# How many games would Magnus Carlsen need to win to get an ELO of 3000?

For the purposes of this question, assume that he wins every game. Go according to his current schedule. Assume the opponents keep their current rating. If you run out of schedule, assume the rating of Carlsen's average opponent.

The answer is that it depends heavily on his future opponents and schedule. Instead, lets first answer an easier problem. If we assume his opponents' average ELO of say 2770 (the current average of the #2-#10 players in the world), how good does Magnus need to score against them to achieve and maintain an ELO of 3000?

Based on ELO calculations, he would need 10^(3000-2770)/400 ~ 3.758 wins for each loss, ie an average score (counting wins as 1, draws as .5, losses as 0) of .7898.

Alternatively, we can use the ELO formulas to calculate (with the help of Excel) Magnus would require 52 consecutive wins (no losses, no draws, just wins) against 2770 opponents to raise his ELO from 2852.6 to 3000

For context, the longest win streak in high level chess was Bobby Fischer's 20 straight in 1970.

• When you calculate the 52 number, are you assuming all those games are played in the same month?
– D M
Mar 29 at 3:03
• Good answer. It would be great if more indepth details are given. Mar 29 at 7:09
• @DM - I calculated this in an idealized world where ELO is recalculated after each match. This has two impacts: One is that we ignore rounding ELOs to the nearest integer. Two is that each match he wins, he gains fewer rating points. Effect two would cause this 52 number to be an overestimate. It is hard to determine the impact of effect one. Mar 29 at 16:59
• @Starshipisgoforlaunch - I don't know his schedule for the next 50+ games. Neither does Magnus, not does anybody else. The horizon is too far away. Mar 29 at 17:00
• How is it impossible @ShadYantra Mar 29 at 18:28

A player's FIDE rating is updated according to the formula

`Rnew = Rold + K(W-We)` where

``````K  = 10, according to (https://www.fide.com/docs/regulations/FIDE%20Rating%20Regulations%202022.pdf).
W  = actual score.
We = expected score.
``````

Expected score is calculated using table `8.1b Table of conversion of difference in rating, D, into scoring probability PD, for the higher, H, and the lower, L, rated player respectively`.

Let,

``````Own rating Carlsen    2853
Opp rating            2770
Rating difference       83
Expected score per game  0.61, according to FIDE table.
Rating update per game   3.9 <- 10 * (1 - .61)
``````

To achieve a rating improvement of 3000 - 2853 = 147 Carlsen needs 147 / 3.9 = 38 consecutive wins.

Take a player with rating 3000. To maintain this rating, the player must score 79% against an average opponent rating of 2770. Or 70% against Carlsen himself.