Chess can be made fairer by rearranging the pieces
Changing the rules of chess can make the game more complex
Richard Levine/Alamy
Chess can be improved by rearranging the position of the starting pieces to produce a more difficult or fairer game, a physicist has discovered.
A standard chess game always begins with the pieces at the back of the board arranged with an element of symmetry. Starting from the outside, for both white and black, are pairs of rooks, knights and bishops, with a king and queen in the middle. But because this arrangement is fixed, the best chess players can memorize the best moves to open a chess game, which can lead to predictable and boring games.
In the 1990s, the late chess grandmaster Bobby Fischer proposed a variation of the game that reduced this reliance on memory. Fischer suggested effectively randomizing the starting positions of the pieces at the back of the board – apart from the basic rules dictating where bishops, rooks and kings should be in relation to each other – with the white and black pieces taking the same random arrangement. This format, called Chess960 because of the number of possible starting positions, has recently gained popularity, with players including former world champion Magnus Carlsen participating in tournaments to better test their chess skills.
Because the pieces are random, Chess960 seems fair to both players. But after analyzing the 960 possible starting positions, Marc Barthélemy of the University of Paris-Saclay discovered that this was an illusion.
White, who moves first, always has a slight advantage in standard chess. But Barthelemy discovered that some Chess960 configurations gave White a much larger advantage, and that a few actually gave Black a small advantage. “Not all positions are equal,” he says.
Barthelemy arrived at these conclusions by using an open source chess computer, Stockfish, to analyze each starting position and measure the difficulty for black and white to decide on a move. To do this, Barthélemy compared how easy it is to find the best and next best move, according to the computer. If one of the two moves is much easier to find than the other, then the player is in a simple situation and should have no difficulty deciding on a move. But if both moves are equally easy to find, then the situation is more complex and the player faces a more difficult decision when selecting a move. Using this approach, Barthélemy could evaluate each starting position in terms of complexity and assess whether any complexity favored black or white.
He found that a starting opening of BNRQKBNR, with each letter representing a piece (the knight being “N” and the king being “K”), was the most complex, while QNBRKBNR was the most balanced between white and black in terms of difficulty. Such positions could be useful to tournament organizers to ensure that games between players are fairer, Barthelemy believes.
But Vito Servedio, of the Complexity Science Hub in Austria, says randomness ensures an inherent level of fairness and that prejudging certain Chess960 setups over others could lead to players being overprepared. “It’s fairer because you start on the same footing with your opponent,” explains Servedio. “A grandmaster knows thousands of opening lines in standard chess, but cannot know the opening lines of all [Chess960] positions. »
Barthelemy also found that standard chess is not particularly extreme, compared to some of the other 959 positions, both in terms of fairness and complexity. “Very surprisingly, the standard position in chess is not particularly remarkable,” says Barthelemy. “It’s not particularly balanced or asymmetrical, it’s very average. I don’t understand why history has decided this position.”
“In the zoo of positions, it’s in the middle,” explains Servedio. “Is it a coincidence or not? We can’t tell.”
Bartholomew’s complexity measure is not the only possible way to analyze the difficulty of a chess game, says Giordano de Marzo of the University of Konstanz in Germany. “In many situations, the difficulty of a position is that you only have one move and you have to find it,” says de Marzo, rather than deciding the best move between the best and second best options.
It’s unclear whether higher complexity like that measured by Barthelrmy actually corresponds to people perceiving the game as more difficult, de Marzo says – although he speculates that it could be the case. “If you find that more complex positions result in longer thinking times, then I would say that’s a very strong argument for this measure.”
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