If you ever played Poker you probably came in contact with Game Theory. Chess is a 2-player game with complete information about what position is actually on the board. Lot’s of factors are unknown though. Very often you don’t know what the best move is, you can only approximate it. You don’t know your opponent’s next move, you can only anticipate it. You don’t know what your opponent knows, you can only assume it. You don’t know how good his physical or mental constitution is, in fact you can’t even be sure about know your own condition. You don’t know the risk level that your opponent is willing to accept. What is he or her playing for?
The most important question is what to do in must-win situations. Let’s say you are an upcoming player who wants to reach 2700 then you can’t archieve that goal by just drawing 2500 players. Should you follow a pure strategy and only play a certain opening that is supposed to be maximally complicated for instance? Well, in that case you may be setting yourself up as a sitting duck.
Going back to Poker, let’s assume you are playing a heads-up limit-game. Your strategy for acting second is this: If your opponent bets on the river you call, otherwise you check behind. Once your opponent realizes what is going on, he will only bet his strong hands and check with his medium and weak hands. After a while you figure this out and change your strategy: When he bets you fold, when he checks you bet your strong hands. What will he do after a while? He will bet his medium and weak hands and check his monsters in order to check-raise you. Once you notice that, you will start calling his bets and check behind again, and we are back to square one. It’s just an endless cycle of adjustments.
What is the alternative? The alternative is playing a mixed strategy. You act randomly based upon optimal frequencies. Since your opponent is unable to detect a pattern, he cannot adjust to it and prevent you from maximizing your expected value. Finding out what these optimal frequencies are is obviously what this branch of science is all about, but that doesn’tt matter here. What matters is how chess players can make use of it.
Chess players can create a portfolio of openings and randomize. Ivanchuk took this approach to the extreme. He has a memory like a harddisk because he is a savant like Rainman. If you are not a physical freak like Chucky you can still do it to a lesser extent, with two openings for instance. You could even switch between major variations within an opening, let’s say the Nf6 or Bb4 in the French or Bf5 and Nd7 in the Caro Kann. Before the game you simply flip a coin, if you have more than two options you simply throw a dice.
Another concept that comes from Game Theory is the so called “free-roll”. Back in the day some casinos in Las Vegas offered the opportunity play one round of Roulette on the house. In Poker the classical free-roll is As Ks vs. Ah Kc on a Qs 7d 2d flop. If it comes runner-runner spades (~5% chance) the first hand wins, otherwise both players split the pot. In chess the concept can be applied by playing highly irrational forced lines, hence the forced draw. If your opponent makes all the only moves, it will be a draw, otherwise you will have a winning tactic. Grischuk plays like that.
How does all of this relate to Carlsen? What is he doing? Carlsen is taking a calculated risk in order to escape from the prison of the forced draw. He gifts his opponents + 0.25 in the opening, but the game will last at least 50 more moves, where his moves are 0.025 pawns better on average. He will eventually be a pawn up and it will all boil down to technique where he is outclassing everyone.