Nakamura and McShane’s big mistake
I love following this Millionaire Chess tournament. It’s really quite a spectacle: untitled players can pick up tens of thousands of dollars, one top player gets to go home with $100,000, and there’s even the bizarre “Win a million” lottery to keep us interested. And with so many ‘novelties’, it’s not surprising that there’s always the potential for controversy.
The biggest of these happened yesterday in the final round of qualification for Millionaire Monday. The main organiser GM Maurice Ashley was visibly irate when discussing the nine-move draw between the top seed Hikaru Nakamura and English GM Luke McShane. (You can see all the interviews of the draw controvery here.) He called short draws “a stain on our game”. Poor Hikaru and Luke suffered a fair bit of backlash in the chat channels and on Twitter for their performance, although they handled their interviews extremely well (particularly Luke, one of the real gentlemen of chess).
Hikaru also spoke well, aside from two notable exceptions. In the interview you’ll hear these two sentences: “the risk wasn’t worth the reward, frankly”, followed later by “I don’t think I did anything wrong”. At this point, the economist in me was highly dubious, although I have no doubt that both Hikaru and Luke actually believed this to be true.
I don’t know Hikaru personally, but in recent years I’ve been impressed by his interviews, and particularly how gracious and appreciative he is about being able to play chess for a living. And in games where the result is clearly not prearranged and either player would have to make a concession to avoid the repetition, I have no moral problems with a draw – so in this, the players are right. But in my opinion, one of the greatest innovations of Millionaire Chess is that its unique prize structure should naturally prevent boring draws. This is because the risk really is worth the reward in most cases.
So at this point, I did what any math/chess geek would do: I wrote down the problem 🙂 And without going into too many details, it turns out that the short draw was almost certainly the wrong decision for the players to make for themselves. Even under some very tolerant assumptions, the expected payoff from playing on, for either player, was greater than the expected payoff from accepting the repetition.
In my analysis, I had to make a bunch of assumptions, although I think they’re all pretty reasonable. I took into account that by playing on, the players would most likely have a very long game that would sap their energy somewhat (Luke had had a couple of really tiring previous games, while Hikaru said he had been feeling unwell). This would decrease their performance in the tie-breaks (if they occured) and the rest of the event. I also assumed that whoever chose to avoid the repetition would have to make a concession that would decrease their chances in the game from what they were at the outset. I assumed that, all else being equal, Hikaru’s chances in tie-breaks and the final-four were above that of an average competitor, while Luke’s were average (…after a short draw, while a bit lower if he played on). Finally, as it turned out, almost the maximum number of players on 4.5 points who could get to a tie-break with 5.5 points did so, while really made Hikaru’s and Luke’s decision look silly – but they couldn’t have known that when they took the draw. So I relaxed this assumption a bit so that a normal number (five out of eight potentials) reached the ‘tie-break score’ of 5.5.
The analysis is a lot more complicated than this, but you can already get a rough idea of things by checking out the prize list. It’s incredibly top-heavy, and so under almost any realistic assumptions, a player in their shoes would want to maximise their chances of making the final four, above all else. If Luke played on, his chances of beating Hikaru were slim – but they were still much higher than making it through a tie-break with seven other players, including Hikaru. And for HIkaru himself, despite being one of the best rapid players out there, the odds still suggested the same decision.
(For those interested: my final numbers suggested that Luke’s expected payoff was roughly $4,000 higher from playing on, while for Nakamura, avoiding the repetition was worth about $8,000 in expectation.)
Of course, ‘in expectation’ is such an economist thing to say; probabilities are one thing, but only one outcome can actually occur in real life. For Nakamura, he made it through the tie-breaks (though not without some very bumpy moments!), and so it looks like things have paid off. But that’s not the right way to think about things. It’s like winning your first ever spin of roulette: just because you got paid doesn’t mean you made the right decision. I would definitely advise Hikaru in future to do these sorts of calculations (or better yet, get someone else to!) before crucial money clashes.
(Luke, on the other hand, is not a professional chess player and probably doesn’t care that much about the money. While he didn’t make it through the tie-breaks, he’s still had a good tournament and has good chances of picking up a big consolation prize in the rest of the open. But still, from a purely academic perspective, the decision-making was dubious!)
Of course, this was mainly just an academic exercise for a bit of fun (although professional players may want to take note – I’m open for consultation 
). But there is one policy implication, and here I’m specifically talking to Maurice and organisers like him. The lesson is: Don’t be discouraged! The Millionaire Chess team have done exactly the right thing in their structure to promote fighting chess. It’s hardly their fault if the players haven’t yet worked out how to act in their own best interests. But this will happen through experience (and maybe through posts like this…), so there’s no need to panic.
For the time being, I’m going to sit back, relax and watch the final fight – in which, typically, I expect Hikaru to defy the odds, win the tournament and thereby blow a big, fat raspberry at my analysis 
S…… I…… X……………M……O…… V…… E …………..G……A…… M…… E……!!!!!!
It took me longer to type this and more effort than for them to play the “game”.
Will I get 100,000 bucks for it?
I think most comments here ignore the human side of the players and unfairly criticise them. And I believe that the mathematical study itself is also relatively pointless in this respect (sorry Dave!).
