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The discussion on board sizes in the Infinite Chess comments is very
interesting for what it does not have, in spite of several versions of
'infinite' chess and the efforts of George Jelliss and Ralph Betza.
There is nothing that approaches infinite, although Ralph Betza's
'chessboard of chessboards' [64 8x8 chessboards arranged in an 8x8
array] with its 512-square sides and over a quarter million squares does
give you a little area to play in. But all the 'infinite' boards have
limitations on how far away from other pieces any piece can move [making
Mr. Betza's behemoth the largest actual board discussed]. They have
flexible boundaries that can stretch and extend in any direction, but all
the games have a finite number of pieces, so there is a maximum area the
pieces can occupy if they are required to be within a specified distance
of other pieces. Even if the requirement is merely being within some
distance of one other friendly or enemy piece, and the pair of pieces go
racing out across the 2D plain, 2 pieces don't take up a lot of room. And
the rules tend to be written so that isolated pair cannot happen. The
average size of these boards is probably under 20x20. Even with more
pieces, the size probably wouldn't get much above 30x30, the total board
area being near 1000 squares. This is wargame size. A chess board is
generally about 100 squares in area (~30-300), and a wargame, about 1000
(~300-3000), very roughly. While there are some exceptions, this is
accurate. Just not precise. Apparently, 'infinite' for chess variants
means 'as big as a wargame.'