Checking if Elo system is oppressive [With proofs]

Eh don’t complain not liking cc Ang go to another chess site

Lil bro joined 24 days ago what is he talking about 90s?

Are those real chess games played by an actual human? Because your simulation was made by a robot. When did it experienced human factors? It doesn't know how humans play chess.

Oh i forgot this piece of info, by july this year almost 60k members of chess.com was closed due to fair play

Over 22 million points were refunded. It would make a huge difference.

Like I said, I’m not trying to be mean, I just want to say my thoughts.

So here are my thoughts: chess is not rigged and people shouldn’t complain for losing one game. No personal attacks

ChatGPT is a chatbot, designed to emulate a human conversation and beat the Turinge test.

Whatever function that would be labelled "ChatGPT" that is not purely conversational, will be other softwares and/or lines of code added to it. Like an autoradio added to a car.

That's for ChatGPT, regarding what it is, and what it is not.

Then the Elo:

Everybody, among arbiters and chess laws makers, is aware that the Elo rating system is based on a curve that tends to infinite in both directions (toward 0% and toward 100% points scored), and that, therefore, any result under 5% or over 95% is to be taken with a pinch of salt.

The Elo rating system doesn't tell the strenght of a chess players, but do summ up the actual results of the said chess player after they played a number of games superior to zero. The more games taken into account, the more likely the Elo rating will provide an idea of the strenght of the player. The fewer, and the less reliable the Elo rating will be, regarding how it does hint the strenght of a chess player.

Since the Elo rating system is based on actual results of games actually played between human rated players, it will include things such as the capacity to avoid playing blunders, and the capacity to exploit blunders, then luck, health, stress, etc. So in the end, as it actual is, the strenght of a chess player is never just how they play chess, as in, it's not just calculation capacities and positional judgement. It's the "sports" stuff aswell (including self control, etc).

Here you go.

Hence this is pure BS. Lol.

That is what you claim to be. No sources, no evidences, no nothing. Not to mention I'm not "France", I'm just me.

Well, that's not even anything logical what you just said. You must be very miserable in your life, so you have got no better hobby than to trash talk me in this forum thread.

Plus, well, since you claim to believe I'd be a bot, how come you're wasing your time talking to me? Huh? C'mon.

ChatGPT already could debug and write code snippets, so it's not at all a stretch to have those snippets run in some kind of secure VM in the cloud (better be damn secure, though, since you are essentially allowing hackers to tell ChatGPT what they want to run on your servers...) and spit back answers. Unless you can actually verify the code 100% accurately yourself, whether the results are any good is up in the air. Not only are just regular old bugs possible, but it is also possible that ChatGPT interprets something you asked using assumptions that are not the same as your own assumptions...running the code correctly but suffering from garbage in, garbage out (GIGO). If you tell ChatGPT apples and oranges are the same and to run some code as if they are equivalent, it would happily give a meaningless result.

@Legrand14 Yeah yeah, you just decide it's so, like no one plays ever at 2100 right? This is stupid what you're doing. I won't reply to you anymore until you talk normal again.

I addressed this already.

Take a Ferrari car, add whatever to it, music devices, communication devices, atc, it's still no parts of the car itself.

Now, "Ferrari" being fashion, you'll soon find all sorts of things labelled "Ferrari" cos it sells. So, no, ChatGPT is a chatbot, and that's all it is, no matter what labels people dedide to put on their softwares.

@Legrand14 reported for racism.

Dude what about my profile? I lose too. If I was a cheater I'd be like 2000. As it is, I still lose to 1500s in blitz. And who's the one with personal attacks now? I should be the one complaining. How would you like it if I called you a cheater without proof

And I will talk to chatGPT. At least a bot is more polite than you.

Wow

wdym

MORE PROOF BELOW. WARNING: THE REALIZATION MAY SHOCK YOU.

