The average number of moves in a game of chess is about 40. This would be an average of about 80 positions in each game, but many positions are shared between games. More sharing occurs at the beginning and end of the game.
New positions arise as games are played. As we add new games to the database of chess games, how many new positions will be added by each game?
In probability terms, if the number of new positions added by a game is a random variable, what is the expected value?
The practical result of this answer might be how large a key would a position table need in a database.