
From March 14 to April 1, 2013, FIDE and AGON – the World Chess Federation’s
commercial partner – are staging the 2013 Candidates Tournament for the
World Chess Championship 2013. It will be the strongest tournament of its kind
in history. The venue is The IET,
2 Savoy Place, London. The Prize Fund to be shared by the players totals €510,000.
The winner of the Candidates will become the Challenger to Viswanathan Anand
who has reigned as World Champion since 2007. The main sponsor for the Candidates
is State Oil Company of the Azerbaijan Republic SOCAR,
which has sponsored elite events chess in the past.
Candidates statistics going into round 13
After a thrilling Round 12 victory with the black pieces against Levon Aronian,
Vladimir Kramnik has jumped into the sole lead at +4, and suddenly is the tournament
favorite! There are very few scenarios where Kramnik shares first place and
wins on tiebreak, so his best hope is to win the tournament outright, which
is now quite likely:
After Round 12, Vladimir Kramnik appears to have a 65% chance to win
the tournament and become the World Championship Candidate.
By itself, Kramnik's unlikely defeat of Aronian with Black was not devastating
to Magnus Carlsen's chances. If it had been coupled with a Carlsen-Ivanchuk
draw, then Carlsen and Kramnik would be sharing first place at +4, and since
Carlsen's Sonneborn-Berger score is superior to Kramnik's, a shared first with
Kramnik would be almost as good as clear first ahead of Kramnik (from Carlsen's
perspective).
And by itself, Carlsen's unlikely loss to Vassily Ivanchuk with White would
not have been devastating to Carlsen's chances. If it had been coupled with
an Aronian-Kramnik draw, then Carlsen and Kramnik would be sharing first place
at +3, and Carlsen sharing first with an undefeated Kramnik gives Carlsen the
tiebreak 100% of the time. That last one is worth repeating – now that
Carlsen has lost a game, if you remember just one thing from this article, remember
this:
Carlsen sharing first with an undefeated Kramnik gives Carlsen
the tiebreak (and tournament victory) 100% of the time.
But the two unlikely outcomes, combined with each other, are devastating to
Carlsen's chances. In one day, the chances of Kramnik winning clear first place
have jumped from 5% to 60%, and now Carlsen's only consolation is that he still
holds a superior tiebreak against Kramnik, and will likely win the tournament
if he can just grab a share of first place:
After Round 12, Magnus Carlsen appears to have a 35% chance to win
the tournament and become the World Championship Candidate.
Thanks to his head-to-head loss against Kramnik, Levon Aronian must now finish
ahead of Kramnik in order to win the tournament, and so there is a very long
list of things that must happen in order for Aronian to triumph. First of all,
Aronian must win his last two games (ending at +3) and Kramnik must lose his
last two games (ending at +2). Further, Carlsen must finish at +3 or worse
(he is currently at +3). If Aronian and Carlsen finish in a two-way tie for
first at +3, then Aronian wins the tiebreak due to having more wins. With so
many requirements, Aronian essentially has no chance to win the tournament anymore.
Peter Svidler could theoretically finish in shared first at +2, with Kramnik
losing twice to finish at +2 as well, and Carlsen and Aronian both no higher
than +2, but it turns out that due to the head-to-head considerations (Kramnik
having defeated Svidler and Aronian now) there is no group that could finish
in shared first at +2 (including Svidler and Kramnik) where Svidler survives
the tiebreak against Kramnik. So that is why Svidler literally has no chance
of winning the tournament, despite a microscopic chance of sharing first place.
After Round 12, the odds are 7,100 to 1 against Levon Aronian winning the
tournament and becoming the World Championship Candidate, and none of the other
five players has any chance at all. However, even the upcoming games not involving
Kramnik or Carlsen may nevertheless have vital importance, since they affect
the Sonneborn-Berger tiebreaker score for Kramnik and Carlsen in the event that
Kramnik loses at least once and finishes in shared first place with Carlsen.
