Dragon wrote:Imagine that 19x19 is solved. What do you think, KataGo (the best network, by default) makes the best move 1 time out of 5? out of 10? maybe a difficult question, but your opinion is interesting

Well, if 19x19 go is solved, how was it solved? Surely by the best network. In that case, the best network will always make the best move, always. At least, the best move in the sense of a move that guarantees the win, if a win is possible.
But what do we mean by the best move? Do we mean a move that optimizes the score, win or lose? That's not how today's top bots are trained. In the future, who knows?
There is an even stricter criterion for the best moves, technical correctness. Here is an example.
$$Bc Technically incorrect
$$ -----------------------
$$ | . . . . . O O X . . . |
$$ | . . . . O O X . X . . |
$$ | . . O O O X X X X . . |
$$ | . . O . O 2 3 , X . . |
$$ | . . O X O X X , X . . |
$$ | . . O X X X O X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 1 X X . X O X |
$$ | . . O O O O X X O . O |
$$ | . . . . . O O X X O . |
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$Bc Technically incorrect
$$ -----------------------
$$ | . . . . . O O X . . . |
$$ | . . . . O O X . X . . |
$$ | . . O O O X X X X . . |
$$ | . . O . O 2 3 , X . . |
$$ | . . O X O X X , X . . |
$$ | . . O X X X O X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O . 1 X X . X O X |
$$ | . . O O O O X X O . O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]
To see a reasonably strong amateur, say a 3 kyu, play like this, you'd just have to shake your head.

gains only ½ pt., when a play at
2 would gain 1 pt.
$$Bc Technically correct
$$ -----------------------
$$ | . . . . . O O X . . . |
$$ | . . . . O O X . X . . |
$$ | . . O O O X X X X . . |
$$ | . . O . O 1 , , X . . |
$$ | . . O X O X X , X . . |
$$ | . . O X X X O X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O , 2 X X . X O X |
$$ | . . O O O O X X O . O |
$$ | . . . . . O O X X O . |
$$ -----------------------
- Click Here To Show Diagram Code
[go]$$Bc Technically correct
$$ -----------------------
$$ | . . . . . O O X . . . |
$$ | . . . . O O X . X . . |
$$ | . . O O O X X X X . . |
$$ | . . O . O 1 , , X . . |
$$ | . . O X O X X , X . . |
$$ | . . O X X X O X . X . |
$$ | . . O . . O O X . . . |
$$ | . . O O O O X X X X X |
$$ | . . O , 2 X X . X O X |
$$ | . . O O O O X X O . O |
$$ | . . . . . O O X X O . |
$$ -----------------------[/go]

gains 1 pt., and then

gains ½ pt. The net result is the same.

is not only bigger, if the ko situation were different, it would take away a potential ko threat for White. There is no case where a Black play at
2 is better than

, so there is no reason to consider it.
What if a bot played like this? All you can do is shrug. Bots are trained to win games, and even if a bot is trained to optimize the score, that does not mean that it is trained for technical correctness. If a technically incorrect play optimizes the score, so what?
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Edit: I do not mean that playing the largest play is technichally correct. Sometimes it is, sometimes it isn't. For these two plays it is.
Edit2: However, playing a smaller play cannot be technically correct. It is possible to find a whole board position where it is not as good as the larger play.