This is a computerised version of the old classic which lets you play the game online. The aim is complete more boxes than your opponent.
You and your opponent take it in turns to join up two adjacent dots with a line.
If any player fills a box they must make another move.
You can play 1 or 2 player. But watch out, the computer strategy is driven by a reasonably intelligent algorithm!
n lg3 is not O(n). It outgrows O(n)... In fact, any exponent on n that is larger than 1 results in an asymptotically longer time than O(n). Since lg(3) is about 1.58, as long as you subtract less than .58 from the exponent it is asymptotically greater than O(n).