So if we set aside all those other six players from consideration, it is just
a question now of Kramnik and Carlsen. Here are the key findings from my Monte
Carlo analysis, considering the myriad possible ways those two players could
finish in shared first, including how the final scores of the other six players
would impact the Sonneborn-Berger scores of Carlsen and Kramnik,
-
If Carlsen catches Kramnik by winning one more game than Kramnik during
Rounds 13/14, and neither of them lose any more games, then once-beaten
Carlsen would share first with an undefeated Kramnik and Carlsen would win
the tournament due to the tiebreaker for Number of Wins.
-
If Carlsen catches Kramnik because Kramnik loses one of his next two games,
then it will come down to the Sonneborn-Berger scores, which depend on all
the total scores of the various players that they beat or drew with or lost
to. It appears that if it comes to this, there is a 63% chance that Carlsen's
SB-score would be higher, a 24% chance that Kramnik's SB-score would be
higher, and a 13% chance their scores would be identical, leading to a need
for rapid games.
So, if Kramnik and Carlsen share first place, there is a 92% chance that
Carlsen wins the tiebreak based on Number of Wins or Sonneborn-Berger score,
and only a 5% chance that Kramnik wins it based on Sonneborn-Berger score, and
a 3% chance that their tiebreaker scores are completely equal and therefore
rapid games are required.
Therefore a shared first place for Magnus Carlsen is likely going to be
good enough to win the tournament.
- Simulations tell us that Kramnik is about 80% likely to finish
at +4 or +5, and Carlsen is about 80% likely to finish at +3 or +4. That
gives four possible combinations that are very plausible - and in three of
those four, Kramnik wins outright. In the fourth - where they both finish
at +4 - it is Carlsen who almost certainly wins the tournament, since… repeat
after me…
Carlsen sharing first with an undefeated Kramnik gives Carlsen the tiebreak
(and tournament victory) 100% of the time.

And here is a complete list of the possible remaining scenarios, sorted by
their likelihood:
Kramnik wins outright |
63% chance
|
Carlsen shares first with Kramnik and wins from tie-breaker #2: most
wins |
20% chance
|
Carlsen wins outright |
11% chance
|
Carlsen shares first with Kramnik and wins from tiebreaker #3: SB-score |
28 to 1 against
|
Kramnik shares first with Carlsen and wins from tiebreaker #3: SB-score |
73 to 1 against
|
Kramnik and Carlsen share first and have exactly the same
tiebreaker scores, so rapids are required |
140 to 1 against
|
Kramnik shares first with Aronian (and possibly Carlsen) and wins
from tiebreaker #1:head-to-head |
318 to 1 against
|
Aronian shares first with Carlsen and wins from tiebreaker #2: most wins |
7,900 to 1 against
|
Aronian wins outright |
75,000 to 1 against
|
If Kramnik finishes unbeaten but Carlsen catches him by winning more games
during the last two rounds, then Carlsen automatically wins the tournament. It
is only the less likely shared first, the one where Carlsen catches Kramnik
because Kramnik loses a game, that will consider Sonneborn-Berger score (since
in that scenario they would have the same number of wins). This is relatively
unlikely, as you can tell from the small slivers in that pie chart that mention
"tiebreaker #3: SB-score", but it is still worth investigating, since
it is the hardest to conceptualize. It was much more likely to matter 24 hours
ago, before Carlsen had lost a game, but we will still look at it.
Again, remember that Sonneborn-Berger is calculated as the total score of the
people you beat, plus half the total score of the people you drew. For this
tournament, we can also think of it as the sum of scores of the people you beat,
minus the sum of scores of the people you lost to. And you can also ignore people
that both players did equally well against - they both beat Svidler and Grischuk,
so we can ignore their scores. Carlsen beat Boris Gelfand twice, so (for the
purpose of SB-score) he really wants Gelfand to do well in his remaining games
(particularly the one against Kramnik!). Whereas Kramnik beat Aronian and Radjabov,
so (for the purpose of SB-score) he wants them to do well (particularly Radjabov's
game against Carlsen!).
The two simplest examples where Sonneborn-Berger will matter are the ones where
Kramnik loses one more game and otherwise Kramnik and Carlsen draw their remaining
games to finish on shared +3. This might mean Kramnik losing with White to Gelfand
in Round 13, or with Black to Ivanchuk in Round 14.
