2014 Gashimov Memorial Round 10

Carlsen beat Caruana, winning clear 1st place. Meanwhile, Radjabov finished on a solid 5.0/10 with a 2793 performance - exactly equal to his peak rating before its big decline. We will certainly be watching to see if his rating makes a full recovery.

2014 Gashimov Memorial Round 9

Caruana greatly boosted his chances by defeating Mamedyarov today. He is tied with Carlsen at 5.5/9 while the rest are at least a full point behind. Thus, the Carlsen-Caruana game will be decisive.

Carlsen wins clear 1st: 43%
Carlsen wins or ties for 1st: 84%
Caruana wins clear 1st: 16%
Caruana wins or ties for first: 57%
Everyone else: 0% chance of winning 1st place

Carlsen will have the advantage of the white pieces, which these estimates do not account for. But there is also a strong incentive for both players to avoid risks, so the estimated draw rate may be too low.

2014 Gashimov Memorial Round 8

Nakamura recovers by triumphing over Mamedyarov, while Caruana prevailed over Radjabov. The standings after 8 rounds:

Unfortunately, when I "improved" the forecasting computer program, it started giving me results that could not possibly be correct (i.e., Karjakin has a better chance of winning the tournament than Carlsen). I haven't been able to identify the bug yet, but luckily we can still do the calculations by hand.

The critical game will be the Round 10 battle between Carlsen and Caruana. If Carlsen wins, then he is guaranteed at least a tie for 1st regardless of what happens in his game with Radjabov. Based on games between 2700 players with a similar rating gap, this event happens 43% of the time. Case 2: Carlsen loses to Caruana (16% chance). But Carlsen can still secure 1st place if he beats Radjabov (55% chance) while Caruana draws or loses to Mamedyarov (72%). Even if Carlsen draws Radjabov, he can still win the tournament if Caruana loses (22%) and no one on 4/8 wins twice. Case 3: Caruana and Carlsen draw. Then Carlsen is assured 1st place if he doesn't lose to Radjabov (89.5%), but even a loss doesn't always cost him the tournament. After adding up the probabilities, we see that Carlsen has about an 85% chance of tying for 1st. This seems like a reasonable figure: yesterday Carlsen was around 90%, but now his main pursuer is Caruana, who is much higher rated than Radjabov. Thus, Carlsen's chances should have declined slightly from 90%, and they did.

Most of Caruana's chances rely on him defeating Carlsen, but there are ways for him to win if he draws Carlsen and prevails against Mamedyarov. Caruana has about a 20% chance of tying for 1st.

Radjabov, Karjakin, and Nakamura face far steeper odds. There is about a 95% chance that the winner of the tournament will need to score at least 6/10. They need to win both of their last games and hope that the leaders stumble. Their chances are less than 10%.

2014 Gashimov Memorial Round 7

Carlsen scores again, and now it is very likely that he will win the tournament. Radjabov drew today and still has some chances of taking 1st place. The model also thinks that Caruana has a shot due to his high rating. The latest forecasts, based on 40,000 simulations:

Standings after 7 rounds:

2014 Gashimov Memorial Round 6

Carlsen's chances surged today after his victory over Mamedyarov. At the beginning of the tournament, I mentioned that Radjabov would be an interesting player to watch. His rating reached peaked at 2793 before falling dramatically to 2713. With 6 rounds completed, it looks like Radjabov's great comeback is well under way: he is tied for 1st and has yet to lose a game.

Standings after 6 rounds:

Gashimov Memorial Round 5

Bottom seed Radjabov upsets Carlsen in a hard-fought game. Then Mamedyarov beat Caruana, throwing the forecasts into confusion. Right now it looks like anything could happen.

Current standings:

2014 Gashimov Memorial Round 4

Caruana defeated Carlsen in a fine game, shaking up the forecasts considerably. Carlsen remains the favorite due to his stratospheric rating, but victory is far from inevitable. The latest winning probabilities:

2014 Gashimov Memorial - Round 2 update

Carlsen defeated Nakamura today, making the forecasts far less exciting. His winning chances climbed to nearly 92%:

2014 Gashimov Memorial

Round 1 began today. Group A is a 6-player double round robin with quite an elite group: Carlsen, Caruana, Nakamura, Karjakin, Mamedyarov, and Radjabov. Of course, no fancy stats model is needed to see that Carlsen is the clear favorite. But as we saw in the Candidates Tournament, having the highest rating does not guarantee victory. How confident can we be in Carlsen's chances?