Very simple example. For believers to finally understand. Let's say we have 3 players: p1, p2, and p3. p1 and p2, as well as p2 and p3, have played enough games to gather some stats:

p1_vs_p2_winning_ratio = 0.8
p2_vs_p3_winning_ratio = 0.6

According to the Elo formula, p1's strength is 241 Elo greater than p2's strength, and p2's strength is 70 Elo greater than p3's strength. We can assign ratings to them based on their strength:

p1_rating = 1311
p2_rating = 1070
p3_rating = 1000

p1 has never played against p3, but the graph is still connected because p1 played against p2, and p2 played against p3.

But what if we introduce two more players, p4 and p5? They would play against each other, but not against p1, p2, or p3. Can we place them into the same pool? Not yet.

Let's say p4_vs_p5_winning_ratio = 0.7. Therefore:

p4_rating = 1000
p5_rating = 1147

This is the correct difference between p4 and p5, but we can't know how both players compare to p1, p2, or p3. The 1000 rating is just an arbitrary starting point, could be 1500 or 200, doesn't matter.

Now, let's say p4 has finally played against p1 enough times to gather an average winning ratio of 0.65. That would mean p4 is 107 Elo stronger than p1, the strongest player in the first pool. And p5 is stronger than p4, as he wins against him.

Now, there are two ways to join the graphs (pools) and assign ratings to create a single pool:

1. The second pool's ratings become higher, while the first pool's ratings remain the same:
   p1 = 1311
   p2 = 1070
   p3 = 1000
   p4 = 1418
   p5 = 1565

2. The first pool's ratings become lower, while the second pool's ratings remain the same:
   p1 = 893
   p2 = 652
   p3 = 582
   p4 = 1000
   p5 = 1147

In both cases, the Elo differences reflect actual strength and predict win probability. When pools were isolated, p4 is rated 1000 while being stronger than p1, who is rated 1311. In this example, we've manually merged the pools. This is easy to do when the player base is small, and players play frequently.

This is just a direct conversion of probabilities into Elo differences. A perfect scenario. And I repeat, we could have started at 1500 instead of 1000 - it doesn’t matter. Strength is never an absolute value. What matters is the Elo difference.

With a larger player base, a so-called rating system is used (with certain increments to the ratings). Like on chess.com, after each game, your rating changes slightly up or down. It depends on your and your opponent's rating (and rating deviation, which stabilizes quickly after just a few games, so we can ignore it, assuming players play daily).

If you win, it's +16 * (1 - win_probability(your_elo, opponent_elo))
If you lose, it's -16 * win_probability(your_elo, opponent_elo)
Win probability is calculated as 1 / (1 + 10 ** ((opponent_elo - your_elo) / 400))
** means exponentiation (power function). Check yourself, 200 vs 200 win is +8. This is what we see on chess.com

Now, let's simulate games between these players and assign them a starting rating of 200.

https://pastebin.com/raw/22TK4mUu

The code ^^^^^ If you can understand it, of course. If you do, why not write your own? And if you can't, why keep discussing ChatGPT’s coding abilities?

Winning ratio is all we need to know to predict the outcome of games further. It's random but follows the probability. For equally strong players, winrate is 50%. No need to simulate actual chess game and piece movement. Thanks to that, simulation is very quick.

Anyway, let’s review the output (sorted by rating):

Strength Rating
4 1565 555.31
3 1418 507.73
0 1311 338.96
1 1070 272.19
2 1000 163.87
Now Difference with the above player:
(Left column is correct, based on our initial input values)

Strength Rating
4 NaN NaN -- expected, no stronger player
3 147.0 47.58 -- 147 is correct, but 47 is off by 100 Elo, so a win rate estimate mistake of 14%
0 107.0 168.77 -- 107 is correct, but 168 is off by 61 Elo, 8.6% prediction mistake
1 241.0 66.77 -- off by 175 Elo, 23% prediction mistake
2 70.0 108.33 -- off by 38 Elo, 5.4% prediction mistake.

You see that the actual strength difference between player 5 (index 4) and player 3 (index 2) in the above table is 561 Elo. That's real. However, the rating difference is only 392 Elo. This is wrong.

That’s how inaccurate the results are, even after 10,000 games! Let’s do another run.

