As a non-expert, may I ask (as the term does not appear in the paper): How valuable is the Shannon number in order to evaluate "complexity" in your context?
Since both numbers are out of the realm of brute-forcing, the bigger achievement is because of the more fluid and strategic nature of Go compared to chess. Chess is more rigid than Go, and playing Go employs more 'human' intelligence than chess.
Quoting from the OP paper:
"During the match against Fan Hui, AlphaGo evaluated thousands of times fewer positions than Deep Blue did in its chess match against Kasparov; compensating by selecting those positions more intelligently, using the policy network, and evaluating them more precisely, using the value network—an approach that is perhaps closer to how humans play. Furthermore, while Deep Blue relied on a handcrafted evaluation function, the neural networks of AlphaGo are trained directly from gameplay purely through general-purpose supervised and reinforcement learning methods."
"Go is exemplary in many ways of the difficulties faced by artificial intelligence: a challenging decision-making task, an intractable search space, and an optimal solution so complex it appears infeasible to directly approximate using a policy or value function. The previous major breakthrough in computer Go, the introduction of MCTS, led to corresponding advances in many other domains; for example, general game-playing, classical planning, partially observed planning, scheduling, and constraint satisfaction. By combining tree search with policy and value networks, AlphaGo has finally reached a professional level in Go, providing hope that human-level performance can now be achieved in other seemingly intractable artificial intelligence domains."
I will admit to not following AI at all for about 20 years, so perhaps this is old hat now, but having separate policy networks and value networks is quite ingenious. I wonder how successful this would be at natural language generation. It reminds me of Krashen's theories of language acquisition where there is a "monitor" that gives you fuzzy matches on whether your sentences are correct or not. One of these days I'll have to read their paper.
For language generation, AFAIK there is no good model that follows this architecture. For image generation, Generative Adversarial Networks are strong contenders. See for instance:
As a non-expert, may I ask (as the term does not appear in the paper): How valuable is the Shannon number in order to evaluate "complexity" in your context?