Investigating Hou's pairings

by Albert Silver
9/28/2017 – There is a bit of déjà vu in the current controversy surrounding Hou Yifan's pairings Isle of Man. Readers will recall how Hou resigned her last round game in the Tradewise Gibraltar Masters after just five moves to protest what she felt had been manipulated pairings against women in seven out of nine rounds. Four rounds paired against women in the Chess.com Isle of Man International, was unnerving enough to lead her to take a fifth round bye. To set everyone's mind at ease, we investigated and share the results. | Photo: John Saunders, Gibraltar 2017

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‘What are the odds’?

Hou Yifan had to be asking herself this question. After all, while both tournaments certainly include women, Yifan herself among them obviously, less than 15% of the participants in the Masters section are female. Hou has been the overwhelming queen of the game since Judit Polgar’s retirement from competition, and remains the strongest female chess player since her great predecessor. After dominating the women’s competitions, the Chinese prodigy finally announced her withdrawal from them, and would dedicate herself to realizing her potential, seeking to hone her skills against the best players she could face. There is no getting around her huge edge over her colleagues, and it becomes impossible to really progress when you lack proper competition.

Opens such as the Tradewise Gibraltar Masters and the Chess.com Isle of Man Open offer a rare opportunity to face players of all strengths, including the crème de la crème with giants such as Magnus Carlsen, Fabiano Caruana, Wesley So, Vladimir Kramnik, Hikaru Nakamura, and so many more. Hou knows that she may easily face her female colleagues there — not that there is anything wrong with playing them — but she is there to seek new battles and challenges. And women are a strict minority, so the chances are remote, aren’t they?

Hou vs. Shvayger

Hou Yifan vs. Yuliya Shvayger in round four | Photo: Chess.com / Maria Emelianova

Gibraltar flashback

In this frame of mind, the ninth round of the Gibraltar Masters seemed almost a bad joke, as she found herself paired against her seventh female player, Nino Batsiashvili. What are the odds? The odds, even from an intuitive perspective, are remote indeed. So much so that she could not believe they were a genuine coincidence. In protest, she resigned her next and last round game in Gibraltar after five moves.

After five moves, Hou's resignation to a shocked GM Lalith Babu | Photo: John Saunders

The news was echoed around the world, not just in chess circles and media, but mainstream media such as ESPN and Der Spiegel to name a few. Now, roughly eight months later, she has started the next largest Swiss of the year and after four rounds has found herself paired against four female players! What are the odds? Grandmaster John Nunn, a PhD in mathematics, told us precisely calculating it would be an exercise in futility.

"Estimating a probability for this would involve so many assumptions that the resulting figure would be fairly meaningless."

Although it would certainly be interesting to know, the real question that needs answering is whether or not the pairings are indeed honest and the result of a probabilistic fluke (i.e. a massive coincidence), or has there been some slight tweaking behind the scenes, so subtle that it would be hard to prove without an exhaustive autopsy. Readers may be interested to know that just such an investigation was conducted for Gibraltar.

FIDE Arbiters Magazine cover

The first came about not long after the end of Gibraltar, and was conducted by none other than FIDE. In the fouth issue of the FIDE Arbiter’s Magazine (pictured), a new publication issued by the FIDE Arbiter’s Commission, three cases were studied and reported upon by the arbiters, the first of which was the Gibraltar pairings.

Each and every round’s pairings were analyzed in detail to see if even one single case was possibly the result of manipulation. Each case was verified, not by checking a computer, but checking with the system and pairings by hand, a long and laborious process. Each time the female opponent she faced was incontrovertibly correct.

Here is a sample of the analysis on a key encounter in the 8th round against Ju Wenjun:

8th round

After winning her seventh game, Hou Yifan has now 5 points, like other 19 players. There is a MDP (#27). All in all, in the bracket with 5 points, there are 21 players - 10 WS and 11 BS. Let’s look at the full table:

There is a new row in S2, signaling that #67 has already floated down in any of the last two rounds. Thus, accordingly to the FIDE Dutch rules, it means that he is protected from floating down again. The floater will come from the BS – but, as #67 is protected, the obvious candidate to float down is #45.

