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Say a player with a daily rating of 1500 is playing three daily games at chess.com. His opponents' ratings are 1300, 1500 and 1700 respectively. This player has losing positions in all three games but he can choose the order of resignation.

If this player's goal is to minimise his rating drop after these three games, does it matter which game he resigns first? If so, what is the optimal order of resignation?

For me, a practical scenario is that I am playing a daily game against an opponent whose rating is much lower than mine. I am having a hopeless position but am delaying my resignation as much as I can. My hope is to find a "best" day when my opponent's rating is the highest so I can minimize the rating drop after losing this game. Does this make sense?

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  • it should right since ratings are changed after each game? So resign the highest rated first?
    – cmgchess
    Oct 15, 2023 at 7:22
  • Mathematically it makes sense (I gonna ask on MSE if a commutative rating system can exist), psychologically...I better skip a NSFW joke :-) Oct 15, 2023 at 8:17
  • Update: It can't, as I already suspected. math.stackexchange.com/questions/4787169/…. Resign first the one that "hurts" your rating much, i.e. the worst opponent. Oct 16, 2023 at 8:09

2 Answers 2

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For a simple Elo system, it looks like you get the highest ending rating if you resign against the lowest rated player first, which follows with the intuitive responses from the comments.

The best order is to resign in is 1300, 1500, 1700, which would yield a final rating of 1457.0785. The worst would be to resign in would by 1700, 1500, 1300, which would yield a final rating of 1456.0237.

One caveat is that the ratings are typically going to be rounded off between each round, and the errors that rounding introduce can cause some of the other orders to yield the same results, but there the conclusion still remains that it is best to resign against the lowest rated player first.


Rating Opponent Expected Score Post Loss Rating
1500.0000 1300.0000 0.7597 1477.2076
1477.2076 1500.0000 0.4672 1463.1902
1463.1902 1700.0000 0.2037 1457.0785
1500.0000 1300.0000 0.7597 1477.2076
1477.2076 1700.0000 0.2171 1470.6938
1470.6938 1500.0000 0.4579 1456.9561
1500.0000 1500.0000 0.5000 1485.0000
1485.0000 1300.0000 0.7436 1462.6910
1462.6910 1700.0000 0.2033 1456.5933
1500.0000 1500.0000 0.5000 1485.0000
1485.0000 1700.0000 0.2248 1478.2546
1478.2546 1300.0000 0.7362 1456.1697
1500.0000 1700.0000 0.2403 1492.7924
1492.7924 1300.0000 0.7521 1470.2296
1470.2296 1500.0000 0.4573 1456.5118
1500.0000 1700.0000 0.2403 1492.7924
1492.7924 1500.0000 0.4896 1478.1035
1478.1035 1300.0000 0.7360 1456.0237

Expected Score = 1.0 / (1.0 + 10^((Rating - Opponent) / 400))

Actual Score = 0.0

New Score = Rating + kFactor * (ActualScore - ExpectedScore)

Note: these scores are based on a simple Elo system, not the more complex Glicko system that Chess.com uses. Later, I might try to understand how those calculations work and adjust my answer.

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  • I think Lichess definitely keeps fractional rating around. I don't know about chess.com.
    – koedem
    Oct 17, 2023 at 21:26
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Chess.com follows the Glicko rating system. I'm considering your player has played enough games to have a "confidence" rating, i.e. you get +8/0/-8 for a W/D/L vs an opponent having +- 25 to yours.

For every 25, 50, 75... points difference your opponent has, the rating change will alter by 1. It forms an A.P.. You can use the formula: Higher elo - lower elo >= 50n - 25 where n gets you the alter in a rating change.

Against 1300, the rating gap is 200 -> n = 4 -> They'll lose 8+4, i.e. 12 elo.

Against 1500, the rating gap is 0 -> n = 0 -> They'll lose 8+0, i.e. 8 elo.

And similarly, against 1700 the rating gap is 200 -> n = 4 -> They'll lose 8-4, i.e. 4 elo.

For your example, it will not matter in which order the player resigns. They'll have the same elo in all 3 cases. This can be easily checked by putting the elo in the above formula after each game for all 3 cases.

Note: This is NOT how the actual Glicko Rating works. I've presented the things in a simple way of how elo works on chess.com(enough games played) for the readers to understand!

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  • I find some parts of this answer confusing. The rating change for any Elo based rating system is not linear in the rating difference. But furthermore, even if it were the case, then you would still want to resign the game with the biggest rating loss first as to decrease your rating and change the rating difference to be worse for you and therefore to lose less rating in the later games.
    – koedem
    Oct 17, 2023 at 11:52
  • @koedem Yes, the rating change is not linear in general. I have already mentioned in my answer that I've taken the case of having a 'confidence' rating. You lose the same rating in all 3 cases no matter in which order you resign because the rating gap is not high enough to alter the rating change. If you don't believe me, why not test it yourself with a real account? Oct 17, 2023 at 12:46
  • That is not how Glicko works. There is no threshold for having a "confidence rating". You just have a rating deviation which is a real number greater than 0. If you play more games it will be lower but that doesn't change the fact that no matter what your RD is, the rating change is not linear. More so, of course there is a difference whether your rating difference is 200 or 212 (or even 201). Rating change too is a real number. You can gain 0.01 rating more or less if the change in rating difference is small and it would still make a difference.
    – koedem
    Oct 17, 2023 at 14:03
  • To append on that, a chess website may show a rating to be established if the players RD is lower than some value, but that is not something in Glicko itself and shouldn't change how the rating calculations are done, it is merely to help players who are not aware of how Glicko works, why their rating may change more or less depending on their RD. Similarly, a site may only display an integer value as rating but that doesn't change the fact that behind the scenes it should be a real number.
    – koedem
    Oct 17, 2023 at 14:16
  • @koedem Thanks for the comment. I am aware of that, but for simplicity and due to the mention of chess.com in the question, I decided to frame my answer this way! If you think there's something wrong, feel free to add an answer of your own :) Oct 17, 2023 at 14:45

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