But the game is not solved, which is where MCTS comes in. It picks a move, and plays through it, selecting moves that are good but varied, until it learns more about which side would likely win (typically by expanding a leaf of the search tree). Each playthough is a visit. Each visit allows updating its estimate of the win probability for that move, and thus, changes the policy probabilities.
More visits typically anchor the policy estimates into reality further, yielding better play. In fact, this is how the policy network learns.
On a good consumer GPU (RTX 3060), I get 1.6K visits per second, so 100K takes about a minute. That makes a game last three to five hours typically.
But the paper emphasizes that even with 10M visits per move (>1h per move), KataGo loses 72% of games against this exploit[1].
[0]: https://arxiv.org/pdf/1902.04522.pdf
[1]: https://goattack.far.ai/pdfs/go_attack_paper.pdf#figure.capt...