The MDP (#27) is a BS who, since in the bracket there is parity, should meet the first WS (i.e. #11). If we then exclude the candidate to float down (#45), we remain with 16 players, 8 WS and 8BS. Hence, we can use the usual trick (#22 is WS, so we are interested only in pairs S1-WS vs. S2-BS).

These pairings yield no problems. The opponent of Hou Yifan (#22) is #38, i.e. Ju Wenjun.

Readers can find the entire issue and others, in PDF, at the FIDE Arbiter's website. It was an impressive article, done methodically, so as to remove any doubt on the conclusions at the end.

It should be pointed out that had the claims been so ludicrous as to be without merit, the authors would not have gone to such extensive trouble in their investigation. Nevertheless, roughly eight months later, we have the same situation in extremis: four rounds, four women. Can lightning really strike the same person twice? In so short a period no less? Needless to say, we — and many others — are completely sympathetic; on social media and news sites, the striking coincidence seemed to stretch the boundaries of credibility to the limit.

Getting to the bottom of things

The first thing we did was to consult the arbiters on-site, directly. It wasn't a matter of suggesting foul play, but to know whether it might not be some software issues, that took into account the presence of female players or any other specific group, biasing the pairings in some remote way.

Chief Arbiter IA Peter Purland answered promptly, showing in his reply just how seriously they took the matter of pairings in general:

I can confirm we are using Swiss Manager version 12.0.0.171 (21 June 2017) and Swiss Master version 5.6 (build 12). These programmes do not use the same pairing programme.

Our procedures are that I input results and make pairings with Swiss Manager, Deputy Chief Arbiter IA Arno Eliens does this in Swiss Master independently. Then we compare full pairings of both programmes and only if these are exactly the same do we publish the pairings.

Kind regards,
Isle of Man International Chess Tournament
Chief Arbiter IA Peter Purland

Was it possible that some form of manual intervention had been done at some level? What about genders? It is, after all, a data field used in such pairings programs, perhaps that had been used in the computer's algorithms? Once again, our questions were answered clearly and promptly (emphasis added):

Gender is a field in players' data — as it is in FIDE data. However, it is not used in the pairing algorithm for computer pairings. We do not use the manual pairings option (except for the first round to insert the random pairings made).

For further specifics of the software used, we would like to refer you to the programmers.

Indeed, in the interest of due diligence, we did consult the programmers, asking them to look at the pairings, and tell us with certaintly whether they were the result of pure, unfettered software pairings, with no outside input. Heinz Herzog is the author of Swiss Manager, the most widely used, and progenitor of Chess-Results.

I checked the first 6 rounds of the Masters Open. I can confirm, that the pairings was done without manual intervention.

Best regards,

Heinz Herzog - Swiss Manager

These findings have been passed on to Yifan, who was forced to wonder what bizarre twist of fate had made her victim to such an incredible series of coincidences. Nevertheless, she was reassured, as were we all, that everything was in order. Having received a half point in her 5th round bye, Hou Yifan is paired in round six against GM Panchanathan Magesh Chandran...a man!

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Born in the US, he grew up in Paris, France, where he completed his Baccalaureat, and after college moved to Rio de Janeiro, Brazil. He had a peak rating of 2240 FIDE, and was a key designer of Chess Assistant 6. In 2010 he joined the ChessBase family as an editor and writer at ChessBase News. He is also a passionate photographer with work appearing in numerous publications, and the content creator of the YouTube channel, Chess & Tech.

