Well one reason is that it still won't be a 'single' player - what they've done here is like having a group of thousands of 1100 players vote on a move. What you're suggesting is to then pick a random player each move and go with them. There's no consistency, maybe on move 10 the player is blind to an attacking idea, but then on move 11 suddenly finds it...
I think they are saying, if your neural network was probabilistic and you thought there was a 90% chance of someone doing move A, but a 10% chance of move B, then you shouldn’t always get move A if it was human like - you would sometimes get move B.
I.e. most of the time if you leave your queen hanging and under threat your opponent will take it, but sometimes they just don’t see it. That’s the difference between playing a bot and a human a lot of the time - humans can get away with a serious blunder more often at low level play.
That's exactly what I'm saying - except more like the model is saying there's a 90% chance that a randomly chosen player at this level would make the move.
Yes, if you don't condition on the past moves then the distribution you're modeling is where you randomly pick a 1100 player to choose each move as you say. What I'm saying is that there will be no wisdom of the crowd effect.
