Detecting Cheating in Chess

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Detecting Cheating in Chess

With the advent of algorithms capable of beating highly ranked chess players, the temptation to cheat has emerged as a potential threat to the integrity of this ancient and complex game. Yet, there are aspects of computer play that are measurably different than human play. Dr. Kenneth Regan has developed a methodology for looking at a long series of modes and measuring the likelihood that the moves may have been selected by an algorithm.

The full transcript of this episode is well annotated and has a wealth of excellent links to the things discussed.

If you're interested in learning more about Dr. Regan, his homepage (Kenneth Regan), his page on wikispaces, and the amazon page of books by Kenneth W. Regan are all great resources.


Detecting Cheating in Chess

Kyle: So just a quick note before we start this interview. In order for me to keep the data skeptic podcast coming out in a weekly basis, I sometimes need to record in advance especially when I know my schedule and other responsibility make it hectic. Thus, this interview was record a little bit ago and I've been really eager to share with all my listener but my guess get a couple of references like last weekend or a week ago. So if you follow the chess world, just realize that the timing will not quite work out but for everyone else that does not change the narrative so please enjoy.

Kyle: Welcome to another episode of the data skeptic podcast. I'm joining this week by Dr. Kenneth Regan from the Department of Computer Science and Engineering from the University of Buffalo. Thanks for joining me.

Ken: Thank you very much for inviting me to be in the show.

Kyle: So I've been really enjoying these past couple of weeks getting to read your contribution to the blog Gödel's Lost Letter and P=NP as well as your work on computation complexity. But the topic I want to invite you on to talk about this week is one that, as far as I can tell, you one of the world's leading experts on which is about detecting cheating in chess.

Ken: Yes that's right and I've been very active on the past weeks more than I perhaps wanted to be.

Kyle: Oh excellent, well serendipitous then. Maybe we can start with your background on how you first got interested in chess to begin with.

Ken: Well I was a junior player. I learned the moves when I was 5 from watching my dad played with my uncle. And then, at the age of ten I discovered that there where such thing as chess tournaments. And my family very graciously took me into New York City and local chess clubs to play on them and I reaches to just about master strength very quickly. I was a master I think very briefly before age 13 but certainly at age 13. I was one of a number of my friends, all great people, juniors on the New York area chess sciene and elsewhere who would one point work close to the youngest masters since Bobby Fischer. I was also invited as a panelist on the National TV Broadcast of the Fischer vs. Spassky match in 1972 before my 13th birthday. Then I played tournaments as I got to be with junior champion in 1977. It was just absolutely a wonderful thing as a kid but I did not, however, intend to go chess as a career.

Kyle: What made you go into Computer Science?

Ken: I originally wanted to do Mathematical Physics at Princeton. I found physics fairly tough going in an undergrad. But I got into mathematics, and then discreet mathematics which is the mathematics of computing. And then when I went to Oxford my advisor Dominic Welsh got me interested into computational complexity and that pushed me toward computer science.

Kyle: So maybe we could start with defining what it means to cheat a Chess. (Time: 3:00) I assume we're not talking about it doing something nefarious like switching pieces around.

Kyle: Right. Haha. What do you mean when you say, "detecting cheating"?

Ken: Well it's an unfortunate reality of the game is not only for supercomputers able to beat the world's champion as happened when Deep Blue beat Gary Kasparov in the 1990's. And in the middle of 20 aughts even the handheld computer programs and laptops were able to beat humans and that has created a temptation, unfortunately, in some cases for humans to consult a superior computer during what are supposed to be human only game.

Kyle: So am I getting unfair advantage by using my computer to check a move or something?

Ken: That's right and people are quite checking their smart phones in bathrooms especially.

Kyle: aha, interesting. So how about one go about detecting that?

Ken: Well, there are a certain patterns in the moves that indicate proximity to the patterns that come about from computer programs. Number one telltale is just the strength and quality but I look into other factors also that can distinguish computer like play.