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Martas Martas 10/1/2017 08:13
@Rudoch - using your example with 20 red, on it's own nothing is wrong about it. But once somebody would win huge amount of money because of 20 red in row, you have to expect big investigation if there was no cheating.
Same applies for chess cheating, if somebody plays too many tough computer moves, he will be subject of investigation. And similar suspicion that pairings were manually modified applies here, probability is too low and motivation for manual modification can be found as well. Unlike (motivation) for events like playing 4 players whose name starts with S.
Rudoch Rudoch 10/1/2017 03:50
@Masquer: I do not ignore the statistics I use it. Ok, let us count a little. What is the probability 20 reds in a row? The red colour in the first round is approx. 48,6% or 0.486 (do not forget green colour, zero number). 20 reds in a row: 0.486 exponent 20 which is 0.00000055 or 0.000055%. Count yourself what is the probability to see the sequence I wrote below: rbbrbrrrbrbbrrrrbrbb. And yes, the same 0.000055%. So 20 reds in a row is a human story only behind the statistics. It is not any exceptional sequence among all possible combinations red/black.
Masquer Masquer 10/1/2017 07:27
@Rudoch: your ignorance of sound statistical concepts is astounding. 20 reds in a row at the roulette and that is normal to you? Give us a break. That would be very unlikely and very suspicious. But I suspect nothing would convince you, since you can't grasp such basic ideas. I suppose a bunch of chimps could type out a Shakespeare play given enough time, according to the type of (non)thinking you embrace.
joshuar joshuar 10/1/2017 06:20
It "looks" like the arbiters aren't Trying to bias the pairings, but it would be interesting to see someone replace "female" with "male" and replicate the pairings to see if the program has a bug that even the programmer doesn't seem to know about.
Rudoch Rudoch 10/1/2017 12:41
@FramiS - and one more scandal: Hikaru Nakamura did not meet any player 2700+ in his 8 first games even if he is currently on the second place! And he faced 4 players with their names starting by letter "S" (Shirov, Sethuraman, Sargissian and Sutovsky) what seems to be very unusual and suspicious! :-)
Rudoch Rudoch 10/1/2017 12:16
@Martas - playing 9 women in a row seems to be pretty exceptional but it is not. I can give you another example. You see vehicle with its registration number AA99AAA and you say: "What a lucky day I saw that exceptional vehicle!" I can reply: "I also saw an exceptional vehicle with number GW62HDK." Yes, your vehicle is more interesting (like pairing 9 women in a row) but the probability to meet AA99AAA or GW62HDK is the same. Another example: You play the roulette in the casino and red colour falls twenty times in a row which looks weird but the probability twenty times red in a row is the same like any other combination of red/black colour, for example red-black-black-red-black-red-red-red-black-red-black-black-red-red-red-red-black-red-black-black.
FramiS FramiS 9/30/2017 11:20
@The_naked_king They are published more or less immediately after the last game. But every one overlooked another scandal Adhiban played in his 8 first games against 6 compatriots which is very unlikely, the pairings must have been rigged. Adhiban will offically protest.
The_naked_king The_naked_king 9/30/2017 09:44
Just one more question, once a round is over, why arent they able to immediately let us know who is playing who ?
Enter the data into the software and publish the pairings, but no....they always need time to cook the pairings, keep on !
Martas Martas 9/30/2017 08:06
@Rudoch - if we stay only in chess (same logic applies in many other places), low probability is basis of investigation regarding cheating, if somebody plays too many top computer moves, he will become target of investigation, because of low probability that he would manage to find all those moves on his own. Once there is reasonable motivation for cheating, lot of effort is spent to prove or refute the suspicion for good reasons - remember Ivanov's case and many GMs who didn't want to play tournaments with him.
Same logic applies for possible manual changes of pairings in order to have more matches of Hou Yifan with women, if something like this would be found it would be pretty embarassing.
The fact that probability is the main reason (but not the only one) for suspicion is not an argument to stop any investigation. Or would you say that cases when somebody plays many computer moves during the game should be ignored as well?
Btw. playing 9 women in row in tournament with less then 20% of women would be pretty exceptional. Or do you know some cases like this to support your last sentence?
fgkdjlkag fgkdjlkag 9/30/2017 05:13
Open-source pairing software is an interesting idea
1. pairings are easily verified by anyone
2. if there are abnormalities in the code that creates a biased result, such as Hou Yifan being paired against too many women (which seems very sexist - as someone else pointed out, it would cause an uproar if a man complained he was playing too many women, and it should create an equal uproar in the current situation, which based on the comments and discussion, it has not), it will be quickly discovered

