Berlin Candidates - Second Week

In last week's report on the 2018 Berlin Candidates Tournament (see Berlin Candidates - First Week), we saw three players with a plus score after three rounds:-

2.5 Kramnik; 2.0 Caruana, Mamedyarov

Another six rounds have been played, again leaving three players with plus scores:-

6.0 Caruana; 5.5 Mamedyarov; 5.0 Grischuk

In past reports on Candidates tournaments from previous cycles, like Moscow Candidates - Second Week (March 2016), I presented a crosstable from the offical site. I could find no such chart on the official site for the current tournament, so I took a snapshot of the crosstable from the news site that most of the English-speaking chess world uses for up-to-date chess information.

FIDE Candidates Tournament 2018

Source: The Week in Chess

The chart shows who will be playing whom in the last five rounds. The schedule for the critical games between the current leaders is:-

Round 10: Mamedyarov - Caruana
Round 13: Mamedyarov - Grischuk
Round 14: Grischuk - Caruana

In my 'First Week' report, I developed a chart from the last three Candidates tournaments projecting winners at different points in the events. The same observations were offered by GM Ian Rogers in his report on the first half of the Berlin event, Caruana Leading Candidates Race: “I’ll Try to Stay Calm.” (uschess.org; 18 March 2018):-

In the modern era, the winning recipe for qualifying to challenge the World Champion from the Candidates Tournament has been to be in the lead at the halfway mark. In fact one has to go back to 1959 to find a Candidates Tournament where the winner was not leading halfway through the event. [...] The winners in 2013, 2014 and 2016 – Carlsen, Anand and then Karjakin – were always tied with Levon Aronian at the halfway point, before going on to outpace the Armenian.

I double-checked GM Rogers on his facts from the earlier cycles and discovered that in the eight player, four stage round-robin 1959 Yugoslavia Candidates, the unlucky Paul Keres was leading at the half-way point with 10.0/14, a half point ahead of Mikhail Tal, who eventually won the event. In the 1962 Curacao Candidates, which used the same structure as in 1959, GMs Petrosian and Geller were leading at the half-way mark with 9.0/14. Petrosian eventually finished a half-point ahead of Geller and Keres. That tournament was marred by accusations that the three leaders colluded to draw against each other (which the crosstable confirms) and to play for wins against the other participants, the non-Soviets in particular.

For those suspicions of collusion, the Candidates stage of subsequent World Championship cycles was changed to a system of long matches which -- except for a handful of cycles using a single-event knockout system -- persisted until a round-robin tournament was reintroduced for the 2013 London Candidates. For more about Soviet collusion in Candidates tournament of the 1950s, see Calculating Collusion (February 2010) on this blog.

Predictions based on the leader at the halfway mark also held for two title tournaments in the 2000s. At 2005 San Luis, GM Topalov was ahead of the next player, GM Svidler, by two full points after seven rounds. At 2007 Mexico City, GM Anand was ahead of GM Gelfand by a half point after seven rounds.

The only Candidates tournament for which I haven't developed a cumulative score by round is the 1985 Montpellier Candidates. That event was unusual in that it qualified the first four players into a short series of matches.