To answer this, I used the same model that I applied to the Candidates (I'll discuss the performance of that model after the tournament). The Elo ratings provide the expected score in each game. To estimate the draw percentage, I first searched my database for games by 2700 players. Inside this collection of games, I matched each game in the tournament to games with a similar rating gap. For example, Mamedyarov is rated 47 Elo above Radjabov. The model's draw rate for their match is based off the draw rate between 2700 players where the rating gap is between 37 and 57 points. The likelihood of a draw in the other games is computed in the same way.

The results? Here are the probabilities before Round 1, based on 40,000 simulations. Since multiple players can share 1st place, the probabilities in the first column will add to more than 1. For the same reason, the second column sums to less than 1.

Naturally, Carlsen's chances are far superior to anyone else's. But his odds seem surprisingly modest; 75% or 85% would have been my first guess. After he won his first game, the model revised its expectations upward:

Those who have followed the chess news closely may remember that Radjabov used to be one of the world's very best. Back in April, his rating reached an impressive peak of 2793, but has since plummeted to 2713. Such a plunge is very unusual at this level. It will be interesting to see if he can come back this tournament.

Is 1.e4 the best first move?

I studied this question in my ChessBase article "1.e4 - 'Best by Test'?" Part 1 and Part 2. We all know that the databases show a higher percentage score for 1.d4. What is less well known is that White tends to pick d4 when he is the favorite and e4 when he is the underdog. Part 1 demonstrated that once this tendency is accounted for, the gap between 1.e4 and 1.d4 vanishes - both moves perform equally well.

But in Part 2, we see that there is more to the story. The average of White's and Black's ratings also matters. At the higher levels, the advantage of playing White increases. After correcting for this, e4 ever so slightly outperforms d4. If you switch from d4 to e4 in your next 1000 games with White, you will score two points (we suspect that this result will not cause droves of d4 players to change their repertoire). To be careful, I also checked for transpositions using the ECO classification of the games in my database. The results were unchanged.

Many times on chess forums, players lament that opening theory is going too far and that chess is being "played out" - there will be less and less scope for originality and creativity. Usually this is followed by recommendations that we alter the rules or switch to Chess960/FischerRandom. My results did shed some light on this debate. If chess really were being exhausted, we would expect that opening theory would eventually nullify White's advantage, since a perfectly played game will be drawn. Thus, over time White's percentage score should move towards 50%. I did find some evidence of this: there is a statistically significant drop in White's performance over the last few decades. However, the rate is extremely slow; Black's chances improve by only 0.01% per year. I concluded that we still have another couple of centuries before chess is played out.

The World Chess Championship

These articles from 2013 were my debut as a chess and statistics writer. "Are the Chess World Champions Just Lucky?" Part 1 and Part 2 in ChessBase examined the results of World Championship matches. When Fischer crushed Spassky 12.5 - 7.5, there wasn't any doubt that he was the superior player. On the other hand, players such as Khalifman and Kasimdzhanov were never considered legitimate world champions. How can we tell if the winner of a match really is the better player? Fortunately, statistics provide a way to answer that question.

The second part of the article proposed a new format for the World Championship and gave forecasts for the 2013 Anand - Carlsen match. Of course, everyone knew that Carlsen was the favorite, but most people also acknowledged that Anand had reasonable chances of keeping his crown. The model (refined further in Part 3) went out on a limb by placing the probability of a Carlsen victory between 86% and 93%. In retrospect, this confidence in Carlsen looks entirely justified, but it was a bit provocative back then.

The reader feedback in Part 3 raised some fascinating questions. My favorite was the one about Fischer's proposed format for the 1975 World Championship match with Karpov. How unfair would it have been to Karpov? He would need 10 wins - 8 wins to prevail, while Fischer only needed 9 wins - 9 wins to retain his title. I used statistics to measure the unfairness and then compared it to other formats where the champion had draw odds.