TT.2022: strange probabilities

Each of 400 people has been waiting for 4 years ( ~100 TT) 
for their chance: to show results with probability ( <1/100 )

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I can assume that more than 95% of them realized this 
"opportunity". But!

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( 1 ) as a rule these were modest cases of the form ( ~ 1/200 )

or 2-3 times ( ~ 1/50 ), etc. --- I consider at least ( < 1/500 ), 
but mostly ( < 1/1000)

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( 2 ) as a rule these were the results ( < 8.5 points out of 11)

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( 3 ) in my opinion, 90% of "those 95%" have already exhausted 
their "reserve of luck" on minor sensations
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( 4 ) as a result, we have 58 "unfulfilled" people out of 400 
( I think that 400 is a lot, but this can be discussed separately) 
and a "heavy burden" falls on them:

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20 cases ( <1500 )

of which 12 cases ( <1/13000 )

of which 3 cases ( < 1/1000000 )

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P. S.
Your reasoning copies the position of boss Chess^com:
https://www.youtube.com/watch?v=P-foqzESGc4

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Nevertheless... In 2022, Chess^com closed about 10 ( FM/IM )-accounts 
that "overcame" the low probability in my understanding. Here you can 
see that the final TT-tables contain usernames of closed accounts:

https://www.chess.com/article/view/titled-tuesday

> Each of 400 people has been waiting for 4 years ( ~100 TT) > for their chance: to show results with probability ( <1/100 )

Maybe I misunderstand you, but no, I described the case for 0.0117% (1/1500), not 1% (1/100). And conclusion from my quickly made estimations is that such results ARE EXPECTED. Even more, a bunch of players among those 400 should statistically show this amazing 1/1500 results once or twice in a while even in the absolutely fair-play system.

Note, that I was considering only a sub-group of TT players, so "amazing" but actually "statistically expected" cases should have happened for like 50-100 people among all who played TT from time to time for several years. It's all quick estimations, not actual calculations, but the logic stays the same.

What Kramnik proposes (as I understand) is to ban people for such random statistical deviations for months, while these results are actually statistically EXPECTED to happen even without cheating.

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> P. S. Your reasoning copies the position of boss Chess^com:

My position is my own, but if it concurs the one of chess.com, maybe they are also not that bad at math? Maybe they also have people with proper education, unlike Kramnik who barely have high school education, as he probably was missing school a lot. After all, he became GM during school, and quite probably was not paying enough attention to the education, including math and statistics, way before that.

0.0117% ~ 1/8547 ( not 1/1500 ) -------- 0.01% ~ 1/10000

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If the player per 4 years ( with your 0.25 ~100 TT ) showed it at least

once ( ~1/100 ) - then he already "doesn’t owe anyone anything" : )

He has already used up the expected "potential of luck".

Any further successes are too much.

.

Your reasoning makes sense if we assume that these 400 players

have ( or are waiting for ) only very large successes.

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Happened 3 times in 2022 ( < 1 / 1.000.000 )

Happened 12 times in 2022 ( < 1 / 13.000 )

This is much more difficult to "explain scientifically"...

> 0.0117% ~ 1/8547 ( not 1/1500 )

Yes, I stand corrected, of course, I meant 0.0117% ~ 1/8561, as your image says for this Mark Plotkin.

The point is, that it is normal, that some IM with rating 2750 on the web site and 2400 FIDE will get 9+ points once in 4 years playing only every 4-th TT. Even more, with 98+% probability there are will be at least one such IM.

Now the interesting part: should you remove this guy from your images, because for his level this result is kind of EXPECTED, or you still have something against his result due to he has only 0.0117% chance in single event? What should be your conclusion for such case?

9 out of 11 can be dialed in different ways...

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If there were 2 losses at the start, the set of opponents will

be weak and the chance will not be sensational ( ~ 1/200 )

Usually weak players come from below and do not meet superstars

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If you lose points in the last rounds - the average rating

of your opponents will be 150-200 points higher ( 2850-2950 )

This is the scenario most often "accompanied" by a chance ( < 1/10000 )

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The probability depends very much on the set of opponents.

Assuming that each of the 400 players ( in 100 TT ) was able show

9+/11 ----- no more than 10% will have "correct" opponents ( ~40 players )

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Now about 400 players : )

Look at the TT tables for 2022-2024 and you will be surprised

at how few players with a rating (2750-) scored 9+ points out of 11

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For example, in 2024 ( 30 TT-tournaments ) there was only one case:
23.01.2024 / Late --- 9.0/11 2292 FM Aleks Sahakyan ( Chess^com: 2716 )

Probability: 1 / 3900

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I will remind you at the end of my messages:

Happened 3 times in 2022 ( < 1 / 1.000.000 )

Happened 12 times in 2022 ( < 1 / 13.000 )

Hello , Michael, thanks for your work and statistics. I would like to note that I have never been banned from the lichess, my only account there is signed with my first and last name. I saw that there is a closed user account on Lichess with a nickname like mine in chesscom, but it’s not me.

I'm sorry...
The public was misled.

Best regards!
Good Luck!

How do you calculate the probabilities of the result of a single game between 2 people in TT?

E.g. Player1 with 2800 blitz rating on site and Player2 with 2500 blitz rating on site.

I am pretty sure that even for this first step your approach is not good enough to be reliable. So, please describe the way you calculate this "simple" step.

https://www.chess.com/forum/view/tournaments/tt-2022-strange-probabilities?page=1#comment-101751169

1. The question is how you estimate this? What is the model?

2. Does it takes into account that some players are MUCH better in 3+0 than in 5+3, and for others is can be the opposite?

Because rating of user on chess.com does not reflect time control differences, as I understand.

