I agree with you there, but IMO master level poker play has less to do with genius-level analytic thinking than master-level chess. Like, you wouldn't be able to understand past three positions of a Kasparov/Karpov match, if they sat down and tried to explain why they made the moves they did.

On the other hand, I don't think the final table play of the most analytically in depth poker pro--let's say Chris Ferguson in the 2000 WSOP--would be that hard to understand, if he sat down and explained all his decisions for you. It would mostly have to do with pot odds and player reads, would be my guess.

I think the best poker player in the world has all kinds of edges on average players, but the most significant ones are in the realm of personal control and focus.

Of course, this is all total speculation. I could be completely wrong.