Checking if Elo system is oppressive [With proofs]

UPD to whoever is reading this: start reading from the last page and go back as I reveal proofs that are more substantial and easier to understand there. Below simulation was just a topic-starter. You'll find more revelation on further pages.

Using ChatGPT powers I simulated 1000000 chess games in a pool of 1000 players. Pairing was rating based with small diffusion to emulate online presence factor. Win/loss factor - just like prescribed by Elo. All players had hidden strength in Elo: 90% of players - from 1000 to 1400, 10% players - from 1400 to 2800. Initial rating was 200, rating floor - 100.

Graphs:

Blue: initial strength distribution.

Green: rating after simulation show that the largest group is minimal-Elo players. Mid-Elo group received artificial bump despite the fact that strength of players was constant during simulation!

Full table with data for each player (names are all fake based on names of real great players and names repeat but that doesn't matter because each player has unique id):
https://pastebin.com/raw/JqGKun3K

Conclusion:

best of the best climbed to the top easily.
Low elo players unfairly end up in a various rating ranges, apparently because of luck, not because of lack of skill. And now you can't blame virtual players for lack of skill. Because game result was dictated by their actual hidden strength.

So in the end we have cases like:

 id player_name hidden_strength_Elo final_rating_Elo

176 Magnus Portisch 1097 509

468 Vladimir Svidler 1263 497

571 Sergey Short 1239 1042

That means actual strength could be 1200, but rating could be 500 OR 1000.

Or look at this oppressed guy:

 id player_name hidden_strength_Elo final_rating_Elo

467 Boris Nepomniachtchi 1203 355
With strength 1203, his rating is 355.
Each player here played 1000 games!
Some more oppression:

 id player_name hidden_strength_Elo final_rating_Elo

266 Hikaru Gajdosko 1112 100

322 Magnus Capablanca 1003 132

Magnus is weaker than Gajdosko but Gajdosko is stuck at 100. Is this fair?

This all aligns with my observations and experience here on chess.com and explains why many people astonished by randomness in apparent strength of their opponents that have same rating.

Thoughts?

ChatGPT is evolving. Free version can't do much, sure, but most advanced runs analysis, you need to wait for a while and it returns with graphs and tables

intresting.quite intresting.

For comparison, current global rapid leaderboard on chess.com:

Peak is at 400. But I guess that's because most people don't play much Rapid and their initial rating (400) remains around 400. Those who play mostly sit in 100-300 category. And after the peak we see same decreasing slope I had with my green graph. Occasionally those 400s step into a fight. Their actual strength is very random. But low-Elo player get punished like if that opponent's 400 rating was real!

The data is not coming from the language model itself. It's a result of actual program execution. So it is indeed a "custom written program" in this case.

And I think, you overestimate the complexity of this task.

500 vs 1200 - 1.75% win chance for 500.

I understand what Elo is perfectly.
Hidden Elo strength in this case would be a comparison to engine's (like Stockfish) Elo. If player wins 50% games against Stockfish in 1400 Elo setting, that's what I call hidden Elo strength of that player.

1263 and 497? You misunderstood my table. 1263 in that table is hidden Elo strength, 497 - resulting Elo after simulation. At the same time a different player in simulation has 1239 hidden strength (close to previous player's strength) but final Elo is 1042. That's the problem: players are rated identically but have wildly different actual strength.

No one said about losing 50% of games with large Elo difference.

Why do you think so? It's actually precise to the very last digit and easy to prove by running stockfish 1400 against stockfish 1701 multiple times - 15% winrate in the long run. Easy to calibrate. And it doesn't matter, that's just a way to describe that each player has certain strength even if player is unrated.