For comparison Leela Zero gets around 60% accuracy on predicting its own next move.
With this sort of accuracy you can reduce the search part of the algorithm to an effective branching factor of 2-4 rather than 40, nearly for free, which is a pretty big win.
If the prediction (policy) net had a 100% accuracy, you wouldn't need the tree search part at all.
Part one of Leela ranks several chess moves. Part two picks among those.
60% of the time part 2 chooses the #1 ranked move.
One addition: The second part can be run for an arbitrary amount of time, gradually improving the quality of the returned move.
The 60% figure comes from the training games, which are played very quickly, and so don't have a lot of time for refining, thus increasing the prediction accuracy.
In real games, tcec-chess.com/ this "self accuracy" would probably be a bit lower.