It’s a knockout

‘Chess is a sea in which a gnat may drink and an elephant may bathe.’ I’m fond of that adage, which speaks to the depth of the game in a way that numbers cannot. But how many possible games of chess are there? The mathematician Claude Shannon wrote a paper in 1949: ‘Progamming a Computer for Playing Chess’, in which he estimated that there are at least 10¹²⁰ (i.e. 1 with 120 zeros) possible games of chess. He noted that with such an astronomically large number, a perfect solution by brute force was infeasible. The reasoning is straightforward. The Dutch psychologist Adriaan De Groot (a contemporary of Shannon) estimated that a typical position may have 30 legal moves, so one move for each side makes for approximately 900 possibilities. Call it 1,000 (i.e. 10³) to make the sums easy. After 40 moves for each side, that is (10³)⁴⁰ = 10¹²⁰ possible games. Quite an ocean.

But in the opening stages, a vast amount of bathymetric research has already taken place. Grandmasters don’t know all the moves in all the positions, but they do know all the standard ideas and plans within their opening repertoires. As a result, most ‘new’ moves that they have to face won’t trouble them at all. Finding an innovation that will challenge one of the world’s best grandmasters can take days or weeks of study. Every year, it gets a little bit harder.

The promise of Freestyle chess (aka Fischer-Random, Chess960, or Chess9LX), where the pieces are shuffled on the back rank before the game begins, is to reset the clock. In this form of the game, even grandmasters struggle to navigate the opening moves, since the familiar setups and plans from traditional chess are of little use. In a sense, this difficulty makes it a playground for elite players, who can give free rein to their skill and imagination, rather than mining their databases for hours before each game.