Magnus Carlsen’s Endowment

Game 12 of the ongoing Chess World Championship match between Magnus Carlsen and Fabiano Caruana ended in an unexpected draw after only 31 moves, when Carlsen, in a clearly better position and clearly ahead on time, made an unexpected draw offer.

The match will now go into a series of tie-breaks, played with ever-shortening time controls, as the world looks for a winner. Given the players’ historical record, Carlsen is the favourite for the rapid playoffs. And he knows it, since starting in game 11, he seemed to play towards taking it into the playoffs.

Yesterday’s Game 12 was a strange one. It started off with a sharp Sicilian Pelikan like games 8 and 10, and then between moves 15 and 20, players repeated the position twice. Now, the rules of chess state that if the same position appears three times on the board, the game is declared a draw. And there was this move where Caruana had the chance to repeat a position for the third time, thus drawing the game.

He spent nearly half an hour on the move, and at the end of it, he decided to deviate. In other words, no quick draw. My suspicion is that this unnerved Carlsen, who decided to then take a draw at the earliest available opportunity available to him (the rules of the match state that a draw cannot be agreed before move 30. Carlsen made his offer on move 31).

In behavioural economics, Endowment Effect refers to the bias where you place a higher value on something you own than on something you don’t own. This has several implications, all of which can lead to potentially irrational behaviour. The best example is “throwing good money after bad” – if you have made an investment that has lost money, rather than cutting your losses, you double down on the investment in the hope that you’ll recoup your losses.

Another implication is that even when it is rational to sell something you own, you hold on because of the irrationally high value you place on it. The endowment effect also has an impact in pricing and negotiations – you don’t mind that “convenience charge” that the travel aggregator adds on just before you enter your credit card details, for you have already mentally “bought” the ticket, and this convenience charge is only a minor inconvenience. Once you are convinced that you need to do a business deal, you don’t mind if the price moves away from you in small marginal steps – once you’ve made the decision that you have to do the deal, these moves away are only minor, and well within the higher value you’ve placed on the deal.

So where does this fit in to Carlsen’s draw offer yesterday? It was clear from the outset that Carlsen was playing for a draw. When the position was repeated twice, it raised Carlsen’s hope that the game would be a draw, and he assumed that he was getting the draw he wanted. When Caruana refused to repeat position, and did so after a really long think, Carlsen suddenly realised that he wasn’t getting the draw he thought he was getting.

It was as if the draw was Carlsen’s and it had now been taken away from him, so now he needed to somehow get it. Carlsen played well after that, and Caruana played badly, and the engines clearly showed that Carlsen had an advantage when the game crossed move 30.

However, having “accepted” a draw earlier in the game (by repeating moves twice), Carlsen wanted to lock in the draw, rather than play on in an inferior mental state and risk a loss (which would also result in the loss of the Championship). And hence, despite the significantly superior position, he made the draw offer, which Caruana was only happy to accept (given his worse situation).



How computers have changed chess

Prior to computers, limited depth of analysis meant chess strategies were “calibrated to model”. Now they’re calibrated to actual results and that results in better strategies (unconstrained by aesthetics)

With the chess Candidates tournament starting in Moscow today (to decide World Champion Magnus Carlsen’s next challenger), I’ve been watching a few chess videos of late, and participating in discussions on why Anand has been finding it hard to play of late.

One thing that people have widely agreed is that computers have changed the way chess is played, and the “new generation” (Carlsen, Hikaru Nakamura, Fabiano Caruana, Anish Giri, etc.) have learnt the game in a completely different way from the old-timers, which dictates the way they play.

For example, these new guys play the kind of positions that earlier generations wouldn’t dream of playing. Given a position and a bunch of moves that seem similarly strong, the moves the new generation picks is different from what an older player would pick. And computer analysis is credited with this.

The basic advantage with computer analysis is that positions can now be evaluated easily to a much larger “depth” (number of moves from current position) compared to earlier manual analysis. In the manual analysis, you could evaluate the position for a few moves after which you would reach a position that you would judge manually. Judging different possible continuations this way, you would evaluate a position and figure what was a good continuation.

The problem with limited depth search was that after a certain depth, you simply had to use your judgment on what was a good position, and this judgment (the “boundary condition” that went into your model) would have a profound effect on how you evaluated different moves. Over time, all you cared about was the aesthetics of the chessboard, and not really how you could translate the position to victory (or a draw).

In other words, in the days before computers, chess players were building their strategies by calibrating them to a model rather than by calibrating them to actual results on the board. And this resulted in a bias towards “pretty strategies” and those that gave advantages that were obvious.

With computers, however, there is no such constraint on the depth of ply. You can analyse the position to far greater depth and get really close to the result in the course of your analysis. And so you don’t really care about the aesthetics of the positions you reach, as long as you know how they can translate to the result you want.

So the “new generation”, which has always been trained using computers, see the game differently. People of Anand’s generation (there’s also Veselin Topalov and Levon Aronian in the ongoing Candidates tournament) learnt the game with classic aesthetics and optimise their play to get there. Carlsen’s generation has no such biases and they play to what is the¬†actual advantage irrespective of aesthetics.

And that’s how the battle is building up! This should be an interesting tournament!