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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.

Glorfindel
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Starship - On Strike
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    Highly related question: [Why is Magnus Carlsen's Elo rating not higher, given that his win rate is so high?](https://chess.stackexchange.com/questions/37375/why-is-magnus-carlsens-elo-rating-not-higher-given-that-his-win-rate-is-so-hig). You might also be interested in https://en.wikipedia.org/wiki/Elo_rating_system – Allure Mar 29 '23 at 01:31

2 Answers2

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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.

DongKy
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    When you calculate the 52 number, are you assuming all those games are played in the same month? – D M Mar 29 '23 at 03:03
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    Good answer. It would be great if more indepth details are given. – ShadYantra Mar 29 '23 at 07:09
  • Could you answer my actual question. As in using his current schedule as well. – Starship - On Strike Mar 29 '23 at 11:27
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    @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. – DongKy Mar 29 '23 at 16:59
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    @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. – DongKy Mar 29 '23 at 17:00
  • Magnus is at peak of Elo and achieving 3000 is impossible in Western Chess – ShadYantra Mar 29 '23 at 17:11
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    How is it impossible @ShadYantra – Starship - On Strike Mar 29 '23 at 18:28
  • I mean just for the part that we know @DongKy – Starship - On Strike Mar 29 '23 at 18:28
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    @Starshipisgoforlaunch - I can't be bothered to look up his schedule and his opponents' average ELO for a question where a precise answer isn't that important. But if you provide them, I'll feed it into the ELO machine and let you know what it spits out. – DongKy Mar 29 '23 at 18:35
  • All right then @DongKy – Starship - On Strike Mar 29 '23 at 18:49
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    Because 100+ score need 15 yrs atleast.. it is sigmoid endpoint nearing to saturation. – ShadYantra Mar 29 '23 at 18:50
  • @Starshipisgoforlaunch - As a start, I think Norway Chess is his next tourney. Based on ELO, hes expected to score 5.8/9. If he scores 9/9, he gains 32 rating points, to go from 2853 to 2885. Suppose the next month he played in the same tourney against the same opponents (who somehow didn't lose ELO; maybe they played some other games to get back to their current ELO). He'd then be an even bigger favorite, expected to go 6.3/9. Going 9/9 again, he'd gain 27 points. Repeating this, he'd sucessively gain 32, 27, 25, 22, 20, 8 points, getting him to 2997 after going 9/9 six times in a row. – DongKy Mar 29 '23 at 19:14
  • @ShadYantra hard and impossible are different. Don't call them the same. We can agree that Magnus will probably play at least 52, 54, 55 games. You cant say for certain that he doesn't win them all. – Starship - On Strike Mar 31 '23 at 09:35
  • Magnus will retire by 5 yrs, it seems like. Why he boycotted World Championship, is a concern.. – ShadYantra Mar 31 '23 at 11:07
  • And you say magnus wont play more than 52 to 55 games? @ShadYantra – Starship - On Strike Mar 31 '23 at 20:20
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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.

clp
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