Kyle: Presumably if computers were gonna play the same way humans would, you wouldn't be able to detect it. What is it that computer are doing differently?

Kenneth: Well, one of the things is that very rarely they make a perceptible blunder (4:22)

Kyle: Hhhmm

Kenneth: Okay, if you manage to beat a computer and there happen cases of that then you have found something very deep in the position that appeals to your human intuition but that is not easy to demonstrate via a moderate depth search. So you've found something very hidden. Whereas humans make little blunders all the time. In fact, even when I'm playing I'll realized, "Oh didn't see this idea of my opponent Luckily my position still holds together?" So computers just never make large scale overt plunders. There are also some stylistic tendencies. They tend to keep a lot of their options open in a position whereas I've be able to demonstrate humans, if they see an attack, will try to play it and force an early crisis on the game.

Kyle: Interesting, so can you say the certainty that a move is given by a computer vs a human?

Ken: Not any one move, no.  Although there are some people who react, "Oh this was obviously a computer moves". However in aggregates of a 100-200 moves then I can get an overall statistic on how computer-like to play us.

Kyle: So I'm guessing it's comparing two probability distributions?

Ken: That's right and that's how I originally conceive the whole problem. I was going to model it as the distance metric between the probability distributions. One representing the computer and this is very important because you can't just say deterministically what is the computer's move. That depends on many variables including the depth of search, the identity of the computer programs, even how much hash memory you've given it. There's a variation there and of course the human being is a distribution, often fallible distribution, of option. I was originally going to use a metric called Fidelity, which is a distance between distributions measure the computational physics in particular. That name was also a pun on on FIDE which is the acronym of the World Chess Federation and the idea of faith and playing in good faith. But then, one of my former student returning on a visit suggested a different distance measured called Jensen-Shannon divergence which solves a problem with Kullback-Leibler Divergence of being too hair triggered in the treatment of plunders but it lacked other properties that I needed which was a great shock. So I wound up doing something highly elementary.  All I do is I mapped given analysis of positions in a game and parameters denoting the strength and particulars of the human player. I mapped each chess moves to probabilities as if I were painting that move on the faces of many sided dice and then I treat the chess position as the roll of those dice. So I say like for this player the 49% chance of selecting the Knight G5 move, the Queen G4 move is 27 percent and so on down the line. Once I do that I'm able to tap in to the very simple high school stats theory of Bernoulli distributions (7:30): rolls of dice, flips of coins, and not only project the expected mean number of agreements but also the projected variance from Bernoulli distribution theory and thereby project confidence intervals, and since I'm estimating the sample means, the central limit theory come into play. So I'm dealing with the normal distribution and can use a Z-score framework for my statistical projection.

Kyle: Very interesting. Are there certain situations that are more revealing than others? So I'm wondering int particular cases of a game configuration where one move that can make you alive and any move that can end a game for a particular player.

Ken: Right! And that is actually the main statistical principle on which the equation on my model that goes from the chess position to the probability is based. If there is a clear stand out move then not only will the computer find it but it's highly likely that the good human player will find it. That actually was the explanation in the incident began my involvement. Whereas even if you have just 10 moves in a game where for each move there were 4 highly reasonable options which my model will assign probabilities they would be 20-25% for each. Yet if you consistently select the option that show as preferred in my computer task modulo that it too was a distribution and there's some variance, but less. But if you match the computer on 1 of 4 options, 10 moves in a row. That's upward of 1 million to 1 unlikelihood.

Kyle: Tell me more about the training data you have. I presume you have a database of human game you can study and also a computer is there to give distribution. Where is that data set coming from?

