Nakamura’s huge run continued today. Not only did he win his second consecutive game (so much for our earlier complaints that he was drawing too much!) but he also benefited from an upset victory by Jakovenko over Caruana. Nakamura is now tied with Caruana and Dominguez for first place at Khanty-Mansiysk, and if the tournament ended today would earn 140 Grand Prix points for his efforts, enough for a comfortable second place finish in the final standings (behind Caruana) and a berth in the 2016 Candidates Tournament.

Despite his loss, Caruana’s odds of a top two finish in the overall Grand Prix standings remain a comfortable 92%, and Nakamura boasts a 76% chance (up from just 31% two days ago). Overall there is more clarity in the race right now, going into tomorrow’s rest day, than at any point so far in this event. Here are how the standings would look if the event ended now, and each player’s current and pre-event odds of qualifying for the Candidates Tournament by finishing in the top two:

Player |
Live Rating |
Baku |
Tashkent |
Tbilisi |
Khanty-Mansiysk |
CURRENT TOTAL |
ODDS (PRE K-M) |
ODDS (CURRENT) |

Fabiano Caruana (ITA) | 2806.1 | 155 | 75 | 140 | 370 | 71% | 91.8% | |

Hikaru Nakamura (USA) | 2803.1 | 82 | 125 | 140 | 347 | 49% | 75.7% | |

Evgeny Tomashevsky (RUS) | 2740.3 | 82 | 170 | 25 | 277 | 52% | 6.2% | |

Dmitry Jakovenko (RUS) | 2753.1 | 30 | 140 | 80 | 250 | 9% | 11.1% | |

Boris Gelfand (ISR) | 2750.8 | 155 | 15 | 80 | 250 | 7% | 8.7% | |

Sergey Karjakin (RUS) | 2757.8 | 82 | 75 | 80 | 237 | 8% | 6.5% | |

Shakhriyar Mamedyarov (AZE) | 2735.0 | 35 | 125 | 75 | 235 | 0% | 0% | |

Leinier Dominguez (CUB) | 2750.2 | 10 | 75 | 140 | 225 | 0% | 0% | |

Teimour Radjabov (AZE) | 2738.0 | 50 | 50 | 110 | 210 | 0% | 0% | |

Dmitry Andreikin (RUS) | 2717.9 | 20 | 170 | 10 | 200 | 0% | 0% | |

Alexander Grischuk (RUS) | 2780.9 | 82 | 40 | 55 | 177 | 3% | 0.09% | |

Peter Svidler (RUS) | 2739.8 | 82 | 20 | 55 | 157 | 0.1% | 0% | |

Anish Giri (NED) | 2768.2 | 40 | 75 | 40 | 155 | 1% | 0% | |

Baadur Jobava (GEO) | 2696.2 | 75 | 40 | 25 | 140 | 0.2% | 0% | |

Maxime Vachier-Lagrave (FRA) | 2723.6 | 75 | 40 | 10 | 125 | 1% | 0% | |

Rustam Kasimdzhanov (UZB) | 2703.8 | 35 | 15 | 75 | 125 | 0% | 0% |

On the other hand, nothing is decided yet. While the picture is finally clear in the sense of having two obvious favorites, rather than three or more players with similar chances, the number “100%” doesn’t show up in any column. There’s still roughly a one in four chance that Nakamura fails to qualify, and several long shots who could potentially overtake him in the final three rounds. I find it interesting to note that Jakovenko and Gelfand both have better chances of qualifying for the Candidates now than they did when this tournament began. Jakovenko’s 11% chance, for instance, certainly can’t be ignored. Much stranger things have happened.

Here is a map of each player’s most likely final score (in yellow) at this event, and their odds of achieving each possible score. This should emphasize how much remains unclear in the final results – no player in the field has better than a 36% chance of achieving any one specific score:

As for the final standings at this particular event, now that we have a three-way tie with just three rounds left, a clear winner is looking less likely. Here are each player’s expected Grand Prix points earned on average (EV) and odds of winning the event outright, along with each players “Score Today”, or how many Grand Prix points they would earn based on the current standings, so that you can see at a glance who is favored to improve their situation in the last three rounds and who is more likely to regress:

Player |
K-M EV |
Score Today |
Odds of Clear 1st |
(Pre-Event Odds) |

SHARED FIRST | 39% | 28% | ||

Hikaru Nakamura (USA) | 125 | 140 | 22% | 14% |

Fabiano Caruana (ITA) | 120 | 140 | 17% | 17% |

Leinier Dominguez (CUB) | 123 | 140 | 15% | 2% |

Sergey Karjakin (RUS) | 87 | 80 | 3% | 5% |

Dmitry Jakovenko (RUS) | 86 | 80 | 2.8% | 3% |

Boris Gelfand (ISR) | 83 | 80 | 1.8% | 3% |

Peter Svidler (RUS) | 67 | 55 | 0% | 2% |

Alexander Grischuk (RUS) | 62 | 55 | 0.29% | 11% |

Anish Giri (NED) | 47 | 40 | 0.00% | 7% |

Baadur Jobava (GEO) | 26 | 25 | 0.00% | 1% |

Evgeny Tomashevsky (RUS) | 31 | 25 | 0% | 3% |

Maxime Vachier-Lagrave (FRA) | 13 | 10 | 0% | 3% |

Notice that all three co-leaders are expected to earn, on average, fewer Grand Prix points than they currently stand to pick up. This is because maintaining a lead is fundamentally difficult. You don’t just have to outperform one player behind you (which you might be a favorite to do), you must avoid being passed in the standings by ANY of the players behind you. Seldom would anyone be favored to outperform the entire field – perhaps excepting Magnus Carlsen who is not a part of this event.