-
If Kramnik loses with White to Gelfand in Round 13, then it is a disaster
for Kramnik's Sonneborn-Berger score, and essentially means that Carlsen
will always win the tiebreaker against Kramnik if they share first place.
Their relative SB-scores would be very sensitive to Gelfand's final score
because Carlsen would have beaten Gelfand twice, whereas Kramnik would have
lost to him.
-
On the other hand, if Kramnik loses with Black to Ivanchuk in Round 14,
and otherwise Kramnik and Carlsen draw their remaining games to finish on
shared +3, then their SB-scores could swing one way or the other based on
what happens during Alexander Grischuk's games in the final two rounds.
This is because Kramnik beat Aronian, so he would want Aronian to do well
against Grischuk in Round 13 and boost Aronian's total score, whereas Carlsen
defeated Gelfand twice, so (again) he would really want Gelfand to do well
against Grischuk in Round 14 and boost Gelfand's total score.
It is an interesting counterpoint to the idea of using rapid games as a tiebreak
– using Sonneborn-Berger first does make it much less likely that rapid
games are needed, but on the other hand it potentially places very large importance
on the outcome of games between players who no longer have any chance to win
the tournament.
It is a bit depressing that there are only two rounds left, and all of this
is still so complex, but perhaps this is a good way to characterize the tiebreak
situation with regard to Sonneborn-Berger score:
-
The better that Boris Gelfand is doing in his games, the more likely it
is that Carlsen is happy to share first place with Kramnik.
-
The better that Alexander Grischuk is doing during his Round 13 game against
Levon Aronian, the more likely it is that Carlsen is happy to share first
place with Kramnik.
Standings after twelve rounds

Pairings for the next rounds
Round 13 March 31 at 14:00 |
Teimour Radjabov
|
-
|
Magnus Carlsen |
Alexander Grischuk
|
-
|
Levon Aronian |
Vladimir Kramnik
|
-
|
Boris Gelfand |
Peter Svidler
|
-
|
Vassily Ivanchuk |
Playchess commentary: GM Daniel
King
|
|
Round 14 April 1 at 14:00 |
Magnus Carlsen
|
-
|
Peter Svidler |
Vassily Ivanchuk
|
-
|
Vladimir Kramnik |
Boris Gelfand
|
-
|
Alexander Grischuk |
Levon Aronian
|
-
|
Teimour Radjabov |
Playchess commentary: GM Maurice
Ashley
|
|
Schedule and results
Round 1 March 15 at 14:00 |
Levon Aronian
|
½-½
|
Magnus Carlsen |
Boris Gelfand
|
½-½
|
Teimour Radjabov |
Vassily Ivanchuk
|
½-½
|
Alexander Grischuk |
Peter Svidler
|
½-½
|
Vladimir Kramnik |
Playchess commentary: GM Daniel
King
|
|
Round 2 March 16 at 14:00 |
Magnus Carlsen
|
½-½
|
Vladimir Kramnik |
Alexander Grischuk
|
½-½
|
Peter Svidler |
Teimour Radjabov
|
1-0
|
Vassily Ivanchuk |
Levon Aronian
|
1-0
|
Boris Gelfand |
Playchess commentary: GM Chris
Ward
|
|
Round 3 March 17 at 14:00 |
Boris Gelfand
|
0-1
|
Magnus Carlsen |
Vassily Ivanchuk
|
0-1
|
Levon Aronian |
Peter Svidler
|
1-0
|
Teimour Radjabov |
Vladimir Kramnik
|
½-½
|
Alexander Grischuk |
Playchess commentary: GM Yasser
