Chess is a game that requires the players to assess ever changing arrangements of the chess pieces on a board of sixty-four squares. There are an estimated 10^43 possible positions, the vast majority of which will never appear on a chess board. Each individual chess game contains dozens of chess positions, and most of the time a majority of these positions are new. Carlsen became world champion by correctly assessing more often than Anand the chess positions they created together. In excess of 850 positions appeared in their ten games. Assessment of these positions required considering many hundreds more that did not occur.
The positions presented here appear to have been the most significant in determining the outcome of the match.
White to move
The first game followed previously played games as far as White's twelfth move. In the diagram, Black has just played 12...Nd5 creating both the first unique position in the match and the first critical position. White is already worse, and Carlsen understood that. He played the best move 13.Qb3 and it led to a draw by repetition a few moves later.
White to move
In the second game, the critical position was one that had occurred before. 18.Qg4 offers White prospects for a slight advantage with complex play. Anand chose to play it safe with 18.Qxd5, and seven moves later the game was drawn by repetition in an equal position.
Black to move
World Champion Anand appears to have missed a second opportunity to gain an advantage in the third game. He played 29...Bd4 in this position. 29...Bxb2 might have given him chances for clear advantage.
White to move
Anand's 16.Ne1 appears inferior to 16.Ne2. The a-pawn eventually fell, but White was able to generate less play for the material than if he had permitted 16...Bxa2 (although Carlsen would not have been compelled to make this capture). Anand's plan from this stage in the early middlegame conceded the advantage to Black over a series of moves.
In the press conference after game 10, Carlsen pointed to games three and four as revealing to him that Anand was vulnerable. He was then able to relax and play his normal style of chess. Carlsen's style produced opportunities for Anand to err.
Black to move
45...Rc1+, which was played by Anand in this position was an error. 45...Ra1 saves the game. This ending is not simple. The g-pawn appears to be the dangerous one, and Anand went after it after the check.
White to move
Computers can find the draw that follows from 60.b4, but both Anand and Carlsen thought the critical moment in the game had come some time earlier, perhaps 38.Qg3. It is interesting to contemplate that if White's b- and c-pawns were not on the board, Anand's 60.Ra4 would be consistent with the manner than the weaker side can hold positions where the stronger side has g- and h-pawns.
White to move
Neither player made any notable errors in game 7. After Anand's 27.exf5 in this position, the game quickly ended in a repetition.
Black to move
Anand found the correct 23...Qd8 in this position, and all the pieces were swapped off a few moves later. After some cursory pawn moves by both players, the position was wholly locked.
White to move
In a desperate situation, Anand went all out for checkmate in the ninth game. Carlsen defended well, and having survived the assault gained the upper hand. Here, White can probably hold and settle for a draw after 28.Bf1, but Anand played 28.Nf1 and resigned after 28...Qe1. Anand's error was made ten moves earlier, perhaps, when he anticipated this position.
Chess players must assess most positions long before they appear on the board.
Black to move
Anand's 28...Qg5 gave Carlsen the chance to play for a fourth win. He chose a line that he thought was winning, and then found the knight ending complex enough that he decided to force a draw to end the match. After 29.e5, White had a clear advantage, although it might have been more significant with greater precision on Carlsen's part.
Carlsen's most significant errors cane in the final game, when they no longer mattered.
*The World Chess Champions have been:
Wilhelm Steinitz (1886-1894)
Emanuel Lasker (1894-1921)
Jose Capablanca (1921-1927)
Alexander Alekhine (1927-1935)
Max Euwe (1935-1937)
Alexander Alekhine (1937-1946)
Mikhail Botvinnik (1948-1957)
Vasily Smyslov (1957-1958)
Mikhail Botvinnik (1958-1960)
Mikhail Tal (1960-1961)
Mikhail Botvinnik (1961-1963)
Tigran Petrosian (1963-1969)
Boris Spassky (1969-1972)
Bobby Fischer (1972-1975)
Anatoly Karpov (1975-1985)
Garry Kasparov (1985-2000)
Vladimir Kramnik (2000-2007)
Viswanathan Anand (2007-2013)
Magnus Carlsen (2013- )
FIDE World Champions (official classical title in dispute 1993-2006)
Anatoly Karpov (1993-1999)
Alexander Khalifman (1999-2000)
Viswanathan Anand (2000-2002)
Ruslan Ponomariav (2002-2004)
Rustam Kasimdzhanov (2004-2005)
Veselin Topalov (2005-2006)
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