Candidates tiebreak scenarios

by Macauley Peterson
3/26/2018 – The first thirteen rounds of the Candidates Tournament brought top-class chess, brilliant games and many surprises. And the finale is set up to be exciting: four players can still hope to win the tournament and become the challenger of Magnus Carlsen. Fabiano Caruana takes a small lead into the final round, but with two other players within a half point of first, we can see a maximum of three players tied after Tuesday's final round. Who has the best chances? Read on... | Pictured: Sergei Karjakin in profile | Photo: Niki Riga

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Advantage Caruana

One controversial aspect of the Candidates Tournament is that any ties will be settled by a system of tiebreak criteria, and now certainly not over the board in a playoff.

Standings after the penultimate round

Chances clearly now favour Caruana, the leader by half a point, but things are still far from decided. In many tiebreak scenarios, it's Mamedyarov with an edge.


What to look for in round 14

It will be interesting to see how Caruana handles the situation. He's in much better shape than he was heading into the final round of the 2016 Candidates in Moscow, when he faced Karjakin, needing to win. This year, a draw would give him reasonably good chances, and he has the black pieces. But nothing is certain, and he would, of course, prefer to have the luxury of playing for two results since he's untouchable with a win. Conversely, a loss would be a disaster.


Caruana plays black, but how much risk will he take? And what mood will Grischuk be in?

Sergey Karjakin vs. Ding Liren

Karjakin plays with white against Ding, and this game will be absolutely critical for both. Ding, a full point behind Caruana, must of course win, and then hope other results go his way. Karjakin has more routes to tournament victory. But he most likely has to win. The only scenario in which a draw is enough for Karjakin is if Mamedyarov and Caruana lose. But if Karjakin does win, then the pressure on Mamedyarov and Caruana will be huge.

Alexander Grischuk vs Fabiano Caruana

In the last round, Grischuk has white against Caruana. Grischuk's games have been wild and anything is possible. But one thing is certain: Grischuk is eliminated from any chance to win the tournament. The best he can do now is give his countryman Karjakin a big boost by beating Caruana.

Alexander Grischuk is out | Photo: World Chess

Vladimir Kramnik vs. Shakhriyar Mamedyarov

Mamedyarov has Black versus Kramnik, but a draw is unlikely to be enough, so he will have to play aggressively and keep his options open. Kramnik can help Karjakin considerably by beating Mamedyarov.

Levon Aronian vs Wesley So

This game between the two players at the very bottom of the standings has a tiny bearing on the Sonnenborn-Berger scores (see below), but not enough to influence the tiebreak calculation. And with nothing at stake for the players individually, look for a fairly quick draw after a long tournament that both players would be glad to forget.

How will a tie be broken?

There are three levels of tiebreaks, but the odds are we'll only need the first to determine the winner.

Tiebreak criteria #1: Direct encounter

There is a reasonably high probability that two or more players will end up with the same score. But with a relatively high number of decisive games in Berlin, many such ties will actually be decided on this first criterion, the player's head-to-head results. That's good for Karjakin in a tie with Caruana as the Russian's twelfth round win would throw the tournament his way. However, Karjakin does not want to be the first with Mamedyarov: here too there was a draw and a win, but the win went to Mamedyarov. Mamedyarov's score with Caruana is equal — two draws. That means if the three of them tie, either on 8 or 8½ points (and it doesn't matter which), then Mamedyarov wins.

There's one more remote scenario that could be decided here. If Ding beats (and eliminates) Karjakin, Mamedyarov draws and Caruana loses, then we would have a three-way tie on 8 points. In this case Ding's head-to-head score against Mamedyarov and Caruana is superior. Still, on balance, advantage Mamedyarov.

Tiebreak criteria #2: Wins

If the direct match between the tied players does not result, the number of winning entries in the tournament counts. Here, Karjakin and Caruana have won four games so far, more than any other player in the tournament. However, if Mamedyarov wins, he will also have four wins. So a scenario in which Mamedyarov and Caruana tie, it will need to be broken by the third and final criteria. The exception would be if Caruana loses, and Mamedyarov and Karjakin both draw. Then there would be a three-way tie on 8 points, and Mamedyarov wins, as noted above. Advantage Mamedyarov.


Mamedyarov is favoured in many tie scenarios | Photo: Niki Riga

Tiebreak criteria #3: Sonneborn-Berger score

Should the number of games won bring no decision, then we go to the Sonneborn-Berger score. This could happen if there is a two-way tie between Mamedyarov and Caruana on 8½ points. In this case, their results against the other players in the tournament come into play. The main idea is that points (wins or draws) scored against higher-ranked players in the standings are more valuable than those against players who performed poorly. The final calculation requires all results to be projected, but a Mamedyarov win which would be required would give him the tournament on S-B score over Caruana. Advantage Mamedyarov.

