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)|
|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.