Ken: So there is two mode of chess analysis with the computers. This multi-pv mode where the computer is given equal depth of search to all of the reasonable options in the position. And then, there's the single pv which is the regular playing mode of the computer where it focuses its resources on the move it think best and one/ two competing moves. A lot of the art of practical computers when they play against each other in championships is how quickly they can prune away the suboptimal moves. Whereas for my model I need to know the values of all the reasonable moves that a player might be considering and the general landscape or shape of the position whether as you just said it is a forcing position that there is only one move to stay alive or when there's a lot of option and all the various grade and in between. So now for my training sets I have about 10 thousand games of the multi-pv data and I took all games where each player on the game was at one of the century points on the chess rating system. So chess uses the ELO rating system which is popular. People uses that on the other sports or even Nate Silver's website is using it on the Nat'l Football League teams. But in chess the human players basically top out on the 2800s, 2600s is sort of the strong grand master 2400s International master, which is what I am, and 2200s master and so on and classes of 200 expert, 2000 expert, 1800 class A in the United States, 1600 class B and so forth. So for each of the level above 2000, I basically exhaustively chose in their databases now approaching 10 million games for the entire recorded history of chess. From those databases I take all game where both player were within 10 or so of a century point, run those games and I get my training data for the A rated player and then I'm able therefore to relate my two main model parameters to strength on that ELO scale. Then supplementing this I have a vast amount of single PV data. Basically every top level game in the entire recorded history of chess over two hundred thousand games total which may have sound a lot out of 10 millions but a lot of the 10 million games are ones not played in the most standard chess competitions or played by lower players and I also routinely screen about 80 thousand games out of world's top events every year. This is what has been codified as the screening mode. So I can get a first look at the play and relate it to distributions of tens of thousands of other performances by players of all ranks to see how much of an apparent outlier it is. (12:39) Now, this is exactly the situation that I had this past weekends. There is an anti-cheating group on facebook and on Saturday I know that post about a surprise winner of a tournament and whispers. When I run the screening test indeed, the person was on the edge of what I've coded as 'the red zone' saying "Look at this a little bit further"

He defeated a grand master almost 500 points rated above him in the last round. But when I run the full test which is based on the training data using the multi PV mode, it gave a z-score even under 1.5 let alone the minimum 2 to claim any kind of statistical significance. Meaning that basically the guy had rolled with a lot of punches and indeed he was dead lost against the grand master in the last round but the grand master got over hasty. So I post a feedback saying this on facebook and it seem to quiet the rumors for the moment. But it's actually one of several test cases for the viability of statistical input that I'm getting. The thing is I confirmed to the arbiters of the tournament had acted correctly based on the less regular information that they saw. So they don't have scientific computing resources but they have good chess marks and were able to observe a lot of the things about the game the choppiness, the force situation, the fact that he was lost against the grandmaster, and reach basically the correct and same conclusion.

Kyle: That's good to hear. I would imagine that you're never saying with certainty anyone cheated. You're just talking about the probability that this happened. And. . .

Ken: That's right.

Kyle: To what degree do you want to have confidence before an action should be taken?

Ken: That's right. So I'll tell little bit about the background and history of this. Upon until 2+ years ago,(14:31) the highest Z-score that I got in cases I was involved in was about 3.5 which corresponds to 4300 about to 1 odds against null hypothesis. Although very important, what it really means is that the incidence of such a deviation occurring naturally among non-cheating players. And every week, there are more than a thousand players taking part in tournaments around the globe, tournaments significant enough to be aggregated on a website called The Week in Chess, run by Mark Crowther in England, whose games I can get to test for the tournaments that published their own games on their own website. So if you have that and you get 4,000 player performances every month. So if you got 4,000 to 1 odds, if you look at every game for a month, you'd see that happen all the time. So you have to be aware of how your sample was selected or whether there are any other factors that brought it to your attention apart from people going over the games with computers in noting a high correspondence. So my role was that there had to be independent evidence. Now in one case 4 years ago, there was independent evidence based on text messages that had been preserved since a cellphone was used to transmit communication. The content of the messages could not be entered into a civil court case for under privacy reasons. But the fact is they're being there and the times could be entered an evidence. And that was an independent factor so then my input was that I had this deviation over three. There was another reason that had selected this performance for attention so the full significance I said came into play. Also, I was able to distinguish the moves on games when there been lots of transmissions from the other game to the tournament played by this player. And that was a very clear distinguisher; the quality distinction was 3200 versus 2550. So certainly, apart from the confidence assertion, there certainly was that distinction.

