the AI would have to plan like 3-11 steps ahead half way through a game so that's O=32^11 maximum iterative steps with a lot of shorter routes that take less time to determine tracing down to a next step decision to make an optimal move,
AI can learn commonality trough circular slices of the grid covering the grid in action with overlapping circulation and from this it could find optimal leaning when ii's thinking upto 11 steps ahead.
At the beginning it has to think closer to 5-9 steps ahead and as the game comes to a close less computation is required.
There is some optimal range of steps you need to access in advanced and a maximum number of variations you need to be aware of and optimal ways of organising the whole approach below 32^11 steps for any given move to hit close to the optimal algorithm for playing the perfect game of chess.
Go would require far more wisdom of paths ahead unless someone else can crack it's code.