[no_gravity]

Thinking about it again, maybe we don't need to encode off-the-board information in the tree at all.

The tree would start from the starting position and then branch out to all legal moves in each step. So each node in the tree would have the previous moves encoded in it's position in the tree.

So my initial upper limit of 10^71 nodes might hold true. No need to encode information about castling, black or white to move, en passant etc.

Repeat positions are another issue though. Do we have to encode them? My 10^71 tree would not contain them. At first I thought we can leave them out. Now I'm not so sure anymore.

A move that leads to a repeat position is certainly not necessary to win a game. You could play the winning moves right away.

But it can be necessary to force a draw. Hmm...

You might be right. Maybe the "repeat position" issue kills the upper limit of 10^71 nodes in the tree of chess moves. So we have to resort to your upper limit of 10^22680.