But upon until January 2013, I did not get any Z-scores above 3.5 and then suddenly ones above 5 tending closer to 6 tumbled out for a case of a Bulgarian player playing in the tournament in Zadar, Croatian. And that prompted me to run an open letter and write a blog post raising this as a further level of problem, a really philosophical problem of what role statistics should have in adjudicating this kind of case. The player Borislav Ivanov have never been totally caught although there was a wand beep on the shoe and in another tournament people observe briefly a wire on his chest. But he was never really apprehended. He was allowed to walk out of the tournament after being defaulted. Actually, even came back for his last two rounds, in one of them was undisturbed. I of my own hypothesis but it still is mark that no one knows exactly how he's doing it but of course they had to phrase "if he's doing it". Let alone that when I combine all these tournaments, I get Z-scores over 7 and we were talking getting to above billions to one to trillions to one odds range.

Kyle: Yeah, that's a higher standard of evidence. I think you were saying when we talked earlier the Higgs Boson standard is 5 sigma, so...

Ken: That's right.

Kyle: Fairly convincing from statistical point of view

Ken: I mean that I was able to use the 5 sigma standard because my unit is a thousand player performances is one week of the weekend chess. If 4.75 sigma is 1 million is to 1 odds, then I can say that is 20 years of chess tournaments at a level were likely to be most concern with. And if you use 5 sigma it's almost 3 million to 1 that could be 60 years, meaning that you would expect to misclassified someone at 5 sigma, to make an errors once every 60 years. And then the question is: is that an acceptable rate of error? So then I was able to point to, that's the same as the standard that's used in Physic for scientific discovery, but watch out the Higgs Boson has now risen above 7 sigma so that looks safe but a video announcing a gravity wave discovery a year ago begins by knocking on the door of the cosmologist whose theory was supposedly verified and the guy says, "It's 5 sigma" but it wasn't. They made a systematic mistake in their modeling of intergalactic dust and the result is Physics Today said death knell  for their work in February. So that went away, apparently. (19:40)

Kyle: What sort of sigma value do you think we might achieve if we entered an actual algorithm in a tournament, and someone just read the moves directly off the computer?

 Ken: Ah yeah! Then if the algorithm played over 200 moves I would be pretty confident of getting deviation above 5 sigma. Although it will be enough that wouldn't be perfect correspondence because my work does not try to forensically identify a particular algorithm.  Instead it's testing for the general computer-like nature and the different chess programs do not agree with each other. Moreover when they played by themselves they tend to get themselves into positions that have a lot more options, where even at their own level in their own projections of agreement rate would be closer to 50 percent than the over 60 percent that one would get for the same computers playing human games so that may even make their agreement rates look lower. It's definitely a complication for my model that the computer programs don't agree with each other to such an extent. It imposes upper limits on the sensitivity

Kyle: Sure

Ken: But it does seem that I get... well the policy of the Z-score above 2.75 in my work as a commission member on the world's chess federation and with the new regulations that was approved last year, z-score of 2.75 is enough to claims statistical support in a case where there is independent evidence and z-score above 4.0 is enough to open an inquiry. We don't however though have to write of judgment for 5.0. (21:30)

We backed off that because a lot of people are understandably uncomfortable with using statistic to past judgment, statistic alone.

Kyle: Yes, I'm gonna link to the open letter on That should mention and it sounds like the ah...

Ken: It's January 2013. Yeah! Well a lot happened since then.