Someone above, I believe it was brabo, pointed out one very obvious argument: the players, being tired and all, are bound to assess any such situation more pessimistically than it may really be. If McShane, for example, was feeling really tired (which would be expected; he very rarely plays in tournaments and, when he does so, it’s one-round-per-day events), it can be expected that he doesn’t value his chances of beating Nakamura, a very active and fully committed top-5 player, very highly. I think perhaps he would have tried in a different situation, even after all these double rounds and the accompanying tiredness, if it weren’t such a crucial game for competitive reasons; it doesn’t have to do with the money really, just that these players are, above all, competitive sportsmen and achieving a competitive success does influence their decision-making substantially. I am pretty sure the game would have gone on if they were assured of qualification (or were further down the standings).
All the arguments about spectators, sponsors etc are of course fully valid and understandable. But it has to be taken into account that professional sportsmen are competitors above all else, and this aspect will generally prevail in their decision-making in such (rare but) crucial instances. This particular game is not the right time for the players to consider the public or the sponsors, and such situations, with so much at stake, have been recurring frequently throughout chess (and sporting) history.
As a chessplayer, I cannot possibly accept David’s position that either player would compromise his position by playing, in a chess sense. I think McShane may have been inviting this draw all along, which is why he played 6.Be3; this Open Sicilian stuff is not exactly his home turf. Perhaps he didn’t want to play a slow Closed Sicilian line, as he often does, and selected this one, having something appealing in mind against 6…e5 and expecting Nakamura to switch to it rather than repeat. With no real time for preparation, and being a completely amateur player (in terms of competitive engagement only, of course!), he cannot be expected to fight a theoretical duel with a top-class player in such a sharp line without serious preparation. Perhaps he really wanted to try and beat Nakamura, and took the calculated risk that Hikaru will want to play on as well; who knows…
It could be argued that Nakamura had the moral obligation to play on, being the higher-rated player, the better prepared, the more active and so on. But then it would be unfair to impose this obligation on him fully; after all, he is playing a very strong player, with Black to boot. Maybe he considered switching to 6…e5, but didn’t fancy playing a slow, technical position like that after 7.Nf3 against Luke; a very viable and purely chessical consideration. Besides, his chances in rapidplay would probably be higher to anyone else, yet another argument that may have made it easier for him to agree to the draw.
Above all, people, before condemning these two players for that single draw, keep in mind that both of them have a well-deserved reputation of being fighters. It’s not like they are serial offenders or anything. It can happen to any sportsman, no matter how brave or combative, that on one rare occasion, under a set of very specific circumstances, he will treat a sporting encounter more conservatively, even if the mathematical odds are against his decision; when you are not sure of yourself and/or don’t feel that you can give your 100% to it, odds are irrelevant. After all, it was an isolated incident, and the chess public did not lose much, except a probably conservative 30-40 move game, when there were so many other fights in the surrounding tables… This is to explain why I don’t consider Dave’s analysis fully relevant; of course, the mathematical approach in itself was quite interesting and enlightening!
In my opinion, criticism should be directed towards the organisers instead. They want to encourage fighting chess (although this term, “fighting chess”, can be defined in many different ways – another discussion!), and in general their efforts are in the right direction; so far, so good. But they write a very ambiguous regulation, which leaves room for subjective interpretation and is thus poised to put them in a difficult situation such as this, at some point. And when the time comes to enforce it, they back down. Now they will probably change the wording for next year, which will “prove” that it wasn’t written correctly in the first place. But I wonder, would they have decided in the same way if a different player was playing Black, for example Dave? I cannot help but believe that other, lesser figures (in terms of popularity in the USA at least) would have concerned themselves more with a possible punishment; in this case, Nakamura had all the possible excuses at hand: “I am Black, I am good at rapid, they won’t dare touch me because I am Nakamura”. At least I would think exactly this, if I were in his shoes. Which is all fine in my book, but what does it say about the rule itself and its enforcement? This whole incident made the organizers appear lacking in resolution, all talk and no action, and all this whining by Ashley looks simply ridiculous to me. There is absolutely no chess excuse for acknowledging the exception in that “shall” in this case; but then again, if they somehow forced them to continue, they could just as well play some 30 quiet moves and find a way to draw later on. Such anti-draw rules are very subjective and, in my experience as an International Arbiter, only lead to problems, because every case will have exceptional circumstances and it is impossible to fully appreciate the subjective significance of each of them for each player. It is preferable to have very clear rules, such as “no draw offers allowed – at all or in less than 30-40-60 moves”, and so on. And it’s essential that, when you introduce such a strict rule in your regulations, you abide by it instead of looking for an excuse to ignore it and then speak interminably about the plague of chess and other such crap. It’s a tournament, after all, Nakamura played 11 games (plus some rapids) and made one quick draw; it’s not the end of the world!
Sorry for writing so much! 🙂
*Sigh*
The more I look at it the more outraged I become. Actually it is not a nine move game
B U T A S I X M O V E G A M E !!!!!!
Beyond disgusting.
Yup. Boil them in oil draw and quarter them and feed them to the piranhas.
And deduct six hundred points from their Élő.
No six thousand.
Use them as target practice for antimatter neutrinos.
Six moves!!!!!!??????
Did any of these people who support them or make excuses for them replay this recch gag spew vomit barf chess game?