But I'm assuming the pairing software is commercial?
Rudoch Rudoch 9/30/2017 12:12
@Giraffe. I agree with you that 90% hypothesis better explains the event. I even agree that the pairing with 9 men in a row is much more probable than the pairing with 9 women in a row. But this is irrelevant. You are paired with the chessplayers, with the numbers, no matter if you are man, woman, blond hair, blue eyes, lefthand, mormon, blue colour, gay, hispanian,... There are a billions of combinations how to be paired in the tournament of 160 people and each of those combinations has the same probability. So, 9 women in a row sounds interesting but this is not any exceptional pairing.
GiraffeSanitizer GiraffeSanitizer 9/30/2017 01:42
@Rudoch. When you say that Hou Yifan playing 9 women in a row is equally likely to any other sequence of pairings, that is not strictly true. If she was paired with 9 men in a row, that would be much more probable.

I like your philosophical inclination for appreciating the improbable events that happen every day. But let me ask you: if hypothesis A says an event is 90% probable and hypothesis B says the likelihood is less than 1%, which hypothesis better explains the event?

We are trying to be polite, so we only discuss hypothesis B which yields a very low probability for what has unfolded. Truth be told, there is an hypothesis A which would provide a better explanation.
genem genem 9/29/2017 11:54
@Steven E DuCharm. Greg Shahade has also publicly favored random pairings. But...

Best might be the *same average Elo*: Most fair would be to have the pairing algorithm do its best to have each competitor face roughly the - *same average Elo* - level opponents by the time the last round ends.

Suppose round 1 pairings are random. Then, if you played against the highest rated player in round 1, then in round 2 you might play against the lowest rated player. If instead your round 1 opponent had a middling Elo rating, then so shall your round 2 opponent. For round 3 the pairings are again random, and then round 4 opponents have high-low-middling Elo ratings to compensated for round 3 disparities. And so on for subsequent pairs of rounds.

Unfortunately, for Tournament Organizers and the audience, the Swiss system tends to create more excitement by bunching players' scores more closely together, to heighten the a sense of struggle among the players. Also, it tends to have the last round be between the two players who have the highest scores going into the last round, the final climax.
Rudoch Rudoch 9/29/2017 11:33
@Giraffe and other statistician - unbelievable things are happened every day, every moment. What is the probability that you was born to your parents? Just combine the number of sperms and eggs of your parents and you will find your existance very improbable. But you all are here. Even if Hou Yifan would be paired with 9 women in a row, there is not any reason to be suspicious because the probability of that pairing is the same like any other pairing. Just your brain may see it a little strange but it is not.
Johannes27 Johannes27 9/29/2017 10:53
The no 74 (not even on the top 50) of the top elo list is causing trouble because she wants to change the rules and get drawn with stronger players. Why should Carlsen, MVL, Kramnik and so on want to play against her and not face better opposition ?
Michael Jones Michael Jones 9/29/2017 10:28
@GiraffeSanitizer - at the time of the Gibraltar tournament, I did a slightly more detailed calculation based on the fundamental points of the Swiss system: as far as possible each player is paired with an opponent on the same score, and no-one can play the same opponent twice. If one assumes that after those points, the pairings are random (i.e. she has an equal chance of being paired against anyone on the same score whom she hasn't already played), then the chances of her playing 7 (or more) women were about 1 in 23,000. I haven't done the equivalent calculation for the Isle of (Wo)Man tournament.

