British Go Journal No. 13.  April 1971. Page 10.
An interesting feature of the game of Go is that, unlike many other board games, altering the size or even the shape of the board has only a slight effect on the style of the tactics of the game. Is there any special reason why 19 x 19 is the accepted standard?
In the History section of an old Go Review there is mentioned a period when Go was played on a 11 x 11 board in a region of China. As this version of the game died out, one may assume that the choice of the 19 x 19 board is based partly on experience and not merely on tradition.
Most of us have experienced playing on the 13 x 13 and 10 x 10 boards, and I think many people would agree that, especially in the latter case, the usual approximate equivalence of territory gained below the third line and the influence of stones on the fourth is upset - the territory being of greater value. Whereas on the full board an opening san-san (3:3) move is regarded as defensive and biased towards territory rather than influence, on the 10 x 10 board it is a well-balanced move, while the mokuhadzushi (3:5) and takamoku (4:5) openings seem much too high to be useful.
One possible reason far the 19 x 19 standard, then, is that it is the size which best preserves the subtle balance between third-line territory and fourth- line influence, whereby initially the value of the territory seems greater, but, if the player with stones on the fourth line is able to extend his wall beyond three or four stones in length, while the other player continues to crawl along the third line, the value of the outward influence often becomes greater.
Another reason could be that the 19 x 19 board enables the handicap stones to be placed at a distance equal to the maximum safe extension along the side, i.e., a five-line extension from a four- (or more) stone wall. This is, of course, a quantity independent of board size and, therefore, if one assumes that the fourth line is to be used for handicap stones and that the side stone is to be five lines from the corner stone, the 19 x 19 board is predicted.
However, clearly there is room for experiment with different board sizes and possibly also with rectangular boards. I suggest that such experiments should set out to answer such questions as
I would be interested to hear from anyone who has views or experience on this topic to pass on.