Six moves!
Hey maybe they’re getting married and this was their engagement party?
Finally I was able to see the interviews with all three people involved.
What is amazing is that they didn’t bother to make any excuses they just considered it normal.
McShane simply said that he was too tired to play an alternate move which would have lead to a sharp game and he didn’t feel he was up to it in his condition. So he pretty much admitted to a failure of imagination as in: I had no other safe move to make. Or you could call it cowardice a bad advisor always.
Nakamura on the other hand blamed not himself but McShane as in: What else could I play if McShane kept on making the same move. He didn’t say he had no other ideas nor that he feared sharp continuations but blamed his opponent which is not exactly very ethical.
It was he who was moving the knight back and forth wasting tempo and failing to develop.
In neither players case is it written in the stars that there is no other safe move than the one they made nor was it the best move. There was no proof that the knight had to retreat.
Hey aren’t you supposed to develop your pieces after the ninth move?
I was most sorry for Ashley as he said all the right things but then failed to act on it. As a good bureaucrat he was clinging to the wording of their special rules but as a grandmaster himself he was royally pissed off. But he didn’t draw the conclusion: these two must be punished by expulsion from the tournament. At least refuse to hand the checque to the cheater.
All seem to say what could we have done? Simple. Get the youngest least experienced chessplayer from the audience to make the next move something other than the repetition.
For both. That should give each the heebie jeebies as an incompetent move might throw the game then and there. Good. Serves them right.
If these clowns made a farce of chess let’s make it a real farce. They asked for it.
One of them made the comment it’s only one game. Which is true. But then is it acceptable to cheat only a little bit and only rarely?
Ashley said it correctly, he did it once saw how bad it was and never did it again.
Will these two clowns clean up their act and never do it again? I am not holding my breath.
They are both good enough chess players that they could do this for thirty moves easily
when it would be much harder to call their bluff.
Ashley was right in that also when he said incredulously after nine moves?
I was indeed mortified that Maurice Ashley legitimised the execrable behaviour of Nakamura by being the person who hands him his ill gotten gains. He should have refused to have anything to do with him if he thought as he did that his behavior was a disgrace.
That is like an Olympic official who hands the gold medal to figure skaters or boxers who were handed their wins by corrupt lying dishonest referees and judges who were simply bought or terrorized.
That is why all pro sports make me puke sadly including chess.
Nakamura deserved nothing as he not only DIDNT FIGHT THE GOOD FIGHT he didn’t even pretend to fight.
Shame.
To Alexander Jablanczy
Dude, you *really* need to get out more. Chess has not been exposed as a fraud. Chess is not a fraud. The fraud, if there is one, is perpetrated by tournament organisers who insist, for the sake of ignorant, stupid “chess fans”, that the laws of chess are insufficient, and require to be distorted. Further, they insist that strong Grandmasters must *deny* what they understand about chess and behave in a manner disrespectful to Caissa, again for the sake of these same ignorant, stupid “chess fans”. These Grandmasters include in their number Maurice Ashley, who has been insisting that Nakamura and McShane were in the wrong. He did this *in spite of his knowing better*.
Shame on him for that.
Here’s your answer. Evidently what I already wrote wasn’t enough.
We live on different planets. For me cheating is cheating rules or no rules.
You want rules spelt out so you can finagle yourself some shady technique which the rules haven’t listed and you get your kicks by cheating and beating the system.
I despise that.
I don’t give a damn about rules. If you behave ethically fairly and decently you don’t need rules.
One of the unpleasant things about chess is the clock. Hundreds of years ago gentlemen and gentlewomen BTW played chess and they knew that to be decent that you must make
a move after five minutes in a casual game and spending up to one or two hours is unacceptable when the whole time allotted to an informal game is about one hour. So chess clocks were invented because idiots and dishonest and crooked selfish fools would hog the time.
When I play such boors bums taking fifteen minutes for each move I try to guess what they will move and make my move in ten seconds. So I lose. But I don’t consider it a loss as it is horribly unfair. One thinks for fifteen minutes and the other for ten seconds.
Not a fair fight.
Because there are people like you and these two winners we need clocks mountains of ridiculous rules and arbiters.
BTW verbal and even implied contracts ARE binding just as if they were written and notarized. They only have to be because there are cheaters and liars and fools.
A Canadian girl got a bronze medal in XC skiing. Two Russians got gold and silver.
They found EPA or blood doping in their blood so they forfeited their medals. So a year later the Canuck chick got her gold in a special ceremony. So far so good.
She was clean as far as blood doping EPA etc methods which are specifically forbidden by WADA rules. She was not an Armstrong.
Then she bragged that she either spent six months in Peru or Bolivia or else she slept in
a low O2 rent or low atmospheric pressure tent for years or both.
The effect was the same as EPA or blood doping a la Armstrong.
The hematopoietic system responds the same to low atmospheric and oxygen pressure as it does to erythropoietic hormone. She must have had a Hb as high as Armstrong’s or the two banned Russian women,
My point if you didn’t get it as WADA didn’t that that doesn’t matter if the method of cheating is spelled out letter by letter or not the point is the intent of cheating and the carrying out of the deed.