However, one hopes that the publication of the detailed explanation of the pairings should be sufficient to satisfy people that they were correct; it would have saved a lot of fuss if that explanation had been given during the Gibraltar tournament, rather than waiting for a magazine published after it ended. It's stipulated in the tournament rules that an arbiter should, if a player requests it, be able to explain how the pairings were arrived at; "that's what the computer said" is not a satisfactory explanation, since it says nothing about how the computer derived them. While working out the pairings for a large tournament by hand is, as the article mentions, a laborious task, doing so is the only way to make the derivation of them clear to anyone who wishes to know it, and to refute any claim that they were somehow "fixed".

Incidentally, Hou has increased her chances of being paired against more women by losing to some of them. If she beat them all she'd have to play the men because there would be no other woman on the same score...
fons fons 9/29/2017 07:58
@ flachspieler

I don't think it's that simple. It's a common mistake to think that with real randomness stuff has to be evenly distributed.

https://www.random.org/analysis/

(Rudoch's example was of course not an example of a chance event. Me writing down a long number and then you guessing it correctly: that would be a chance event.)
The_naked_king The_naked_king 9/29/2017 07:16
I dont trust them at all , 0 trust ! As mentioned by Peter B, they should use Open source, so we all can have some transparency.
Are they denying that they did not use the gender variable in this "random " pairings ? I do not buy it! They have just been exposed.
They might have convinced some 80% of the people, but the other 20% are just mature enough to not swallow these cheap tricks.
ps: Even Round 6 is a bit suspect, 10 indian players , playing against each other ? Hummmm
Raymond Labelle Raymond Labelle 9/29/2017 04:37
"She is making all this mess and nobody bans her!"

Here is what Hou Yifan declared about this, before any kind of verification was made (in respect of the Isle of Man tournament).

""It is difficult to imagine that the organisers are doing this on purpose," she said, reached for comment via Skype. "There is no reason for that." (see: http://en.chessbase.com/post/isle-of-man-the-unblemished-record )

I do not think this deserves a ban.
Raymond Labelle Raymond Labelle 9/29/2017 04:35
Reminder: the programs are only a tool to accelerate the process of pairing - which can be done without any computer by applying the Swiss rules. The goal of the program is to apply the rules - not the other way around.

You do not need to know anything about computers to verify if the pairings were made according to the rules and whether a possible discretion possibly permitted by the rules has been used. And if it is a bit tedious, it is less so than making unnecessary computer analysis of the programs: an arbiter has to be able to do the pairings without any computer assistance between rounds. A bit tedious, but doable in a relatively short time.
GiraffeSanitizer GiraffeSanitizer 9/29/2017 04:34
It is important to consider the actual probability of this event. The upper bound of the probability can be easily calculated to be 0.05% or 1 in 2000. I get this with the knowledge that the participants are %15 female, and treating each pairing as an independent event. So that is (0.15)^4. This is an upper bound, which means the actual probability is lower than 1 in 2000. Why is it an upper bound? As we know, the percentage of eligible female pairings will generally decrease as Yifan's score increases. That means in most of her rounds she actually has less than a %15 chance of being paired with a woman.

We also know that this is not an isolated "coincidence." In Gibraltar she faced women in 7 of 10 rounds, which is even more unlikely. Assuming the same male to female ratio, the Gibraltar probability is less than or equal to 0.013%, or approximately 1 in 7700.

This is calculated as (P[Male opponent])^3*(P[Female opponent])^7*10C7. 10C7 is 10 choose 7 to account for all the possible orderings of male/female opponents. Again, this would constitute an upper bound, making the actual probability less than 1 in 7700.

Now we have to remember that these two unlikely events are independent, because of course nothing sinister could be happening behind the scenes. So treating them as independent, we get a combined probability of 0.0000065%. That would be a 1 in 15 million occurrence.