Playoff match

This was always extremely unlikely, but it remained theoretically possible going into Monday's round, albeit only in certain scenarios in which Mamedyarov and Grischuk were to tie for first. Had that happened, a playoff mini-match between the same players would have followed: Two rapid games with 25 minutes plus 10 seconds per move for the entire game. If both games are drawn, two blitz games with 5 minutes plus 3 seconds, and if still drawn, finally, a single sudden-death "Armageddon" game.

Just how unlikely was it? After twelve rounds, out of 6561 possible outcomes of the tournament, only seven scenarios would have resulted in a Mamedyarov vs Grischuk playoff. After Karjakin's draw in round thirteen, there were merely three possible playoff outcomes. And by the end of play Monday that number is zero.

Bottom line: There will be no playoff on Wednesday.

But who's the favourite?

Caruana is the clear favourite. But Karjakin is the only one among the three to have the White pieces in the final round. On the other hand, the players who have been given the burden of being considered a favourite so far have suffered. And so many of the scenarios are perfectly plausible. In any case, it remains exciting.

According to one observer's calculations, Caruana has greater than 50% chances to win, which increase to roughly 2/3 if he should draw against Grischuk tomorrow. Ding meanwhile has less than 2% chances, when one considers the general probability of wins, losses and draws in chess.

Corrections: As pointed out in the comments: If Ding beats (and eliminates) Karjakin, Mamedyarov draws and Caruana loses, Ding wins. For Karjakin to win by drawing, Caruana would also have to lose.


Macauley is Editor in Chief of ChessBase News in Hamburg, Germany, and producer of The Full English Breakfast chess podcast. He was an Associate Producer of the 2016 feature documentary, Magnus.
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mcplayerus mcplayerus 3/27/2018 11:29
Lots of possibilities but let's imagine you are in Caruana's shoes: obviously he can't risk and play all out for a win because he's got black in this game and Grischuk can beat anybody in the world especially now without any pressure (although no motivation either) and playing white. So most probably Caruana will settle for a safe and quick draw and hopes Ding chances to win will be enough to make him motivated enough to hold Karjakin. So the only real danger comes from Mamedyarov but here again you normally expect Kramnik being able not to lose with white. So my bet is all games drawn although some of them might be dramatic ones like the whole tournament was!!
VincentM VincentM 3/27/2018 09:10
In this tournament:
Caruana after a rest day: 4,5/5 (won 1st, 4th, 7th and 13th round, drew 10th)
Caruana no rest day: 3,5/8
I guess he needs his beauty sleep :-)
Peter B Peter B 3/27/2018 07:04
@peterfrost what you say about MVL would be true if the World Cup was the only way to qualify. But MVL also failed to qualify either by rating or via the Grand Prix. In fact in the GP he was very close, but just couldn't find one more win. If he couldn't win under pressure in the GP, there's no reason to think he could do it in the Candidates. Meanwhile, I think the World Cup is important as a "wild card" entry method, to give any player a chance if they're good enough.
peterfrost peterfrost 3/27/2018 06:25
May I add my voice to those cheering that there was only ever a very remote possibility of such a wonderful tournament being decided by a crude speed chess play off. Any form of tie break known in advance is preferable. I also think it is a great pity that had there been a different outcome in a single Armageddon game, we might now be contemplating a Carlsen-MVL title match. We must disassociate classical chess from speed chess as far as possible. I would also agree with those who argue that if we must have tie breaking speed games in the title match, they should be held a the beginning, and not at the end. The title must NOT be decided in a speedy lottery.
Petrarlsen Petrarlsen 3/27/2018 05:03
@ Ajeeb007 :

"“One controversial aspect of the Candidates Tournament is that any ties will be settled by a system of tiebreak criteria, and now certainly not over the board in a playoff.”
Which I think is preferable to blitz tie breaks. Blitz is a different game from classical chess."

I fully agree !...
geraldsky geraldsky 3/27/2018 03:33
I think all games will be drawn. Ding will play aggresively against Karjakin but still end in a draw. If Caruana wins this candidate , Carlsen would be very happy to welcome him.
Ajeeb007 Ajeeb007 3/27/2018 02:55
“One controversial aspect of the Candidates Tournament is that any ties will be settled by a system of tiebreak criteria, and now certainly not over the board in a playoff.”
Which I think is preferable to blitz tie breaks. Blitz is a different game from classical chess.
Peter B Peter B 3/27/2018 01:48
Summary (update): except when Ding Liren is involved, the order of tie breaks is always:

1. Mamedyarov, 2. Karjakin, 3. Caruana,
That is, Mamedyarov wins any tie break with Karjakin and/or Caruana, and any Karjakin always wins a tie break against Caruana.