Obviously a low O2 and low atmospheric pressure tent is a high tech method aiming to imitate condition in the Altiplano. Canadians have the technical and financial wherewithal to do it so what’s the harm?
Well the harm is that they are acquiring UNFAIR advantage by so far unbanned means.
Not by illegal blood components and hormones or drugs but by using
knowledge about the production of blood. Very clever and wrong.
When you race someone you expect the same conditions not an opponent who has a myriad pharmaceutical tricks and others to give him / her unfair advantage.
Is it OK in your opinion to place a magnet above a weightlifter so he could lift more iron?
Even if it is expressis verbis not forbidden?
I heard that a very large number of people cheat on exams. You might congratulate them for getting away with it. While I might not want to draw and quarter them and boil them in oil – just too messy not Messi – I would immediately expel them permanently. No ifs ands or buts.
All we need is incontrovertible evidence of cheating or bad faith or unsportsmanlike conduct. As a former soccer referee I could give a warning a free kick or a yellow or red card for it.
These two bums I give a black card. Permanent exclusion for their collusion.
No one absolutely no one who has any knowledge of chess finds a 9 move game acceptable.
I always laughed at cheaters – it takes more effort to cheat and prepare the cheating sheets than learn the damn stuff. I never understood why these folks were always against open book exams. That’s why. Cheating no longer gives them an advantage.
You seem to admire people who make a lot of money by fair means or foul.
I don’t, I despise them.
I don’t give a damn if Nakamura won a million. That does not make me admire him but despise him even more.
Ill gotten gains are shameful.
Being tired after five ten fifteen hours of chess in two or three days is ridiculous,
As I said interns residents but also soldiers and forest fire fighters or sailors don’t have the luxury of whining about how tired they are they must do their duty. Period.
Even after a week never mind one long day at work.
Many artists musicians writers poets in the heat of creation work non stop for days without rest and they don’t whine but glory in it.
Chess players are tired ?
Poor wimps.
I always felt that when you draw with a pencil or a pastel nothing must touch the surface of the paper but the charcoal or the lead.
Or when painting the tip of the brush. I considered smearing the lines with a fingertip or a piece of paper cheating, bad form incompetence.
Or using the stick end of the brush ant other objects.
Just as in sumie Japanese painting on rice paper there are no other marks on a paper but brush strokes which is its point. You can’t even correct or erase strokes.
So you maintain the integrity and the purity of the technique.
Obviously I consider the collages of Picasso a farce a worthless piece of garbage, in short cheating.
Equivalent to say breaking off eight squares of a chess board to prevent the opponent from using the extreme rank or file. It is not in the rules so in your opinion it would be OK?
It would be amusing performance art or happening but lousy chess.
A game or an art or a sport or a contest has nothing else but its limitations. And the most important ones are its unwritten rules.
You try to win. You don’t cheat. You do your best. You play fair. You make an effort. You try to be creative. Copying replaying other games is in essence stealing,
a form of cheating.
We play and follow others’ chess games because we expect something new. We are bored to death by repetition. That is not playing chess but being a robot.
Like the German football team. Robots. BTW they used amphetamine in 1954 in Bern. They have now admitted it. They were world champions only in cheating not soccer.
Fischer did go insane because of obvious Russian collusion.
Even the Estonian Keres was part of the scam.
As there was between the four top players. They played four draws amongst themselves and played real games only against the four whipping boys at the bottom of the field of eight.
That’s a way to select a world champion? More like a world chump.
Chess is almost as rotten as tennis soccer the Olympics and all pro sports.
Perhaps the real reason for the outrage against Nakamura and McShane is that they made evident absolutely crystal clear so even an idiot could
see it that chess is rotten at the top and stinks to high heaven.
One of the most disgusting episodes in sport was the German Austrian game when they played to a 1:1 or a 2:2 tie I forget which and they blatantly stopped playing passing the ball back and forth between the teams for an hour. Had I been the ref I would have blown the whistle and forfeited the game. The point was that if either team won or even if they tied 3:3 or 0:0 only one of them would have advanced with Algeria. To make sure that they both got through they had to get exactly 1:1 no more no less. They each got one goal then they stopped playing making sure they never got near the goal lest they screw up the scheme and score in error.
It was so blatant that even a babe who knew nothing about football would have seen it.
I would have expelled both Austria and Germany from world soccer for ten years and awarded their spot to Algeria.
There was another world cup when Belgium and Cameroon were by far the best teams.
The referees made sure that they lost their next games and the usual bunch of crooks Germany France Italy Argentina Brazil got through.
Folks it”s all fixed. All you fans are fools if you think any contest is fair.
Especially not the ones in which there is a lot of money.
Money corrupts everything.
Radix malorum est cupiditas.
Can you imagine a world championship in which the champion gets nothing but a laurel wreath like in Greece?
These two bums did the same for chess as the Austrian and German teams did for soccer. Rather against chess and all sport and art and all games of skill.
That may be good poker but I consider poker players to be scum anyway.
They exposed high level chess for the scandal and scam that it is. Alas.
One thing is to be a cheater and a liar and a crook but another thing to actually glory in it.
Disgusting. Shameful. Like the Olympics pro sports finance banking the art market gold mining politics law etc.
If you find disgusting things wholesome we live on different planets.
I don”t.
