This has been a favorite target of AI researchers since the 1950s.

How big is the game tree?

• 20 possible first moves
• 35 possible next moves on average: the branching factor
• If games average 40 moves per side, then the game tree has:
  
  40 ⁸⁰ ≥ 10 ¹²⁰ nodes

• So if every quark in the universe were a supercomputer ...
• Any digital computer (and any person) can search only a tiny fraction of the game tree.