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The branching factor of a game is the average number of new states reachablefrom a given state. It is a widely used metric in AI research on board games,but less often computed or discussed for videogames. This paper providesestimates for the branching factors of 103 Atari 2600 games, as implemented inthe Arcade Learning Environment (ALE). Depending on the game, ALE exposesbetween 3 and 18 available actions per frame of gameplay, which is an upperbound on branching factor. This paper shows, based on an enumeration of thefirst 1 million distinct states reachable in each game, that the averagebranching factor is usually much lower, in many games barely above 1. Inaddition to reporting the branching factors, this paper aims to clarify whatconstitutes a distinct state in ALE.

Estimates for the Branching Factors of Atari Games