Let us put this in perspective. Suppose Yifan was immortal. If she lived 15 million years, she could expect something like this to happen in exactly one of those 15 million years. Considering the human species is about 200000 years old, you have to have a life span 75 times the age of the human species to expect to experience this in one year.
Steven E DuCharm Steven E DuCharm 9/29/2017 04:22
My solution? Random pairings in all rounds.
Martas Martas 9/29/2017 03:09
Johannes27 - you mean losing ELO points is not enough for giving up the game in the last round? Do you have in mind any FIDE rule supporting ban in this case?
And the incident in the World Cup was not a ban, rather scandalous behaviour of organizer - who is as well representative of FIDE, yes I agree, this is absurd.
Johannes27 Johannes27 9/29/2017 01:53
The swiss system pairs players with the same points. The 1st pairs to the firsts player in the middle. If she had scored more points, then she would have played against better players.Please do not also forget that there are many weaker players so the clash between the top players is due to happen by the later stages of the tournament.
She is making all this mess and nobody bans her! However, in the world cup one was banned because of his shorts!! This is completely absurd!
Fisul Fisul 9/29/2017 11:18
Software algorithms sometimes behave in unintended ways. One possibility is that the contents of the gender field affects the pairings that the software outputs in an unexpected way that had been unintended by the software programmers.

One thing that could be checked by someone with the software is that if "male" had been entered as the gender for all players, would the software have output the same pairings as it did with the actual genders entered? Would this still be the case if "female" had been entered for all players or if the contents in the field for players' genders had been entered at random?
Bill Alg Bill Alg 9/29/2017 10:19
Has someone used the exact version of any one of the two programs which Chief Arbiter IA Peter Purland claims that were used (Swiss Manager, Swiss Master), to make the pairings again? Have they changed the genders of all participants to male, in order to discover if it affects the pairings (Vaporator's idea)? _That_ could be called an be investigation. Asking someone "did you cheat?", then when they answer "No", present this as evidence and conclude that all is well? No, sorry, this is not an investigation.
Raymond Labelle Raymond Labelle 9/29/2017 07:08
You do not need to know anything about any computer program to verify the pairings. You only need to know the rules of Swiss pairing - applying them can be done manually. A program only accelerates the process. This article gives an example of the manual application of the rules but also refers to that publication: http://arbiters.fide.com/images/stories/downloads/2017/FIDE_Arbiters_Magazine_No_4_-_February_2017.pdf

In that publication, the full rules of the Swiss system are explained and it shows manually, with full explanations, how they were applied in the Gibraltar tournament.

You here have enough to do it yourself and apply these rules to this tournament, if you wish. Printed copy of the rules, participants and their ratings, bye requests, paper and pencil are enough to do it.

Questions were asked to the programmers, it is true. But I do not see why the programmers of the paring program would be covering up some conspiracy by the organizers of the Isle of Man tournament, especially if lying on the matter can be detected easily, without any use of any program of any kind.

It is true that the rules of Swiss pairing can give some flexibility in the pairings. That flexibility can be used or not. Before using that flexibility, you have a given pairing. It is thus manually verifiable whether such flexibility has been used in making the pairings. Without using any computer program of any kind.
psychess psychess 9/29/2017 06:43
The argument of this article is fundamentally illogical. That is, it argues that nothing happened. It was a bizarre twist of fate. Yet a probability value of 1 in 25,000 is too remote a probability to be explained and when you add in the Gibraltor results it's less probable than 1 in a million. The science of probability indicates something happened that is much more than a bizarre twist fate. There is something else going on here. The article is neither objective or information. It basically makes an argument that claims that the computer made the pairings without giving sufficient detail to understand why other plausible scenarios were not considered. In any tournament, there some flexibility in how pairings are made. I'm surprised the article refused to consider more plausible alternative explanations.
guesting guesting 9/29/2017 06:06
Well, it has been show the calculate for the 8th round, but what about the rounds before it? Show us the calculate about the round 3, 4 and 5, this is more fair.
Peter B Peter B 9/29/2017 04:52
It's time for pairing to be done with an open source program. Then anyone can actually check, rather than rely on the word of the programmers
digupagal digupagal 9/29/2017 02:17
Well she lost to a woman player, maybe it's better for her to first win against woman players and then try her luck against men.

