$$m=\frac{R_B-R_A}{400}$$
What is the expected number of points obtained by player $A$ in an $X$ games match, if a win is worth $1$ point, a draw is worth $0.5$ points and a loss is worth $0$ points?
Note: I am not sure if the games should be considered independent or not. One could also factor in the Elo rating changes after one player wins the first game, and the second etc. I'm not sure how much this would complicate computations, so ignoring this is also fine if considering it would be too complex.
The probabilities of the results in each game of $A$ against $B$ are $$P(W)=\dfrac1{10^m+1}$$ for a win, $$P(L)=\dfrac1{10^{-m}+1}$$ for a loss, $$P(D)=1-P(W)-P(L)$$ for a draw, so expected number of points of $A$ vs $B$ in X games is $$p=X(P(W)+\dfrac12P(D)),$$ or $$p(A)=\dfrac{X}2\left(1+\dfrac1{10^{(R_B-R_A)/400}+1}-\dfrac1{10^{(R_A-R_B)/400}+1}\right)$$