Figure 1:
Chess openings can be described as decision trees, showing each move and associated branching ratios. This diagram shows the three most popular first (d=1) half-moves in the 1.5-million-game ScidBase chess database [12] and their branching ratios. For example, in 45% of the games, white starts with e4 (King’s pawn to fourth row, in algebraic chess notation), 35% start with d4 (Queen’s pawn to fourth row), etc. Each of these moves then have branching ratios to the second half-move by black (d=2). Blasius and Tönjes find that for all games up to d=40, the opening sequence popularity follows a Zipf power law with universal exponent nearly equal to -2, but for small values of d, the exponent is nonuniversal and depends linearly on d. (Adapted from Ref. [1].)