<P> A rough estimate of the number of nodes in the game tree can be obtained as an exponential function of the average branching factor and the average number of plies in a game thus: b where d is the ply depth and b is the branching factor . In Hex, the average branching factor is a function of the ply depth . It has been stated that the average branching factor is about 100; that implies an average ply depth of 43 (there will be 121 open spaces on the board when the first player is to make his first move, and 79 when he is to make his 22nd move, the 43rd ply - the average number of open spaces, i.e. branching factor, during the game is (121 + 120 +...+ 79) / 43 = 100). Therefore, the game tree size has an upper bound of approximately 100 = 10 . The bound includes some number of illegal positions due to playing on when there is a complete chain for one player or the other, as well as excludes legal positions for games longer than 43 ply . Another researcher obtained a state space estimate of 10 and a game tree size of 10 using an upper limit of 50 plies for the game . This compares to 10 node game tree size of chess . </P> <P> An interesting reduction is available by noting that the board has rotational symmetry: for each position, a topologically identical position is obtained by rotating the board 180 ° . </P> <Table> <Tr> <Td> </Td> <Td> This section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (January 2017) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (January 2017) (Learn how and when to remove this template message) </Td> </Tr>

Board game played in the movie a beautiful mind