No real chess player can be happy to have chess exposed as a fraud.
I swear before every Olympics and World cup that I will never watch them ever again and then I relent and still do.
Same with chess tournaments and cups. I wonder why I bother.
Indeed, nobody ever knew that many female dogs.
I should mention that I severely doubt the authenticity of the “Hikaru Nakamura” commenter’s account (especially seeing as it used the authorisation email “sauronshalldie@gmail.com – a reference to this famous tweet). Still, that comment did make me laugh out loud 🙂
Maybe they had the same kind of food, they really had to go to the washroom, bad !
Have to go.
100k bitches!
In the case of Millionaire Chess, then, it was…ineffective, since that hardened criminal of the 9-move draw, Hikaru Nakamura, won a large sum of money. Counter to your assertion, it could be suggested that tournament organisers need to understand that imposing anti-chess measures may tend to discourage top players from participating (regardless of the size of the reward) since the requirements super-added to the laws of chess may mean that what the participants are required to play is not chess, but a chess variant in which the normal drawing rules do not apply.
@Aaron Jones:
The point of my original post was not at all to engage in a moral debate about the draw. Personally, for me the line is as follows: A draw like this, where deviation from a repetition requires a concession, is okay, whereas a two-move agreed draw is not. But my article is only about the math behind expected payoffs, and nothing else.
On the other hand, relevant to your comment, expected payoffs can be used as a reasonable deterrent from short draws, if that is what the organisers wish (but that, again is a further moral argument!). That was I guess the main ‘policy implication’ of my post: I think one of the best ways to prevent short draws is to structure the prizes accordingly, perhaps in conjunction with educating top players about expected payoffs!
So no one is going to address what I said earlier? I don’t even get one response? Honestly, the outrage against these players is absurd. If it were an agreed draw, then I think we might have a right to be upset. It was not an agreed draw, it was a draw by three-fold repetition, which is absolutely and entirely a different matter. Please tell me, for all those who are outraged, what rule was violated? What proof is there of pre-arrangement? If you can’t show me either, then the draw has to stand. That is why the arbiters reached the decision that they did. Can anyone suggest a practical way to prevent such repetitions that doesn’t inherently change the game or handicap the players’ style? If you can, I am all ears. Was it a let down for the fans? Maybe, to a small degree, but there were plenty of other dramatic games. Even the controversy itself was dramatic. Look at Fischer threatening to not play in ’72. That generated huge publicity for the game, and it wasn’t negative publicity either. Controversies like this make chess unique. I don’t want chess to be tennis or football, because it is totally different. Do I want the game promoted and popularized and broadcast, yes! But let’s not compromise the beauty of the game for the sake of popularity. Far too many sports already do that. Chess should be above that.
I forgot to add that there is also a tiebrake consolation of 6000$ see special prizes (not clear if for 1 or all the tiebrake players). If for all tiebrake players then you have a guaranteed income of 6000$. I understand why the organizers add such consolation prize but this won’t stimulate players to take a risk.
I don’t think there is a need for any extra calculations. If you are really that tired or not feeling well as both players stated afterwards then it is very reasonable to believe that your winning chances are close to 0% (if you deviate). If that is the state of mind you have then it makes a lot of sense to take the draw at the first opportunity.
Besides I also want to indicate that any assumption about probabilities of winning chances should take into account a huge drawing chance see http://chess-db.com/public/winprob.jsp Further I need to add although those statistics are based on 10 million games, they can not be just employed for a single game as colour, opening,… are too much influencing the result.
Regarding David’ so-called “math”, I’d be very surprised if either player wasn’t fully aware that their draw lessened their chance of a place in the final four. btw, both are very well versed in poker theory.
My credentials: I am a complete amateur who only plays against stockfish and loses every time. I got hooked watching chess matches last year. I love it.
My previous thought: Early draws are ridiculous. Name a sport in which teams or players routinely play for a tie. Tennis? Golf? Football with either shaped ball? C’mon!
My new understanding: After I heard Luke say he’d played nine hours of chess for the previous three days I began to think. In many many sports players ARE rested, taken out at strategic points so they can come back fresh. So that’s how I see this decision by Luke and Hikaru. Rest for the next quarter. One game is not the match. And that is in the practical performance of sport. So it didn’t bother me.
I thought I saw a utube connexion as I wanted to listen to their lame excuses with the idea of audiatur altera pars – let the other side be heard –for Americans– –
but I somehow lost the link to it or perhaps it was deleted?
There is nothing they could say that would change my mind for a nine move chess game speaks for itself.
And what it says is despicable.
If a surgeon is operating and getting tired after five hours he has no right to quit.
I have worked as an intern non stop for 36 hours or was on call for 48 even 72 hours and didn’t complain nor quit.
BTW we used to have ten and twenty hour tennis games before they invented tiebreaks or penalty shoot outs in football. Quitting is not an option.
If you quit coming down Mt Everest you die.
If you can’t stand the heat get out of the kitchen. Go and sell carnations or daffodils.
I agree with the irate organizer Maurice Ashley. Why didn’t they expel them from the tournament for they did worse than cheat.
I don’t care if it was for chess reasons or economic or even mathematical – poor Pascal and I don’t mean the language but the philosopher – it was disgusting shameful despicable.
