The power of comparative thinking

The game Kramnik-Carlsen from the 2nd London Chess Classic event provided great excitement to all that followed it live, either on stage on via the Internet. After outplaying his opponent, Kramnik seemed to be sailing comfortably to an easy win, but then the improbable happened: he himself liquidated to an ending that proved incredibly difficult and the game was eventually drawn. However, he could have avoided this outcome by using the method of comparative thinking.

By Ilias Kourkounakis

Comparative thinking is a decision-making process, by which a choice can be made without an exhaustive analysis of the position. It can prove to be a powerful analytical aid when complete calculation is impossible, either because of the human limitations of a player or because of time shortage. However, it must be emphasized that comparative thinking should not be used as a substitute for calculation.

A most useful aspect of comparative thinking is that it may be used even when we are not completely certain of the result, but with a certainty that using it maximizes our chances. This can be illustrated almost perfectly in the following critical position from Kramnik-Carlsen:



Here Carlsen played quite cleverly 61…Rc5, without giving it a lot of thought. It is evident that he should lose with best play and his only real hope lies in the K+B+Ps vs K+Ps endgame that actually arose in the game. When he made his decision he did not need to know the result of that endgame, but only that his practical drawing chances were better than if the situation remained unaltered. Consciously or subconsciously, he used comparative thinking to choose 61…Rc5 over other more neutral moves, for example 61…Ra5.

In reply, Kramnik decided to liquidate with 62.Rxd6+. This might have been a good move from a purely “chessic” point of view or it might have not. From the standpoint of comparative thinking, however, it was a clear mistake.

Liquidation of pieces does not necessarily simplify matters, it only simplifies the data available for analysis. In practice, simplification of the data might actually complicate the analysis by requiring a more specific approach and calculations to greater depth, as is the case here. This is exactly why comparative thinking is the appropriate decision-making tool to use in such a situation.



It is clear from the result that Kramnik did not calculate the endgame to the end. It is possible that a player of his caliber actually could, but he need not to. As a matter of fact, he should not even try to. In the K+B+Ps vs K+Ps endgame he can win only in a very restricted front, where the doubled g-Pawns and the Bishop’s obligation to guard the a2 square limit his possibilities of controlling crucial black squares to the King. The main argument of comparative thinking is as follows: Even if the K+B+Ps vs K+Ps endgame is winning, it is clear that the present balance of power wins more easily (for example, by first eliminating the enemy a-Pawn). On the other hand, while the present balance of power is surely winning, it is not 100% sure that the same is the case with the K+B+Ps vs K+Ps endgame. Therefore, not liquidating would maximize his chances, while liquidating might decrease them.

This argument could be easily made by Kramnik if he stopped and considered seriously the difficulties of the resulting endgame for a few minutes. The fact that he made his decision relatively quickly indicates that he did not have any doubts because he did not ask the question, not because he gave the wrong answer.

I believe he should have suspected something, if only because Carlsen allowed the liquidation. Once again, the Norwegian GM did not need to know the result of the K+B+Ps vs K+Ps endgame. From the standpoint of comparative thinking and from Carlsen’s point of view, if that endgame was also lost, it was not more lost than the position of the diagram. Therefore, he could make his decision fairly quickly and without calculating everything.

In conclusion, it is far from my intentions to criticize Kramnik severely for his choice of 62.Rxd6+, especially as this was my own very first idea while I was watching the game and the position remains theoretically winning had he found 69.g5!.

I consider Kramnik’s mistake fully understandable after many hours of play and when in an emotional need to release the tension by clarifying the situation on the board as much as possible. Nevertheless, I hope it has been made clear that his was more a psychological error than an analytical one. Moreover, it was an error that could have been prevented by using the method of comparative thinking at the right moment.

Finally, I cannot refrain from repeating the warning mentioned earlier. Comparative thinking should be used only in positions where precise calculation to the end is practically impossible, or at least undesirable because of the time consumption it demands. If one can calculate everything to the end, then it should be done.

Kramnik-Carlsen London Chess Classic (6) 2010

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Ilias Kourkounakis is an International Master with a B.Sc. in Psychology (University of Toronto) and has been a professional trainer for more than 25 years. He has published 7 books on various aspects of chess, all in the Greek language.