A player with a 0.0117% chance to get a good result in one tournament has around a 1.1632% chance of getting it at least once in 100 tournaments.

100 such players have about a 68.9654% chance that at least one will get that "bannable" good result.

A common fallacy in applying statistics is that people look at only the chance that one particular person had a good result, not the chance that somebody at that person's skill level has a good result. It then punishes people for having the good tournament that somebody was going to have if everybody plays clean.

( 1 ) Stop telling tales about 400 ( <2750 )-players 
who are ready for a sensation like 9+/11 at any moment
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2022-2024: ~ 240TT
2022-2024: only 12 ( <2750 )-players scored 9+/11
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12 out of 240TT: 1/20 - the chance that in a single TT 
someone out of 400 will score 9+/11 ( 5 times per year )
.
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( 2 ) Roulette. Black appears 100 times in a row.

But ( Black / Red )-chances are still 50 : 50
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No one is interested in the past results of these 400.

Their potential to score 9+/11 in the current TT is 1/20
( 5 times per year )
.
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( 3 ) As always
Happened 3 times in 2022 ( < 1 / 1.000.000 )
Happened 12 times in 2022 ( < 1 / 13.000 )

Very minor point: In roulette (European) the Black/Red chances are 48.65:48.65: (2.7 chance of green zero). The stated chance (0.0117%) is between the chances of 12 Reds in a row and 13 Reds in a row. That is a low percentage but it is pretty much guaranteed to happen on a regular basis when there are enough hundreds of spins made (there is an old strategy of betting on Red and doubling your bet every time you lose because eventually you win it all back - but eventually you hit a long string of Blacks and either hit the table limit or run out of money, for instance even after only 10 losses in a row your 11th bet would be 1024 times the size of the initial bet in an attempt to recoup all of your losses and have a profit of the amount of that initial bet).

More on point: with each of 400 different people having an individual 0.0117% chance to score 9+ the chance that at least one of them would get 9+ is 4.57% which is probably what you meant by 5%. The calculation is [(1 - 0.000117) to the 400th power] multiplied by 100 to make it a percentage, and the chance that at least one would get that in 50 TT events is 90.37% (ignoring the self-selection that prunes out some of the participants that are not on top of their game - I've directed FIDE norm events and those players are often on the top of their game). That would mean that, on average, one in 22 of the TT tournaments would have a 9+ scorer (around 5 out of each 100). This is based on the assumption that your 0.0117% chance is correct.

If 5 is a normal year then 3 is a little low and 12 is high but plausible.

In class tournament sections (all players within a rating band) the winner out-performs everybody else in the section. Some figure the winner but be underrated or cheating but that ignores the fact that somebody is going to win, and whoever that somebody is will have gotten the breaks to outperform the field.

0 / 5000000
1 / 1250000
1 / 1000000
1 / 312500
1 / 71428
1 / 69444
1 / 56818
1 / 31645
1 / 22222
1 / 18450
1 / 16949
1 / 13812
1 / 8561 --- 0.0117% ------ @bifree took this as a mathematical basis : )
1 / 7418
1 / 6188
1 / 3668
1 / 3380
1 / 2981
1 / 1853
1 / 1660
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Now two people are building their conclusions on a false basis
.

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Look here again:
0 / 5000000
1 / 1250000
1 / 1000000
1 / 312500
1 / 71428
1 / 69444
1 / 56818
1 / 31645
1 / 22222
1 / 18450
1 / 16949
1 / 13812
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( ? ) How many players and decades will it take to explain such probabilities in 2022
.

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Once again I present the table from the starting message of this topic:

1. How you estimate the basic Player1 vs Player2 outcome?

2. What is your model for that?

3. Does it takes into account that some players are MUCH better in 3+0 than in 5+3, and for others is can be the opposite?

Help / Page 1:

https://www.chess.com/forum/view/tournaments/tt-2022-strange-probabilities?page=1#comment-101751169

Help / Page 2:

https://www.chess.com/forum/view/tournaments/tt-2022-strange-probabilities?page=1#comment-101753441

Help / Page 3:

https://www.chess.com/forum/view/tournaments/tt-2022-strange-probabilities?page=1#comment-101754779

Michael, you just accused someone of cheating, and spread misinformation about them having been banned from a different site. Then, when they corrected you, your response was basically "lol sorry". It's not inspiring confidence that you are taking seriously the possibility that you are falsely accusing people. And even if you don't accept any criticisms of your math, you must still always accept the possibility you are wrong.
Please don't pretend that you aren't making accusations either. Why would you have spread that misinformation about snowlord if you weren't trying to build a case that he is a cheater?

I show probabilities. 
I don't blame anyone.
The snowlord-case demonstrated a fresh example of an anomaly.
And nothing else...
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People write here about anything.
Chess^com does not comment.
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( ? ) Explain what it was ( in just one 2022 year ):
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0 / 5000000
1 / 1250000
1 / 1000000
1 / 312500
1 / 71428
1 / 69444
1 / 56818
1 / 31645
1 / 22222
1 / 18450
1 / 16949
1 / 13812

......

Don't argue in bad faith. Why did you incorrectly state that snowlord was banned on a different site, if not to increase suspicion that he is a cheater?
This is the same as Kramnik. You're not admitting what you're doing. If that's because you haven't fully understood what you're doing, that's worrying. False accusations can be harmful. You should take that seriously.

I apologize again. I can do it 20 more times...

I also removed the message about snowlord from the topic.
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Unfortunately, no one wants to talk about extremely low probabilities...
Explain what it was ( in just one 2022 year ):
.
0 / 5000000
1 / 1250000
1 / 1000000
1 / 312500
1 / 71428
1 / 69444
1 / 56818
1 / 31645
1 / 22222
1 / 18450
1 / 16949
1 / 13812