Another example of randomized Nash equilibrium

From an interview with Vladimir Kramnik.  Note that Kramnik is playing in a regular chess tournament, shortly before with world championship match with Anand:

Is it difficult for you, because of course you cannot show your preparations, your openings for the match, so you have to choose, let us say, not your real openings…

Yes, sometimes. But it is nor really about this, it is about that fact that sometimes it would be too simple if you don’t show anything. That also gives a lot of information to your opponent. Then he knows that what you played you will for sure not play in the match. That is why you need to mix. Some things. I have to show, some things I don’t show. So I am trying to confuse as much as possible my opponent. And this is a bit difficult. Before each game I start to think if he plays this should I play this or should I play that, or even during the game I start to think maybe I should play this or maybe I shouldn’t play it. It is a little bit confusing I would say. It is easier to play when you don’t have such an event in front of you.

Kramnik has been playing indifferently lately, yet when times demand he can be the world’s strongest match player.  Anand is the current world champion, noting that he won the title through a tournament structure.  Match chess is all about adjustments and stamina and defense and preparation and strength of will.  Winning tournaments requires that you beat the weaker players consistently and that has never been Kramnik’s strength.

Anand, by the way, can play speed chess almost as well as he plays classical slow chess.  He is an amazing tactician and a brilliant defender.  But does he have a deep enough strategic style to prevail in a longer and tougher setting?  I’ll let you know how the match goes.