Nakamura and McShane’s big mistake

Posted by David Smerdon on Oct 12, 2015 in Chess, Economics |

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 Laughing). 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  Cool


Mark Houlsby
Oct 21, 2015 at 8:52 am


Hal Bogner
Oct 21, 2015 at 10:16 am

David – thanks for working out and sharing the anaylsis, and stimulating and hosting this discussion. A couple of things:

1. You didn’t mention the biggest risk, which was of Bareev winning (which almost occurred!), which in conjunction with the other results of round 7, would have left them both out in the cold.

2. Maybe Hikaru’s following is all the greater for his high-wire act of going through those dramatic playoffs. (Maybe Maurice and Amy got their money’s worth from that, too.)

3. My suggestion for a new rule to discourage this, to add for next time, is to introduce a financial reduction in prize money (I suggest 10%) to be applied to any player whose game ends in a draw in less than 30 moves for any reason other than by agreement (which is already prohibited).

I first made this suggestion on Dana Mackenzie’s blog, where it was well-received, and Dana offered a nice refinement, too: The length of a game with a 3-fold repetition should be determined by the move when the repeated position *first* appears, not when the draw is claimed.

I’m curious how you would assess or handicap this idea.



Hal Bogner
Oct 21, 2015 at 10:18 am

PS – If you genuinely doubt that Hikaru made that very out-of-character comment, I suggest that you delete it. (And if you do so, please then delete this one, too.) Nobody needs that kind of stuff hanging around, which some people will mistakenly cite as genuine down the road.


David Smerdon
Oct 21, 2015 at 7:54 pm

Thanks Hal. I changed the comment’s moniker to “Hikaru’s alter-ego”, mainly because I found the comment funny and wanted to leave in the satire.

I like your suggestion. Actually it’s similar to what they’ve been doing in the Doeberl Cup in Australia for years now: a ‘fighting fund’ by which BOTH players involved in a decisive final round on the top five boards get a share of a couple of grand. It’s economically the same as your proposal, but I dare say that because of psychological factors like loss aversion, your proposal may be even more effective.

PS I did take account of Bareev’s potential result in my calculations. The math took care of every possible affecting outcome (literally hundreds of permutations).

Mark Houlsby
Oct 22, 2015 at 11:38 am


What David shared was not the analysis itself, rather it was merely the *results* of the analysis which, in isolation, are perhaps a little less valuable.

Clearly it would be churlish to argue that such analyses are not intrinsically interesting (certainly I’d never attempt to do such a thing, even if so inclined [which I’m not]). What is, perhaps, less acceptable, what is possibly even somewhat disingenuous, is David’s having taken a pot-shot at professional chessplayers (who, by definition, play better than he does [and waaay better than I do]) from the comfortable vantage point of academic economics {here I employ the term: “academic” in its broader sense]. Maurice Ashley certainly knows better. From my interactions with David on the Internet Chess Club I strongly suspect that he does, too. Therefore David’s behaviour in publishing the blog post and monitoring these comments has been…a little surprising.


David Smerdon
Oct 22, 2015 at 6:27 pm


I’m not taking a pot-shot at anyone. I argued that the players made the wrong decision from their own selfish, self-interested perspective – much in the same way I might criticise them for making a bad blunder. I cast no judgements on their behaviour from an ethical perspective. I would be very surprised if Hikaru took offence at my comments (for a fact, Luke did not).

And I monitor all comments on my website. Usually I don’t get very many. This article has been somehow…exceptional (here I do not employ the word in its broader sense:) )

Al Elgu
Oct 24, 2015 at 2:50 am

I was at Millionaire Chess II and saw the big hoopla. Game 7 started at 11 AM and these two were already outside at 11:20. Nine moves is a shame, especially for a GM. These 2 probably talked the night before and agreed to draw. Putz!

Oct 26, 2015 at 11:43 am

Alexander says “this kind of cheating by nine move games is in fact WORSE than cheating by other means.”

No. That’s just nuts.

I also don’t get the objection to high-altitude training of various kinds (including simulated.) Where would forbidding that end up? e.g. Chess players wouldn’t be allowed to get to the destination early to acclimatize? Or (example from yesterday) train with partner blowing smoke in their face? etc.

I didn’t read everything you wrote Alexander – I don’t think many would have; it didn’t seem to warrant slogging through pages and pages of it. You lost me at the sentence I quoted. You say all this then ‘Why do I bother’. Indeed! Go do something useful with your life. Good luck.



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