BTW we all agree so stop making excuses for cheats and crooks.
Kramnik was asked if chess was a sport or an art (or perhaps science).
These bums proved that it is neither. Of course it isn’t science.
This is analogous to a prize fight in which after half a round they shake hands saying we are equally matched traded equal blows let’s quit.
Or in a Marathon when after one mile one is 100 m ahead of the next runner and says I have already won let’s quit.
Or an orchestra plays da da da daaamm and quits saying you know the rest of the Fifth symphony no sense playing the whole thing.
If the audience ripped them to shreds they would be right.
Imagine Pavarotti singing four bars of Nessun dorma and then quitting.
In that case there would be an understudy to finish the aria.
Perhaps Nakamura and McShane should have understudies to finish their games for the poor dears are so tired. I can’t control my sobbing.
Not playing out any game or agreeing to an obscenely short draw is worse than cheating which deserve immediate expulsion from the game forever.
These bums think they are clever for they beat the system. They must not be permitted to do that. They failed in sportsmanship and as such must not be permitted to play ever again.
Lets trim the rot from chess FIFA FIDE WADA Olympics pro sports of any kind as these are of course irrelevant entertainments sports games.
If we can clean up such non vital activities then perhaps sometime in a million years we can clean up politics religion economics finance law medicine literature music business science technology all of which are infested with liars crooks cheaters thieves.
These two bums have besmirched chess their livelihood in public. The banksters and financiers, politicians and ideologues and lawyers and media types do their dirty deeds in secret here the gangsterism is there for all to see.
Shame on all except for the organizer.
Just to make it clear from now on I don’t consider Nakamura or McShane chess players but crooks. They should start selling snake oil and become brokers.
Slime rises to the top.
BTW the idea that chess is an elite game or nor for the masses is bunk. American bunk.
There are probably a million serious chess players in Hungary ten million in Russia and two million in Georgia or Armenia.
That Americans don’t play chess is due not to their inferiority or stupidity but laziness and howling anti intellectualism. In a society where drug pushers and pimps and brokers are multimillionaires and teachers and professors are despised and starving what did you expect?
I play chess with a pathologist ER MDs and electricians and steelworkers and the latter are better at it. The best are bums off the street.
Nothing elite about chess.
Nakamura and McShane proved it for they surely ain’t elite.
If there were such thing as elites they would be recognizable by their sportsmanship which concept is foreign to these cheating bums.
Even if a boxing match was fixed they at least finished the first round.
So this kind of cheating by nine move games is in fact WORSE than cheating by other means.
@Yoavd, who wrote: “His gain: 100,000 usd proves that for himself he made a correct decision.”
Unfortunately, from an economic and theoretical perspective, this is completely incorrect 🙂 It’s what psychology calls ‘confirmation bias’, and is like saying, “I drove drunk last night and get home safely, so drink-driving is the right decision.” If we took the same players next week and ran the tournament from the start of the infamous round through to the end, and then did it the week after that, and the week after that, and so on, I think it would turn out to validate my arguments. (Of course, Nakamura might disagree, and it’s hard to argue with someone who’s got $100,000 sitting in his back pocket!)
@brabo:
You made some good points!
1) Both players were familiar with the alternative continuations (Bg5 h6 Bh4 g5 etc for White; …e5 for Black). But definitely it would have been a concession for either player to deviate.
2) I took into account rapid and blitz ratings, though it wouldn’t really change things in this case.
3) Yes; I used subjective probabilities whereby the chances that Hikaru thought he would win were less than: (one minus the chances that Luke thought he’d lose).
Then:
1a) Such Prisoners’ Dilemma situations typically only work in simultaneous games. Chess is a sequential game. According to your comment then, it makes sense for Luke to wait because Hikaru is the last who can make a realistic deviation (by not playing the final ..Ng4), but not because of the money difference.
2a) This is ‘regret aversion’, and you are right. This could be included into the calculations, but then it no longer becomes a payoff calculation but a utility calculation. And in that case, you must include other utility variables, the most obvious of which is that the reputation of the players has been diminished by the short draw. Things get messy 🙂
You are welcome to be skeptical of my article of course, but it’s just a blog post, not a mathematical paper. I invite you to do what several readers have done and make your own calculations! 😉
It seems that Nakamura decided wisely. Statistically he was the favorite in the game with McShane but decided to go to the tie-break without risk. His gain: 100,000 usd proves that for himself he made a correct decision.
In my database i have 3 wins of McShane (all in black!) and 5 wins of Nakamura in the games between them so the result could be either way.
All in all, specially freling not well I believe that the draw was wise.
Of course in the next tournament they can decide that no draw can be agreed before move 30.
The short draw really hurts in terms of sponsors (according to the second-hand rumor mill). Making draws worth less would make arranged draws less likely. (e.g. make draws worth 0, only count wins in final score would make arranged draws disappear). or, use the 3-1-0 system. or, make a rule that players who agree to a repetition draw within 15 moves in the final round and qualify for tiebreaks suffer a tiebreak penalty at least and disqualification at worst OR more positively, give final round winners a bonus relative to the tiebreak qualifiers who qualify via repetition draw.
Personally I am very sceptical about conclusions based on some not published calculations.