After the rest day, round 9 will be played on Sunday. Caruana will have the black pieces against Karjakin as he tries to hold on to his place atop the Grand Prix standings. Our other leader in the current projections, Nakamura, will have white against Grischuk.

That game, Nakamura – Grischuk, presents an interesting scenario (first brought to my attention by Martin Bennedick, @bennedik on Twitter) where it’s possible that Grischuk’s overall odds of qualifying for the Candidates Tournament could possibly be highest if he LOSES this game. To understand why, we must remember that the Grand Prix will determine only two of the eventual eight players in that field. Two other Candidates will be the players with the highest average rating across all 12 rating lists from 2015 who did NOT already qualify in another manner.

Right now that average ratings list shows potential qualifiers as 1. Caruana; 2. Topalov; 3. Nakamura; 4. Grischuk; 5. Kramnik. This means that as it stands right now, if Caruana and Nakamura both qualify via the Grand Prix, Grischuk moves up to second on the list and becomes a projected Candidate (which he currently is not). If Caruana and, say, Tomashevsky finish top two in the Grand Prix, then Topalov and Nakamura would get in by ratings and Grischuk would be left out.

So how much could Grischuk help Nakamura’s chances by losing that game? We estimate Nakamura at 76% to finish in the top two as it stands, but if we assume a Nakamura win over Grischuk while keeping everything else random, those odds climb to 93%! On the other hand, if Grischuk were to shoot himself in the foot and beat Nakamura, Naka’s chances would plummet to roughly 45%.

So why isn’t it a no-brainer that Grischuk is better off with a loss? What’s the downside, that led us to use hedging terminology like “it’s possible” and “could be”? First there is of course a morality aspect. We want to be completely clear that we are absolutely not advocating an intentional loss. Throwing a game is never acceptable, especially in an event of this magnitude, regardless of whether the math indicates you might benefit from a loss. However there’s also a mathematical downside. With the loss, Grischuk’s rating would drop, and he would have only a small lead over not just Kramnik but also Aronian in our projected average ratings. There’s a lot of chess left to be played in 2015, and a strong chance that Grischuk could be overtaken. The principle we discussed earlier where it’s particularly difficult to maintain a lead against multiple challengers applies here as well. With a loss in this game, Grischuk would temporarily be our projected #2, but would be an underdog to hold that spot. On the other hand, with a win, he would gain rating points and his projection in the average rating standings would be much stronger. He would have a commanding lead over those behind him, and while he would be #3 behind Nakamura it would be by a small margin. 45% of the time Naka would qualify via the Grand Prix anyway, and he’d be #2 in rating by a large margin, and the other 55% of the time he’d certainly have ample opportunity as the year progresses to surpass Nakamura in the projected rating standings.

Overall, I don’t have a good algorithm to predict odds of various rating shifts through the rest of the year, so I can’t put precise predictions on how likely players are to finish top two in the ratings race. However the 10 point rating swing of a win versus a loss, carried through 7 future rating lists, will have a lot of impact. All told, I can’t prove it, but I think Grischuk is more likely to eventually find himself in the 2016 Candidates Tournament if he beats Nakamura on Sunday than if he loses on Sunday. I do suspect, though, that a draw might be worse than either, so perhaps it would be in his best interest to play aggressively and see what happens! It’s not entirely clear though. I’d love to hear other thoughts on this scenario in the comments.

Either way I certainly find it to be a very interesting situation to analyze, if you happen to have an interest in game theory as I do.

My sense is that Grischuk should try for as good of a result as he can get against Nakamura, and if that happens to be a draw, then so be it. The cases where Nakamura-Grischuk is a draw *and* Nakamura fails to secure a spot in the Candidates’ through the Grand Prix most likely require Nakamura to stumble at some point in the final two rounds, so if Grischuk can hold his own, or even go +1 in that time, he’ll catch up even more on rating against Nakamura. Being careless of a draw against Nakamura gives five Elo points away not just to Nakamura, but also to Topalov, Aronian, Kramnik, and let’s throw Wesley So and Anish Giri in there, too.

