The difficulty of imperfect information is from cross cutting through information sets and partial observability. With perfect information games like chess or Go, one can solve subgames with guarantees that the equilibrium is the same as for the full game. This is not the case for games like poker, which is why they have been difficult. In addition to that, for n > 2 players, there are no longer theoretical guarantees about converging to a nash equilibrium, which makes designing theory guided algorithms harder. Though empirical performance with n=3 of CFR is encouraging, I know of no results for n > 3.

Earlier this year, DeepStack, a system combining neural nets with search, competed live against humans without any side being dominant. Search policy guided training might improve its results, which are impressive compared to even 5 years ago, but this highlights how much more demanding imperfect information games are.