1) How much are your chances decreasing if you have to play a position in which you don’t feel comfortable against a 2700 (2800) player? Unless you play frequently against such opposition, any guess is pure speculation.
2) Which rating did you take into account for the rapids and blitz games? This should definitely be different than their standardratings.
3) Did you take into account that both players can be convinced that they have a lower chance than reality? There is no need that the sum of the expectations equals 100% in their mutual game. E.g. you can feel both not very well but not know from each other.
Besides the whole calculation doesn’t take into account a couple of other aspects.
1) Suppose your calculation is correct and Luke gets 4000$ and Hikaru gets 8000$ by avoiding the repetition. Then it makes sense for Luke to wait Hikaru to deviate first as he has more to lose. On the other hand maybe a different calculation gives an inverse view.
2) Suppose you deviate and lose horribly. Other competitors can think that you threw the game away and had an agreement.
…
A draw assured both players a seat in the play-offs. What fun! More chess, and not the money, is the main incentive.
Hikaru Nakamura is fairly well versed in poker.
I really don’t understand why there is such heated controversy over this matter. The rule, as I understand it, is that there shall be no “agreed” draws (before move 30), or “pre-arranged” draws. The draw was not agreed, it was a matter of 3-fold repetition, which is an entirely different situation. And unless there is proof of prior collusion, one cannot say (or at least prove) that it was pre-arranged. Thus the rules were not violated, either in letter or in spirit. That is, unless someone can show me a rule that I have missed, which I would be glad to look at. Granted, the result is frustrating for spectators and sponsors, who want to see a fight, but sometimes repetitions happen in chess (even on move nine). Sadly, fans don’t always understand this, but changing the rules to prevent repetitions is fairly difficult. But letting the fans down is not violating the rules.
As to David’s point about financial risk versus reward and the mathematical analysis of this, he makes some good points, although I wonder if all the variables have been taken into account. David infers that the players are concerned primarily with financial considerations based on their comments, and I believe that certainly played a part. However, players at that level are also concerned about rating considerations (particularly since other players like Topalov are trying to qualify for the candidates based on rating). If both players believed that repetition was necessary in order to prevent a worsening position leading to a potential loss, then preventing a loss of further rating points may also be advantageous. I wonder if you would consider a mathematical analysis of possible alternative moves/variations or sequences (such as the ones the players pointed out), taking into account the computer evaluations of the end positions, as well as each players previous performance in those particular lines. I think that would give a great deal more insight into their decision making, since both players brought it up themselves.
Impressive ad hominem there, Steven. Based on what, exactly?
This Mark Houlsby is a first class moron.
Good article David!
P.T.: Maybe these “jokers” (as you style these top GMs) merely considered that–in the interest of their producing better chess later in the tournament–they needed to assert that the tournament rules make a mockery of the essence of chess. If you think that you know better than they do how they ought to behave, why are you not competing against them for these large sums?
@P.T.:
Whether or not the spirit of the rules was respected is another issue. For what it’s worth, I don’t think the two players went into the game intending for this draw to happen, and it’s not fair to force them to compromise their own positions – a real Prisoners’ Dilemma, now that we’re talking game theory 🙂 I have different, and much stronger, views about prearranged draws or agreed draws in early positions where there’s no compromise involved in playing on.
For the record, Maurice did protest about the result, which led to a 97 minute discussion with arbiters. But ultimately the result stood, and given the rules as I read them, that seems (legally) right.
Moral arguments, legal arguments, mathematical arguments – it’s hard to keep track 😉
I think this “analysis” misses the point. (By the way, I’m a mathematician — not a very good one, but someone who does appreciate a good mathematical analysis *if and when* it’s called for.) The point is that, unlike the other honest chess warriors who chose to slug it out even though they were dead tired from having to play two classical games a day for the past several days, these two jokers decided to make a mockery of the spirit of the rules. I’m surprised that a grandmaster like Mr. Ashley, who can see many moves ahead on a chessboard, couldn’t bring himself to see the one common-sense move in this situation: tell these two players to go back to the chessboard and start from scratch — with a stern warning that any more shenanigans of this sort would result in automatic expulsion from the tournament!
Thank you, I see that now. When I posted the question, David’s reply to you had not yet appeared here (for some reason).
I was directing my questions to David. His tweet said, “My math analysis on the draw controversy.” But I saw no math, just conclusions.
Billy Glass, at whom were you directing your question? doug – no it’s not an excellent parallel at all. Football and basketball are team games. Chess is not. Football and basketball involve a lot of running and passing and shots at goal. Chess does not.
While I appreciate Maurice’s goal of increasing the popularity of chess, I highly doubt that decreasing the number of draws (or even completely eliminating the possibility of a draw) will make chess appealing to the masses. The truth is that the average person does not like chess because they do not understand chess, and the average person will never make the necessary effort to learn chess (beyond possibly how the pieces move). The average person prefers simple games that depend on luck more than skill so that even the worst player has some chance of winning.
One can change the rules of chess and completely alter the game, but chess (or deep strategic games in general) will never be popular among the masses. Maybe if you added dice rolls that caused random pieces to disappear from the board. Maybe that would make “chess” (if you could still call it that) as popular as poker.