So what happened is there were more incidents in the spring of 2013, including a junior player being caught with the cellphone in a loo and in a rust by his opponent who happened to be beyond a Romanian National soccer team. And the World Chess Federation realized that isn't just an Association of Chess Professionals matter, this affects the entire game something needs to be done. So to their great credit they put resources and convened commission. And one of the things we did oddly enough actually was we loosened a reaction requirement that we feel have been to strict about completely banning cellphones from playing halls. We put other rules into to make sure so player will not be able to walk around with cellphones during the games. Or have them in their pockets where one player was caught getting buzzes from the cellphone on his thigh that he could decode. So you're not allowed to have the cellphone on your person during a game. But we don't want to completely inconvenience people by not making them able to have the cellphones with them because it might be coming from work and my not have a car that they could stow or room that they can stow the cellphone in.

So I became active with the committee and our committee really constitutes itself in terms of operation this year. And I'm right now writing a formal report on one case while dealing with several others which actually though they are furnishing more input into my new system using multiple programs and showing how consistent they are with each other.

Kyle: Very neat. So I would guess going back to some of the different algorithms, you know they can each have different databases that they're accessing in terms of finishing moves or slightly different pruning strategies or may be heuristics baked in that account of some of the differences but I was really fascinated by the point you made that they tend to play with many more opportunities open at the same time. Do you think that's the defining characteristic of computer vs. human play: the ability to balance so many independent strategies?

Ken: It might be... it's certainly... in practice gives me a 5 percent margin. I analogize that to the idea that computers play the role of Spock to our Kirk like in a star trek episode. You know McCoy and Kirk want to go in an intervening ride right away but Spock's caution make hold it. I think that that's actually I'd like to see that in large into a useful personality aspect of personal digital assistance in general that they are not there to make up our mind for us but rather that to show us the option

Kyle: Yeah

Ken: But yes... That is a... that more way to see is a definite property of computer games on balance they take longer and that they don't have early crisis as quickly as human games do.

Kyle: I'm a relative to chess novice. Let's say for some reason I decided to dedicate myself to the game and I started playing 10 hours a day, six days a week. But rather than studying by you know reading classics, looking a classic games and books and things, I chose to develop my craft strictly by playing against the best algorithms that are out there. Do you think I would develop a style of play that could have a false positive in your detection?

Ken: Well, I'm fielding exactly this question on Facebook from someone like within the past hour. Okay, it's a common point, it is quite possible that players have become more computer-like and not might even be reflected like slight increase in overall quality that I'm registering within the past 10 years. But I don't think you're... I've yet to see a demonstration that someone can become really adept at the game solely by playing with the computer. For players under two thousand what is said to develop your skill the most is pattern  recognition of positions and their tactics which you can get by playing over famous games like you know, like the games played by the Russians in the 50s and 60s are great for this. And I agree with the contention of a documentary, "My Brilliant Brain" by the BBC and National Geographic featuring women's world champion, Susan Polgar. That it is the face recognition, and pattern recognition parts of the brain that are activated most when playing chess. So it's going over computers is going to promote this ability, but it comes from seeing the patterns, I think, rather than contending against the algorithm. And up to 2000 level people are saying it's more important to understand the basic tactical patterns or tactical quizzes. You know, flash a whole page of black to move and win and that is the best way to improve. And then, when you get over expert level then the  deeper parts of strategy fill in.

Kyle: So I would imagine it's only really been possible to cheating in this way in perhaps the last 15 years when the algorithm got to the right level and even the ability to kind of, well, we cellphones quite the same way on the 90's but now we have very small on our pockets. I guess there were some situations that the players are getting a buzzing to indicate the move...

Ken: Yes, there's a meme that your iPad now has the power of the world's top supercomputer from 1994.