Seirawan
|
|
Round 4 March 19 at 14:00 |
Magnus Carlsen
|
1-0
|
Alexander Grischuk |
Teimour Radjabov
|
½-½
|
Vladimir Kramnik |
Levon Aronian
|
½-½
|
Peter Svidler |
Boris Gelfand
|
½-½
|
Vassily Ivanchuk |
Playchess commentary: GM Daniel
King
|
|
Round 5 March 20 at 14:00 |
Vassily Ivanchuk
|
½-½
|
Magnus Carlsen |
Peter Svidler
|
½-½
|
Boris Gelfand |
Vladimir Kramnik
|
½-½
|
Levon Aronian |
Alexander Grischuk
|
½-½
|
Teimour Radjabov |
Playchess commentary: GM Yasser
Seirawan
|
|
Round 6 March 21 at 14:00 |
Peter Svidler
|
0-1
|
Magnus Carlsen |
Vladimir Kramnik
|
½-½
|
Vassily Ivanchuk |
Alexander Grischuk
|
½-½
|
Boris Gelfand |
Teimour Radjabov
|
0-1
|
Levon Aronian |
Playchess commentary: GM Chris
Ward
|
|
Round 7 March 23 at 14:00 |
Magnus Carlsen
|
½-½
|
Teimour Radjabov |
Levon Aronian
|
½-½
|
Alexander Grischuk |
Boris Gelfand
|
½-½
|
Vladimir Kramnik |
Vassily Ivanchuk
|
½-½
|
Peter Svidler |
Playchess commentary: GM Alejandro
Ramirez
|
|
Round 8 March 24 at 14:00 |
Magnus Carlsen
|
½-½
|
Levon Aronian |
Teimour Radjabov
|
0-1
|
Boris Gelfand |
Alexander Grischuk
|
1-0
|
Vassily Ivanchuk |
Vladimir Kramnik
|
1-0
|
Peter Svidler |
Playchess commentary: GM Alejandro
Ramirez
|
|
Round 9 March 25 at 14:00 |
Vladimir Kramnik
|
½-½
|
Magnus Carlsen |
Peter Svidler
|
½-½
|
Alexander Grischuk |
Vassily Ivanchuk
|
1-0
|
Teimour Radjabov |
Boris Gelfand
|
1-0
|
Levon Aronian |
Playchess commentary: GM Maurice
Ashley
|
|
Round 10 March 27 at 14:00 |
Magnus Carlsen
|
1-0
|
Boris Gelfand |
Levon Aronian
|
1-0
|
Vassily Ivanchuk |
Teimour Radjabov
|
½-½
|
Peter Svidler |
Alexander Grischuk
|
0-1
|
Vladimir Kramnik |
Playchess commentary: GM Yasser
Seirawan
|
|
Round 11 March 28 at 14:00 |
Alexander Grischuk
|
½-½
|
Magnus Carlsen |
Vladimir Kramnik
|
1-0
|
Teimour Radjabov |
Peter Svidler
|
1-0
|
Levon Aronian |
Vassily Ivanchuk
|
½-½
|
Boris Gelfand |
Playchess commentary: GM Chris
Ward
|
|
Round 12 March 29 at 14:00 |
Magnus Carlsen
|
0-1
|
Vassily Ivanchuk |
Boris Gelfand
|
½-½
|
Peter Svidler |
Levon Aronian
|
0-1
|
Vladimir Kramnik |
Teimour Radjabov
|
½-½
|
Alexander Grischuk |
Playchess commentary: GM Daniel
King
|
|
Round 13 March 31 at 14:00 |
Teimour Radjabov
|
-
|
Magnus Carlsen |
Alexander Grischuk
|
-
|
Levon Aronian |
Vladimir Kramnik
|
-
|
Boris Gelfand |
Peter Svidler
|
-
|
Vassily Ivanchuk |
Playchess commentary: GM Daniel
King
|
|
Round 14 April 1 at 14:00 |
Magnus Carlsen
|
-
|
Peter Svidler |
Vassily Ivanchuk
|
-
|
Vladimir Kramnik |
Boris Gelfand
|
-
|
Alexander Grischuk |
Levon Aronian
|
-
|
Teimour Radjabov |
Playchess commentary: GM Maurice
Ashley
|
|
The games start at 14:00h = 2 p.m. London time = 15:00h European time,
17:00h Moscow, 8 a.m. New York. You can find your regional starting time here.
Note that Britain and Europe switch
to Summer time on March 31, so that the last two rounds will start an hour
earlier for places that do not swich or have already done so (e.g. USA). The
commentary on Playchess begins one hour after the start of the games
and is free for premium members.