@doug:
Yes, that was an interesting comment indeed! I took into account tiredness in the article, but I think you’re making more of a moral argument with regard to the parallel, as was Maurice. The difference in chess I guess is that players have some control over how long a match goes for. So a counter-parallel could be a serve-volley specialist in tennis who tries to keep the rallies as short as possible because his fitness doesn’t match his opponent’s.
@Billy Glass:
If I get a break from work I might type up the paper notes, but it was hard enough to justify spending the time to do the calculations and article in the first place 😉 Actually a few other people have done their own calculations and got similar figures: that it was the wrong decision by both players, and a little more so by Hikaru, but the overall difference was less than 10k.
To be clear: that reply was to Troll_Troller
Good one! ROFL! My point, as I think you realised perfectly well, is that *when players agree to a draw after 9 moves in a round long before financial rewards have been decided, it’s because they are thinking not about money, but about the way chess is*.
Incidentally, since you seem not to be clear on the point, you should perhaps realise that the song which I cited covers all such behaviour, and, indeed, all the behaviour in this thread.
I enjoyed your post more than any post since the last post that I read which I enjoyed more than your post.
So where is the actual math and analysis? You’ve shared your conclusions, but where can we see your work?
What about the comment that there was 9 hours of chess played the day before ?clearly this speaks to how tired they were and MaryAshley’s analogy of football players and basketball players being tired as well before they go into playoffs or extra innings are over time is an excellent parallel
I completely agree with Mark Houlsby. Why would anyone pay $2000.00 to enter a chess tournament called the “Millionaire Chess Tournament” take the time to consider anything financial at all. The abstrusity of your abstruseness is abstusively abstruse. Chess is about chess, not about the money or anything else. When, in the history of chess, has anyone ever agreed to a draw, especially in the last round of a tournament, just to secure some kind of financial gain or title or anything else that benefits them. Never. The idea of humans adapting to their situation to change the outcome of their decision making process ludicrous.
Mark Houlsby is clearly more qualified than you highly educated people, because as he said, he’s heard a song called Human Behaviour, which is about the relationship between humans and animals and how animals perceive humans through their eyes. Well, I freely admit I don’t see how this relates to chess or money in the slightest, but Mark Houlsby does and that’s all that matters.
Once again, both Mr. Hansen and you, David, are concentrating on “extra-curricular” considerations (as it were). It’s not about money. Perhaps it should be, but sponsors need to understand that chess is never going to garner mass appeal. It’s too abstruse. Expecting players to *change* their “expected chess behaviour” based on *financial considerations* is to pile more abstruseness on top of something abstruse. To understand why this might be, at best, optimistic, listen to Björk Guðmundsdóttir’s song: “Human Behaviour”….
Just a suggestion.
An excellent observation! I’m especially pleased to read this seeing as I am a “behavioural economist”, which is one who specialises in more realistic human behaviour (in this case, you’d argue, non-rational behaviour).
The thing is, humans often tend to ‘learn’, that is, act more rationally with experience. The millionaire open is one of the very few (perhaps the only) tournaments with this incentivised structure, and both these guys were playing in it for the first time. My guess is that if there were more tournaments like this, players would quickly learn to act in a utility-maximising way. Furthermore, if the two players in question were familiar with poker (maybe Van Wely versus Bacrot?), I also predict they would have acted differently. But I guess it’s all speculation.
Your analysis confirms my hunch that the draw was a bad idea, so I’m tempted to agree with everything you wrote. But then there’s the conclusion: “The Millionaire Chess team have done exactly the right thing”. Well, except from the fact that it didn’t work out the way they expected. Actually, it seems to me that it’s one of the basic economic assumptions that is at fault: The players did in fact not act rationally under pressure. They may have convinced themselves that they did, as the interviews suggest, but they didn’t. And if these two highly intelligent and competitive people can’t be trusted to act rationally (one them has even worked as a stock broker if I’m not mistaken), then how can economists expect the population at large to act rationally?
I’ve met Luke in person, and I’ve played him online. I’ve met Hikaru online and played him online. It seems to me that both of them are always up for the fight when it’s appropriate, but it’s not always appropriate. Clearly both regard chess as inherently more important than money (if that were not so, they’d’ve played more than nine moves). Neither cares about fans or image, Luke is one of the most laid-back individuals I’ve met, I shouldn’t be surprised if fans are the last thing on his mind; and Hikaru is focused almost to the point of self-absorption. He’s very accessible to his fans, and really engaging, but he puts his chess interests first, as he should. The tomato vs. suspension bridge reference was to an episode of “The Big Bang Theory” which featured a dispute between Sheldon and Stewart.
In Hikaru’s interview, he definitely describes things in terms of the tie-breaks, and I think it’s more than logical to assume that both players were thinking beyond that one, individual game in their calculations. I do assume that the expected payoff is purely financial, but that assumption could also be relaxed. For example, imagine that the players also care about their image to the fans; in that case, taking a short draw would be even less appealing! So I’m not sure I completely get your point (and especially when it comes to Spanish suspension bridges…)
Hi David, what you write/say is always interesting. It seems to me that what you call “expected payoff” is *financial reward*. This is different from what Nakamura and McShane were discussing. What Hikaru and Luke were discussing was chess. So, if I’ve understood you correctly. you’re comparing tomatoes with suspension bridges. If you don’t get the reference, ask.