Kyle: Ahahaha

Ken: I don't know that's quite true, but it's a meme anyway. So yes that's the problem. Actually 20 years ago there was perhaps what was intended as a proof of concept at the world open. A player was given the name John Von Neuman, the name of a famous computer pioneer and had a computer in his shoe and he was caught while the tournament was going on. He was able to I think defeat or draw against one master rated player and I can say various more things about it, but that and another case in the 90's are considered to be the beginning. But the real beginnings were whispers against the Bulgarian Grand master Veselin Topalov in the candidate's tournament for the world championship in 2005 allegations which my work does not support and then in the ensuing world championship match in 2006 against the Russian Vladimir Kramnick, Topalov himself with accusation of cheating based on the coincidence of moves with the then leading program Fritz 9 which is manufactured by chess base.  So Topalov's manager Silvio Danailov release an accusing letter sighting coincidence statistics but not giving any methodology. Now I actually know that he use a flawed methodology to generate that. I tried reproducing the result independently and 4 the 5 games I didn't but on the 2nd game of that match where Tupalov was wining brilliantly but then lost his way and eventually lost the game, something which really must have upset him. I do get it on the 2nd half of the game reproducibly with 2 different programs, Rypka and Fritz, Vladimir Kramnick matches over 90 percent which is unheard of human percentage in general, but the reason is, the explanation I found is that most of Kramnik's moves were absolutely forced: first to stay in the game and later the only way to keep his advantage. And that lead to statistical principle that I talked about earlier and basically all of my in depth work with the training data and the numerics and the model development have been just quantifying this all important qualitative principle.

Kyle: Yeah, that's (30:00) a really an important distinction. I'm really appreciative that's in your model.

Ken: It's like with ERA. You look at baseball pitcher's ERA and you think oh, there all the same, or whatever. But if one pitcher is pitching in a Wrigley Field with the wind blowing out and the other pitcher is pitching in Atlanta on a clammy day, that makes a different in the expected number of runs. So I'm basically finding which way the wind is blowing in the chess positions by using a deep computer analysis in a fight fire with fire kind of way.

Kyle: So I certainly wouldn't ask you any names if you didn't want to or to slander anyone but speaking broadly do you think there's an undetected problem of cheating or are these isolated cases?

Kenneth: I still think there are isolated cases. I mean there was an article daily telegraph two weeks ago with the British grandmaster saying that chess is really with cheating. I've not seen that evidence. I mean as was voiced in this case over the weekend you know people say acknowledge, yeah, there is a lot of paranoia about it. It is also true I must acknowledge that if a player is disciplined enough to do what is called "smart cheating", cheating only on a few moves over game, my stats are not going to detect that. The point though is that the discipline is an added burden on top of cheating itself. Are there lots of smart cheaters out there? I've yet to see any credible anecdotal reports, any observation of something, anything beside people saying, "Oh this guy has an unbelievable result, here are 10 moves that match in a row in a game." I mean, I do routine screening of all the tournaments and I there a lot of cases of players feeling off 10 straight matches to the computer or more but there are other patterns that do need further investigations and the question is you know judging the frequency is excessive or not well that's a further determination to make.

Kyle: So I'm curious to understand a little bit more from your perspective why chess has become such as interesting and why it's called an unsolved puzzle? We've been playing it for centuries and from what I understand the skill of play has evolved: we're getting better and better at the game. What makes it so complex a game? In a way it's a really simple game, children, as you learned, maybe not all children learn or achieve the level that you achieved, but children can learn the rules and play the games mechanically speaking.  How is that a challenging game emerges out of these simple rules?

Ken: Well that's true; here is where my main professional field of computational complexity theory has an input. In a generalized format where the board could be arbitrarily large and the armies could scale up too, determining which side has the advantage in chess in a given positions is what called a polynomial space complete problem. In fact actually if you remove something called the fifty-move-rule, then it will be jumps up to be an exponential time complete problem where we definitely know there is no efficient algorithm to make a fool proof determination. Polynomial space complete is a level above NP-hard, so if you've heard about NP-hard and NP-complete problems, like traveling sales person problem or tautologies in logic, chess is apparently harder than that. So there's a great kernel of complexity and yes the complexity comes about from a very simple specification, a universal pattern in my professional field.