Sorted by rating:

Strength Rating
4 1565 564.74
3 1418 498.25
0 1311 354.56
2 1000 227.65
1 1070 225.50 ??

Difference with the above player:

Strength Rating
4 NaN NaN
3 147.0 66.49
0 107.0 143.69
2 311.0 126.91
1 -70.0 2.15

This time, the player with a strength of 1070 ended up at the bottom of the list! His rating difference with the player above is just 2 Elo, but it should have been -70.

This shows that the Elo rating system, with its small increments after games, acts more like a sorting mechanism than a true rating system. It sorts players but fails to rate their strength accurately. And, importantly, it does nothing to deal with pool isolation. Localized distortions are to be expected everywhere.

The system is especially inaccurate for lower-rated players. In the example, the stronger player was placed at the bottom of the list. While this doesn’t happen often, it still happens.

Another "unlucky" run:

Strength Rating
3 1418 562.94
4 1565 551.67
1 1070 319.79
0 1311 316.58 !!!!2 1000 100.00

Difference with the above player:

Strength Rating
3 NaN NaN
4 -147.0 11.26
1 495.0 231.89
0 -241.0 3.20
2 311.0 216.58

Oops! Now the 1418-rated player is at the top, and the 1311-rated player is second to last. What? See how inaccurate this system can be? Incredible stuff! Also, the weakest player seems to have hit a rating floor (100), while the player rated 1311 keeps him down.

You'd think 10,000 games should be enough to balance things out, but it doesn’t. Mathematically, it's impossible. The fluctuations are too strong.

Now, what if we use 1500 as the starting rating? A typical run:

Strength Rating
4 1565 1705.34
3 1418 1617.81
0 1311 1532.37
2 1000 1376.95
1 1070 1356.82

Difference with the above player:

Strength Rating
4 NaN NaN
3 147.0 87.53
0 107.0 85.44
2 311.0 155.42
1 -70.0 20.13

It’s still highly inaccurate, both in sorting order (by rating assigned) and in the rating differences compared to strength differences (second table). But at least the rating floor issue is gone with 1500 as the starting point.

So what can we conclude? The Elo rating system can’t properly rate players or their strength relative to others. The difference in players’ ratings has little to do with the actual difference in their strength. It tries to sort, but it often fails (especially at the bottom). Sorting works only within localized pools. This system is full of inaccuracies.
See, it fails to sort and rate even a very small pool of 5 players! You expect it to be correct in a large pool that captures the whole Earth? When localizations are inevitable? And how? By what means? Magic? Just put everything into a black box, shake it, and pretend that it worked because Arpad Elo was a smart guy? This has nothing to do with Arpad Elo. No one questioned that. "Oh no, that's not how it works, we have more players" or "Oh no, you start with an equal rating, everyone starts when others are rated" - that's an invalid argument. Because you compete with equally rated players anyway, low Elos are in a localized pool.

You could already make a bingo table of the same tired responses:

"ChatGPT can't do math, it's only a language model." (Wrong. It's 2024 now btw.)
"You're Janko's second account." (Weak argument, switching to personal attacks to avoid the actual topic.)
"You've only been here 24 days blah blah." (Same.)
"Low-Elo players lack sKiLLzZ they make random monkey moves." (Discriminatory, and a failure to understand rating compression due to rating floors and the randomness of starting opponent strengths.)
"Conspiracies are silly." (This isn't a conspiracy, these are facts.)
"The system will sort things out, you just need to work on your sKiLLzZ and you'll move up." (The system doesn’t work properly and cannot work properly, as I’ve shown. If you don't understand how it works it doesn't mean that it works. There's no magic.)

We need a new rating system, ASAP. Options:

1. Rate players by forcing them to play against a bot, adjusting the bot’s Elo until a 50% win rate is achieved over N games. The player becomes rated and receives the Elo of the bot against which they can win 50% of the games.

2. Use human vs. human statistics, but build graphs and recalculate whenever graphs join (when two players from different pools play each other). Require players to play several games against each other, not just one, to avoid randomness.

3. Add your own. Let's think together!