I read it as “there is no legal position for which the minimum number of moves necessary to reach it is greater than 218” but I also did not read the whole article before coming to check the comments
It’s also rare to have one with more than 50 moves. I’m curious if this class of observation will help establish a true bounds. Especially because we don’t have a definition of what it means - my instinct is to first do that, so “infinity” isn’t the obvious upper bound.
Proving this feels more difficult than proving what’s in the OP article, because here you have to show path lengths between original position and all possible positions have a max length, while OP article had to show all positions have a max degree. Path length just seems like a harder problem compared to node degree.
The upper bound is a few thousand. A game is considered drawn if no pawn has moved and no piece has been captured for 50 moves. And there's also the threefold repetition rule: if the same exact position (counting things like castling eligibility etc) occurs three times it's drawn.
I think the upper bound is 6300, then. Each pawn can move 6 times, times 16 pawns, times 50 moves before a game ending draw, plus each capturable piece that can delay the game another 50 moves (15 on each side)
You read a comment saying it’s rare to have more than 200 moves, then a reply noting more than 50 is also rare, then suggested you were confused and maybe it was unreadable and asked “What?” because…some games have above 50 moves. shrugs
Thanks for note re: upper bound with 75 moves without pawn advancing constraint.