So the thing about what makes chess appealing is that along with the relative simplicity of the rules and complexity that develops is alot beauty. You can storm the King's fortress; it's analogous to battle. The game could be really exhilarating to play especially when you're under attack and able to pull up a heroic defense. Some of the most enjoyable times, even if you go down in flames and lose, sometimes you will enjoy the way that you were able to defend and in fact actually at a game in the European Championship in Jerusalem in February one of the most brilliant conception of all time happened where a player just nonchalantly moved his king and let the opponent capture a Rook with check. It even looks like he accidentally touch his king and had to been touched moved but it was on purpose and the other guy he took the rook and then after the other guy that tucked his king up once square, it was close enough to be affecting an attack against his own king and the guy just had some queens and some pawns against the other guy king, queen, and rook and yet the other guy couldn't get out and it was turned into a brilliant victory. So things like that in the lore of chess books make it a storied and beautiful game.

Kyle: Very neat yeah! So I know we may lose a few of my listeners as we get into some of the deeper topics, and sort of gradate level topics here, but I've always have a passion for Kolmogorov Complexity and I hope to actually cover a little bit detail on the show and I was curious if you could share how that relates to some of your work with chess.

Ken: Well it's interesting enough. This is technically separate from my cheating works. All chess programs share many common feature of the type of algorithm for board representations and they all use a hashing scheme for chess positions. They don't store the chess position in the form of  knight is on s3, king is on g1, pawn is on h6 etc. Instead what they do is they break a chess position down into a code of under 30 bits. You first allocate primary code of 64 bits each for any combination of one of the 6 white to 6 black type of chess pieces on the 64 squares. And then you just add up MOD 2, those vectors, and take 25 or so bits off the end depending on how large a hash table you'll allocated. Now, that's a lot of redundancy. Different position will have the same code and that could confuse the program but in critical points of any given search it rarely get confused and one I'm interested in is the Kolmogorov Complexity of those bits that are use to initialize the hashing scheme and whether there is a demonstrable difference in behavior depending whether the 50,000 needed bits are generated truly randomly from atmospheric noise that or hotbit service or whether they're done pseudo randomly as the programs tend to do and that makes a big change on their Kolmogorov Complexity. So on the Gödel's Lost Letter blog I wrote a post titled Digital Butterflies, because I also show a digital butterfly effect, where I can reproduce a mistake that chess programs make owing to hash conditions. I can isolate it to the size of the hash table and other factors and the question is whether if this kind of difference can be harness in large scale to tell whether 50 thousand bits are random or pseudorandom.

Kyle: How Interesting...

Ken: You can find that by just googling the term digital butterfly and lost letter that's an article wrote 3 years ago. It references George Marsaglia who discovered flaws in the theorem of the generators were used in the 1960 showing that when their alpha was plotted in 3 dimensions, they have 2 dimensional unwanted irregularities.

Kyle: Interesting! Yeah I'll be sure to link to that in the show as well. So just on the chance that there's a chess cheater listening who's hearing about your work for the first time... How nervous should they be getting?

Ken: Well, I wouldn't want them to be nervous , I'd want them not to cheat.

Kyle: Aha, good point.

Ken: I'm hoping that the idea there are sophisticated techniques beyond what they might be thinking about will make people pause – a deterence effect.

