> Shouldnt that number at most be 722^#positions? Since adding a black or a
> white stone is something fundamentally different?

The upper bound of 361^L(19,19) games is from Theorem 7 on page 31 of
http://tromp.github.io/go/gostate.pdf, where you will find a proof.
As the paragraph preceding that theorem explains, the difference from your
suggestion is due to the average position having only 361/3 empty points
available for play.

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