2016 US Chess Championship - Round 3

Nakamura could only manage a draw against the bottom seed, IM Chandra. Caruana and So drew a long endgame and remain tied for first with Robson.

Methodology

2016 US Chess Championship - Round 2

Caruana and So won their games while Nakamura drew Kamsky. Meanwhile, Robson won and remains tied for first.

Methodology

2016 US Chess Championship - Round 1

A good day for the Elo rating system - all the favorites won, with the exception of a draw between Onischuk and Xiong.

Methodology

2016 US Chess Championship

The 2016 US Chess Championship is a 12-player round robin starring Caruana, Nakamura, and So. Due to some technical difficulties, the forecast wasn't ready until about 2 hours after the games started.

Methodology

2016 Candidates Tournament - Round 13

Nakamura beat Topalov, while the rest of the games were drawn. Caruana and Karjakin continue to lead.

Methodology

The key games in the last round will be Karjakin - Caruana and Svidler - Anand. The winner of Karjakin - Caruana will certainly win the tournament. If they draw, then the first tiebreak is head to head score, and the second tiebreak is most wins. Thus,

Karjakin - Caruana draw + Anand draws or loses -> Karjakin wins the tournament. He will have an equal score in his mini-match with Caruana, but more wins.

Karjakin - Caruana draw + Anand wins -> Caruana wins the tournament. Karjakin, Caruana, and Anand will all have an equal number of points. However, Caruana has a plus score against Anand and an equal score with Karjakin, while Karjakin has an equal score against both. Therefore, Caruana has the best head to head score, so he wins based on that tiebreak.

Therefore, the probabilities for becoming the winner of the tournament are

Karjakin: 61.585%

Caruana: 38.415%

2016 Candidates Tournament - Round 12

Karjakin rebounded with a win over Topalov. Meanwhile, Anand lost to Nakamura, so Caruana and Karjakin share the lead.

There is roughly a 35% chance of a tie for first. Most likely, that will be a 2-way tie between Caruana and Karjakin. In that case, Karjakin will probably have the better tiebreaks. The first tiebreak is the head-to-head score between the players. That will likely be a tie, since they drew their earlier game. The second tiebreaker is number of wins, which favors Karjakin.

I have to say that number of wins is a ridiculous tiebreaker. If 2 players have the same score, then the player with more wins is also the player with more losses. Picking the player with more losses doesn't make any sense. More thought should have been given to the tiebreak rules, since the stakes are so high and there is a good chance of tie. At the beginning of the tournament, you can see that the model predicted a 23.5% chance of a tie for first (to calculate this, note that the probability of a tie = 1 - probability that one player wins). This also indicates that we should find a new format for picking the challenger to the World Championship; the double-round robin will so frequently fails to select a winner. This is a project I would like to explore later.

Methodology

2016 Candidates - Round 11

Aronian lost to Svidler. But the big news is that Anand defeated Karjakin, so now he is tied with Caruana for first place. If tiebreaks are necessary, then Caruana will be ahead of Anand, since Caruana won their individual match 1.5 - 0.5.

Methodology