According to the paper *Mastering the Game of Go with Deep Neural Networks and **Tree Search*, the main part of both the policy and value network is a 5*5 conv layer followed by eleven 3*3 conv layer. Therefore, after the last conv layer, the maximum "information propagation length" is (5-1)/2 + 11*(3-1)/2 = 13, which is insufficient for covering the full board.
It might not have been a big problem though, as tree search and MC rollouts should mitigate most deficiencies to a large extent. However, during the opening, realising the correlation between distant stones would be quite important, provided that tree search would not help much while MC rollouts might not provide a unbiased view. It seems to me that DCNN are not perfect for Go. Anyway, apparently that's enough for beating top human level.
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