The fact that the number of valid positions is 19 x 19 in base 3 is wild. You'd have to be almost dan-level to immediately recognize that the pic above isn't actually a real game.
There are only 3^289 possible configurations of pieces on the board, so the fact that the number of legal configurations fits in a 289-digit ternary number is kind of trivial.
Not really. The T19 stone makes no damn sense, there's literally no reason to put a stone there. The T1 stone is an "empty triangle" AND in the corner, and only serves to weaken that position. The A1 / B1 stones are also worthless, and only serve to weaken white's position.
When I played seriously, I was only 14 Kyu (many years ago) and I immediately recognized that the board was not a real game. I'd imagine that any 10 to 20 Kyu player (very weak ranking, probably equivalent to D-rank players in Chess) would immediately recognize that the "game" in the picture was wrong.
The fact that it is 19x19 in base 3 is not that suprising. If you visualize all possible positons (legal or not) then you have 19x19 board of 3 states (black, white, note). So it's 3 * * (19 * 19). Which is 1 and 19 * 19 zeros in base 3. Only some of these positions are legal so the number is lower - quite a bit, that's why there are leading zeros in top left.
The linked paper seemed really clear (I don't play Go, but I do study dynamic programming algorithms). So it may not pop out unless you play- but it looks like the black stones at Q2-R2 falsify the board (as they have no air holes). Actually I think the simplicity of the legality rule makes this even more interesting.
