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.