Changing the rules of chess can make the game more difficult
Richard Levine/Alami
Chess can be improved The physicist discovered that by changing the position of the starting pieces, the game could be made more difficult and fair.
Standard playing chess always starts with the pieces on the back of the board, arranged with an element of symmetry. Starting from the outside, both white and black have pairs of rooks, knights and bishops with a king and queen in the center. But because this arrangement is fixed, the best chess players can memorize the best moves to start a game of chess, which can lead to predictable and boring matches.
In the 1990s, the late chess grandmaster Bobby Fischer proposed a variant of the game that reduced the reliance on memory. Fischer proposed to effectively randomize the starting positions of the pieces on the back of the board – in addition to the basic rules dictating where bishops, rooks and kings should be positioned relative to each other – with both white and black pieces being placed equally randomly. Dubbed Chess960 because of the number of possible starting positions, the format has gained great popularity recently, with players including former world champion Magnus Carlsen taking part in tournaments to better test their chess skills.
Since the pieces are randomly placed, Chess960 seems fair to both players. But after analyzing all 960 possible starting positions, Mark Barthelemy at the University of Paris-Saclay discovered that this is an illusion.
White who goes first always has a slight advantage in standard chess. But Barthelemy found that some Chess960 configurations gave White a much larger advantage, and some actually gave Black a slight advantage. “Not all jobs are equivalent,” he says.
Barthelemy came to these conclusions by using the open-source chess computer Stockfish to analyze each starting position and measure how difficult it was for both Black and White to decide on a move. To do this, Barthelemy compared how easy it was to find the best and next best moves based on computer data. If one of two moves is much easier to find than the other, then the player is faced with an uncomplicated situation and should not have much trouble choosing a move. But if both moves are equally easy to find, then the situation is more complicated, and the player has to make a more difficult decision when choosing a move. Using this approach, Barthelemy could evaluate the difficulty of each starting position and evaluate which difficulty favored black or white.
He found that the opening opening BNRQKBNR, where each letter represents a piece (the knight is “N” and the king is “K”), was the most difficult, while QNBRKBNR was the most balanced between white and black in difficulty. According to Barthelemy, such positions can be useful to tournament organizers because they help ensure fair play between players.
But Vito Servedio at the Center for Complexity Science in Austria argue that randomness provides a natural level of fairness, and that bias towards certain Chess960 configurations over others can lead to overtraining of players. “It’s fairer because you start with your opponent on one leg,” Servedio says. “A grandmaster knows thousands of opening variations in standard chess, but cannot know opening variations in all [Chess960] positions.”
Barthelemy also found that the standard game of chess is not particularly extreme compared to some other 959 positions in both fairness and difficulty. “Very surprisingly, the standard chess position is not particularly remarkable,” says Barthelemy. “It's not particularly balanced or asymmetrical, it's very average. I don't understand why history settled on that position.”
“In the zoo of positions, he’s in the middle,” Servedio says. “Is this a coincidence or not? We cannot say.”
According to Barthelemy, the difficulty measure is not the only possible way to analyze how difficult a game of chess is. Giordano de Marzo at 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 choosing the best move between the best option and the next best option.
It's unclear whether the higher difficulty Barthelrmie measured actually corresponds to people perceiving the game as more difficult, says de Marzo, although he suggests it might be possible. “If you see that more difficult positions lead to more thinking time, then I would say that is a very strong argument in favor of this measure.”
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