Considering how monte carlo actually works, I think it's plausible
to argue that it works best where the distance to endgame is small.

For a 19x19 board, the playing speed may be only a factor of 4 worse,
but the effective learning speed for an opening position might be
exponentially worse.  In other words, doing 4x as many playouts won't
get you to the same quality of play.  I'm not aware of any data about
what the scaling exponent is, but I'll wager 1 is not the answer.

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