She is no extraordinary, Judith was
flachspieler flachspieler 9/28/2017 11:52
@Rudoch: Your number is not equally distributed.
You did the typical thing, many people do when
generating random digits: they select too many odd ones.
You had 16 odd ones and only 9 even ones.

4 9 7 5 6 3 1 2 2 4 8 9 5 7 5 5 7 8 1 3 1 4 5 8 9

Try better next time!
dhochee dhochee 9/28/2017 11:50
psychess, you seem to have trouble with reading comprehension. Did you actually review the linked PDF which covers a manual breakdown of every round of the Gibraltar tournament?

The guy who said he examined rounds 1-6 was referring to Isle of Man, where only six rounds had been paired.

The article and cited analysis was very informative and objective, and at no point requires the reader to trust anyone. You can view for yourself the procedure that was performed to determine that pairings were accurate. It's not all that complicated.
psychess psychess 9/28/2017 11:29
What an incredibly uninformative article. All it does is point out that the pairings were fair in one round of one tournament. The rest of the article just keeps repeating the mantra, "the pairings were fair" without offering any evidence. One guy says he looked at less than half of rounds and they looked OK to him but we're talking about 13 rounds. The articles goes on to make the completely illogical claim that the odds of such a claim are incredibly rare so it must all be a coincidence. Maybe they should just retitle the article "Trust us. Don't look at what's going on here." Then a bunch of comment tody's claim. Yeah don't trust science. Don't trust statistics. Don't trust your eyes. Trust us. Trust FIDE That kid who beat Anand - Anton Kovalyov. Nothing going on there either. I believe what we need is a careful and open look at what happened because something definitely did happen.
Martas Martas 9/28/2017 10:34
Rudoch: your comment reminds me old joke for programmers about function getRandomNumber which returns number 3 and documentation says "was decided by dice roll which is proven to be random".
One thing is probability and statistics, which brings suspicion and conspiracy theories, lower probability means bigger suspicion (ie. lower rated player beating few stronger opponents sometimes leads to computer assistance accusations). The other thing is to prove or refute these conspiracy theories, here probability / statistics are not good instruments, it can be only misused like in your case with number. Similar to try to refute big bang theory by it's lower probability.
drcloak drcloak 9/28/2017 10:29
Of course the programmers and organizers of the event are going to tell you that the pairings are fair and without manipulation. What do you expect them to do, admit to the manipulation? For some intelligent folks on here, many of you sure are gullible and will blindly believe what "authority figures" tell you. A shame really, that you can't think for yourselves. Have fun in your sleep walking state...
drgenial drgenial 9/28/2017 09:38
Hou. Please, grow up.

Win the tournament first and then show us how big you can open that mouth of yours. Eish.
Vaporator Vaporator 9/28/2017 09:36
Arbiters could simulate pairings assuming that all the players are male and see what happens...
Aighearach Aighearach 9/28/2017 09:24
As a software developer myself, I find it deeply and blatantly laughable that the word of the programmer is taken as being somehow definitive. I mean, of course there isn't a bug, and of course he wouldn't be able to overlook his own mistake, if present.

No doubts were likely dispelled, though people who didn't have doubts are using the opportunity of hearing declarative statements to also issue their own declarative statements.
Rudoch Rudoch 9/28/2017 08:59
I am going to say the random number...hmmm....497563122489575578131,4589. What was the chance to say that number? I would guess almost zero. But it happened, I said that. I can not belive that such impossible thing can be happened. Should I complain to gods or what?
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