Chess, mathematics and weight loss
Bangalore Mirror Bureau | Oct 29, 2014, 10.17 PM IST
By: Santanu Chakraborty
We have all played chess as kids. But little do most people appreciate that an exceptional amount of energy is expended by top grandmasters competing at tournaments
Vishwanathan Anand and Magnus Carlsen will continue their celebrated chess duel on November 5 in Sochi, Russia. Two nations, India and Norway, will watch as their heroes battle it out in a game that is tough on both mind and body. We have all played board games like chess and Chinese checkers as kids, but little do most people appreciate that an exceptional amount of energy is expended by top grandmasters playing in high level tournaments. For example in the world championship match between the legendary Gary Kasparov and his former student Vladimir Kramnik of Russia, Kramnik lost almost 10 kilos in the course of the match!
So what exactly is the difficulty of chess?
Part of the answer comes from the mathematics of the game.
Chess, as many of you know, is a game played out on a square eight-by-eight board. Each side gets the following pieces: eight pawns, two rooks, two bishops, two knights, a king and one queen, each with definite rules of movement across the board.
The player with white has 20 possible ways in which to make the first move. The player with black can respond with any one of 20 moves. This can lead to any one of 400 positions (20 multiplied by 20 is 400) after a total of two moves alone. From here on something incredible happens. The number of possible positions after each move increases phenomenally.
The number of possible positions after five moves is over eight lakhs!
And that is only part of the story as only some of these positions are favourable to the player. Good players try to see a few moves ahead. The enormity of this task should be gauged in light of the above numbers. Do you now see how the intellectual effort of calculating various positions coupled with the nervous strain of a high profile match can make even a top player lose 10 kilograms?
It is this astounding complexity that makes no two chess games alike. They are familiar up to a point, and grandmasters will prepare for different opening sequences of moves. But as soon as the game moves beyond familiar territory – the unique part of the ongoing game – what begins to matter are a combination of calculation and imagination.
So in the final analysis, it is a combination of intellectual abilities, memory (especially for the opening phase), calculation (particularly beyond the first few moves) and imagination (when trying to come up with an unexpected sequence of moves) are what make chess such a stimulating game. And for its amazing treasure trove of properties, chess has been studied by Mathematicians, Computer Scientists and Neuroscientists; who keep discovering surprising facts about this age old game.
Perhaps computers will one day analyse every single possible chess game. They face just one small hurdle. Claude Shannon, an engineer and mathematician, studied the complexity of chess and approximated the number of variations in the following manner. In a typical grandmaster game every move has about 30 realistic possibilities.
Each cycle of moves would have 30 possibilities (give or take a few) for white and 30 for black. The number of positions after each cycle would be 30 multiplied by 30, equaling 900 positions. For ease of calculation we will approximate it by saying there are 1,000 possibilities to be considered after each cycle. A typical grandmaster game has about 40 cycles of moves. So the total number of variations to be calculated should be 1,000 x 1,000… 40 times, which is one followed by approximately 120 zeroes. In comparison the total number of atoms in the observable universe is estimated to equal one followed by only 80 zeroes!
So how does a grandmaster do it? Neuroscientists have begun to study such questions and found some surprising correlations. In a famous study chess experts and novices were asked to recall chess positions after only a few seconds. Interestingly chess experts perform much better than amateurs but only when presented with realistic chess positions. In other words, when presented with a scrambled position that would be unlikely to occur in a real chess game, the experts and novices performed similarly.
Chess masters also reconstruct positions in spatially connected chunks suggesting that they are remembering at least some aspect of its shape and visual impression instead of associating each piece with an individual square. These ideas are supported by brain imaging studies that show that experts use brain areas involved in visual processing and facial recognition.
Despite the theoretical complexity of a chess game, determined scientists have built programs that are today, after many years of intense human effort, stronger than any living human being. Ironic: but such is life.
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– GM Susan Polgar