I think it’s also worth pointing out that Grischuk went from being 34 points ahead of Nakamura on Jan. 1 to 22 points behind him in the live ratings in less than five months. Nakamura has gained almost exactly 1% for his Elo rating, and Grischuk has lost almost exactly 1% of his rating in that time. I think there’s this natural volatility for ratings at the 1% level that’s just a fact of life. It’s easy to forget that Grischuk is actually slightly ahead of Nakamura at the moment for the #2 Ratings slot for the Candidates’ Tournament. I think it’d be crazy for him to be heedless of half-points against potential rivals right now. There’s too much chess to play to put much stock in a projection that just fills in current live rating for the months of July-December.

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Grischuk know he’s ‘insignificant’ in the Khanty-Mansiysk GP leg, but will definitely give it a fight in the other venues, i.e., ratings and the World Cup (which is more unpredictable even for Top 10 super-GMs like him). Statistically, he has better chance thru ratings, hence he MUST fight every game as each counts a BIG, BIG ~5 ELO points at his level. And he has just proven exactly this point by defeating his countryman Karjakin — that win just proved that he’s amongst the world’s best.

Between Naka and Grischuk, Naka feels the stronger urge to perform. Am not saying Naka should win, but rather that Grischuk’s attitude is a wait-and-see approach → for me, this implies that his depth on the chessboard will not be as encompassing as it must be.

I don’t think Naka will purposely play for a win bcoz such mindset is instead more prone to commit errors. As Naka played it cool in the first half of Khanty-Mansiysk, it is even more logical for him to do the same now that he leads the GP standings.

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The Nakamura vs. Grischuk dilemma is interesting. I hope (and think) that you’re right, and Grischuk’s best chance is still a win.

But I’d like to point out another small dilemma in round 8: If Tomashevsky had won his long endgame with Dominguez, he would have improved his provisional GP score by 10 points (from currently 25 to 35). But in that scenario, because of Dominguez’ loss, Tomashevsky’s most important rival Nakamura would have gained 15 points! (From 140 to 155). I have no doubt that Tomashevsky’s overall chances would still have benefitted from a win, because in his current situation he simply must improve his score. But it goes to show that strange things can happen with this scoring system, and if a similar dilemma were to arise in round 11, one of the players might find himself in a true must-draw situation: A situation where only a draw is good enough, and a win won’t suffice.

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The probabilities are not known, they are estimated from a past with the presumption that the past predicts the future, and one might know that there is other information. If one e.g. happens to know that MVL is not really in shape, then his chances are, game-by-game, not as good as his rating should suggest. So there is a big element of belief in decisions based upon

chancesof winning/losing.In the last round, however, things will be much clearer. And then Nakamura could theoretically face the following scenario: himself being sure of at least a 2nd spot, 1.5 points clear of everyone behind him – but with a theoretical possibility that Tomashevsky makes it. Nakamura could then be in a situation where a loss against Jakovenko

guaranteesa weaker result for Tomashevsky, and therebyguaranteesNakamura a ticket to the candidates – while other outcomes vs. Jakovenko still leaves it a theoretical possibility that Tomashevsky gets the ticket.In such a situation there will be no element of belief necessary. And, I think, Nakamura would be morally well justified in resigning at move zero – after all the rules are given, and losing in order to reach the primary objective of the GP series, would be nothing but playing by the rules.

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In those instances when a loss is better than a win or draw, can the player not call in sick-lose by forfeit- and save the rating points? Would this not be the best of both worlds?

Alan Kirshner

Toledo Ohio USA

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They can,but think of this instance. It is now round 11. Nakamura is in a lose and win scenario with Jakovenko. Nakamura must lose the game to ensure his own qualification, Tomashevsky has come on strong in rounds 9 and 10, winning both games and if Nakamura does anything but lose, Tomashevsky will be in with the second slot. Jakovenko knows he has no qualification chances through GP or rating so he should only have the game result to consider *but* Tomashevsky is his countryman and friend so he would like to help him secure a place in candidates. What happens if Jakovenko submarines Nakamura’s lose to win strategy by no showing as well?We could get a standoff where both player refuse to sit at the table.

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The advantage of having white – you forfeit first? 😉

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Does anyone have an exact round-by-round scenario that shows that such a must lose situation could even happen? I’m suspicious because the exact standings of all the players in between say, Naka and Toma would matter as well, with various tied scores carving up the GP points in different ways. And Jakovenko is suddenly a possible qualifier candidate as well now.

So, anyone have a round by round situation where Nakamura would face Jakovenko and a loss is a qualifying outcome?

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Interesting stuff!

Another reason why leaders are expected to score fewer points in the final standing compared to the current standing is “regression to the mean”; not only are they expected to place lower relative to other players, they are also expected to score fewer points per game. When the field is relatively close in strength, leaders are at the top because they have, on average, performed better than their rating suggested. While some of this is due to genuine “form”, some of it is due to chance, not indicative of future results. I am sure your models bear that out as well.

In a real tournament, of course, tactics also play a role, and a player may settle for a draw if it ensures a top 2 Grand Prix score, rather than play for the highest possible score. And, of course, the reverse is true as well; someone with an outside chance of qualification may take a greater risk to achieve a win, but thereby decreasing his expected score (because with very risky play, the likelihood of a loss increases disproportionately).

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