Kyle: Absolutely

Ken: One of the other things is during the year 2007 - 2011 they really were no positive cheating cases. There are couples of negative one where I gave the usual explanation. And my work deepen into study of human cognition and decision making and trying to branch out to things like studying the difficulty of test taking. How can you judge the difficulty of the test? I can judge the difficulty of chess decisions and then can I transfer the distributional patterns that result? So there's a large component of my work that is developing human vs. computer cognitive differences and you can try then a website of a paper from last summer's multi-disciplinary preferences workshop associated to AAAI 2014 in Quebec City that detail some of these [Human and Computer Preferences at Chess]. And even one result that isn't in that paper shows that if you have a lot of data, even just 200th of a pawn difference between move is enough for more humans to select the better of the two moves. Differences that would seem inconsequential if you're just talking about one game really do pan out over a thousands of positions.

Kyle: Interesting. So before I ask you kind of the final question that I actually want to go back to one topic. To my understanding, there was a case when you were tracking a potential threat of cheating. And it was actually a power outage that stood in the way of communicating so would you mind sharing that story?

Kenneth: That, yes. So that was during... what I was saying about I called Topalov/Kramnik match. Before that match finished, I was all set with my conclusions of saying, these games were forcing, it was an illusion. And I was on the server run by chess phase: I commentary privileges there. So for the last day on Friday, October 13, 2006, I was gonna go on line and trod out my conclusions one chat line at a time and say: There was no good scientific methodology and there was gamesmanship, I was loaded for bear. But, the night before was the Buffalo winter October storm, and it knocked out power.  I was bailing basements...

Kyle: Oh no.

Ken: Ours and neighbors and by the time power was restored in the next week, Kramnick won the playoff so there was no harm, no foul. And there wasn't so much in need for my input. So that again, I went back to quietly developing my work.

Kyle: I like to wind up my shows by asking my guess for two recommendations. The first I called the benevolent recommendation, a nod to a book or research paper or website that you think the listeners would find interesting. The second being the self-serving recommendation, hopefully something that you get direct benefit out of from appearing here.

Ken: So for a book, I would recommend any of various books that are about the public awareness of statistics. So not just public awareness of science; and I can think of Jordan Ellenberg's How Not to Be Wrong and the book Naked Statistics.

And also Nate Silver's book 'The Signal and the Noise' which is maybe at a higher level. And if you wanna play chess, there's a chess book I recommend called An Invitation to Chess by Chernev and Harkness – old, but good – comes in and out of print. But it's the book that most smoothly take few from absolute beginner to appreciating some points of strategy and even a beauty. And for the self-serving recommendation of course, the blog Gödel's Lost Letter and P=NP

For understanding some of the caveat of my chess work, I recommend my post on that blog titled Littlewood's Law and 13 Sigma from two years ago. LIttlewood's law being the realization that if you define a miracle as a million to one event, well, we have a million waking seconds every month and notice something every second so therefore everybody can say they see a miracle every month. Well, cause it says you know how's selected what kind of miracle. That's where things get deeper. But that's my main caveat article against reading too much into unusual occurrences that I find all the time from screening chess games. So the blog would be, and also my website at Buffalo, just google my name and Buffalo and you'll find it.

Kyle: Excellent! And I'll link to all that in the show notes. Well lastly, if anyone wants to follow the ongoing saga of claim to cheating and the statistical analysis of such claims. Where is the best place they can kind a keep up on the latest and greatest?

Ken: Well, yeah, we don't make it very public. So then, I have to say my website there's a closed facebook groups which talks about individual developments but... my website paper and that's actually a very good paper by David Barnes whose a known Java textbook author and Julio Fernandez Castro [link] in the journal of security on caveats of cheating testing, all of which, I mean my reaction is just "amen".  They mention me and they don't intend give the impression that they aare criticizing my work, it might come off that way. But my reaction is just "aamen". These were the reasons why I separate the screening from the full test. But it points out a lot of the caveat very well. So that's an independent source for me that's good to read about the general problem and they even said it on the context of cheating detection in online games which is a potential branching out application.

Kyle: Really cool. Well thank you once again for coming in the show Dr. Regan. These have been really fun for me and I appreciate your time.

Ken: Thank you very much.