Ding Liren loses a tie break to Caruana alone, but wins a 3 way tie break with Caruana and Mamedyarov.
Mr TambourineMan Mr TambourineMan 3/27/2018 12:54
"Bottom line: There will be no playoff on Wednesday."

Well good god, that posibility to decide a Classical tournament in Blitz mode and Armageddon can´t no longer happen! Hope we can have that in the WC match later also.
Peter B Peter B 3/27/2018 12:44
The summary: Caruana never wins a tie break against Shak or Karjakin. Obviously Shak, Karjakin and Ding have to play for a win. But what should Caruana do?
garyklien garyklien 3/26/2018 11:31
Whoever said that was boring, this is chess what are you looking for. Inaccuracies?
kevinspiteri kevinspiteri 3/26/2018 11:27
Correction to my earlier comment:
Caruana-Mamedyarov: Mamedyarov (tb3)
Reason: To tie at 8.0, Karjakin needs to lose and it becomes a 3-way tie with Ding.
kevinspiteri kevinspiteri 3/26/2018 11:18
3-way tie:
Caruana-Mamedyarov-Ding: Ding (tb1)
Caruana-Mamedyarov-Karjakin: Mamedyarov (tb1)
2-way tie:
Caruana-Ding: Caruana (tb2)
Caruana-Karjakin: Karjakin (tb1)
Mamedyarov-Karjakin: Mamedyarov (tb1)
Caruana-Mamedyarov: (8.0: Caruana tb2, 8.5: Mamedyarov tb3)
SeniorPatzer SeniorPatzer 3/26/2018 11:13
My previous comment was mistaken. Shak has to draw for Ding to win the Candidates in the event that Ding wins his last round game and Fabio loses.
SeniorPatzer SeniorPatzer 3/26/2018 11:05
If Ding wins as Black against Karjakin, then for Ding to win the Candidates, Fabio has to lose as Black against Grischuk, AND Mamedyarov doesn't win with Black against Kramnik.

Ding wins the tiebreaker against Fabio and Shak if all of them end up with 8.0 points.
Petrosianic Petrosianic 3/26/2018 10:50
This is a World Championship, not a tour. Aronian won't challenge and Shak won't unless he wins THIS tournament.
SambalOelek SambalOelek 3/26/2018 10:38
boring calculations theory

the best player is the player who wins the most tournaments during the year! FOr me Mamadyrov and Aronian should be challenging Carlsen

the rest is just a fun factor competition just happening right now
genem genem 3/26/2018 10:29
{"Caruana is the clear favourite. But Karjakin is the only one among the three to have the White pieces in the final round."} . . .
Caruana is entering a final round that could make or break his legacy. Caruana cannot take unsound risks just for the sake of a feeling of winning chances by complications. But with White Karjakin might be able to.
Petrosianic Petrosianic 3/26/2018 09:57
"Ding meanwhile has less than 2% chances, when one considers the general probability of wins, losses and draws in chess."

Those numbers are meaningless. In fact, all of them are. They're based on the odds of a draw in a normal situation, not in a Sudden Death Situation.
macauley macauley 3/26/2018 09:52
Thanks for your helpful comments. The standings were not updated correctly (now fixed), and the Ding wins scenario will indeed be decided in the Direct Encounter, not the second tiebreak.
jestey86 jestey86 3/26/2018 09:35
"The only scenario in which a draw is enough for Karjakin is if Mamedyarov loses and Caruana loses or draws."

This is also incorrect. If Caruana and Karjakin both draw then Caruana will have 8.5 points and Karjakin will have 8.0 points. Caruana would need to lose for Karjakin to win the tournament in this scenario.
Zdrak Zdrak 3/26/2018 09:32
"If Ding beats (and eliminates) Karjakin, Mamedyarov draws and Caruana loses, then we would have a three-way tie on 8 points. But Caruana's four-wins would rule the day, compared to Mamedyarov's three, and Ding's two."

This is wrong, because in this case, head-to-head will come into play first. And Ding will win the head-to-head in this case, because he has the edge in games played among those three players. (he beat Mamedyarov once, and the rest of the games among those three were drawn).
cashparov1 cashparov1 3/26/2018 09:21
Thanks for this great article!
However, you mention the standings after the penultimate 13th round, but the standings shown in the article are the ones after round 12. I think this requires some correcting. ;)