Monday, April 16, 2012

Chess is an infinite game

Chess is an infinite game. To be precise: there is no bound on the number of moves that a chess game can have.

Surprisingly, many chess players are not aware of that fact. This is mostly due to an incomplete understanding of the two rules in chess that are devised to prevent infinite games: the threefold repetition rule and the 50-move rule. They are covered by Articles 9.2 and 9.3 of the FIDE Laws of Chess.

The thing that many chess players do not realize is that both these rules specify the need for a claim by one of the players. If both players decide not to claim, the game goes on.

In cases where the 50-move rule is relevant, the chess position is often asymmetric; one player will be trying to mate while the other player will try to avoid mate, and meticulously keeps count of the moves by his opponent. This situation typically occurs in non-trivial pawnless endgames, such as king+bishop+knight vs. king, or king+queen vs. king+rook. These are classic endgames that are winnable in less than 50 moves; but still, many club-level players do not known how to pull it off.

In case of the threefold repetition rule, both players tend to realise full well that they are repeating positions when it happens, and by repeating they will usually indicate their willingness to accept a draw. However, I maintain that making the draw claim in such a case is the wrong thing to do, from a theoretical, fully rational viewpoint - at least, if time is no constraint. Consider, for example, the position below:

White and Black's Kings are both imprisoned; the only thing they can do is helplessly alternate between the a- and b-files.

Both players do, however, have a second option: they can advance their respective pawns on the right of the board. Of course, that would be very unwise: if either Black or White advanced their right-side pawn, it would immediately be captured by the opponent's pawn, and that pawn now has a free walk towards promotion and winning the game.

So, what to do? After moving around with the king for a few moves, should you just claim the draw? If you value your time, or if you are running out of time, then yes - you should. But if there is even the slightest chance that your opponent will be stupid enough to advance his pawn, don't! You can still claim a draw at any point in the future if both players make their optimal move, but you may actually win if your opponent blacks out and makes a fatal mistake.

Of course, this should be weighed against the risk that you will make a fatal mistake. This is not entirely out of the question; if you have alternated your king five thousand times between a1 and b1, and then your opponent deviously and suddenly advances his pawn, it will take quite a bit of vigilance to not touch the king out of habit.

One slightly more realistic scenario where this could happen is when two chess computers meet; they don't tire, after all. It would be quite epic to see two computers reaching a position that is completely repetitive, and where both may claim the draw - but then they don't, instead opting to play on at a million moves a second, until one of them has only milliseconds left on the clock.

1 comment:

  1. Interesting observation, I can't wait to see the face of my opponent 1 move before he checkmates me and I execute the draw claim :)