cp's OEIS Frontend

This is considered erroneous because it counts as distinct two positions at ply 6 where in one case, an en passant capture is available but illegal, while in the other case, the en passant capture is not available. It is questionable whether two such positions should be considered equivalent, since the definition of position (as opposed to diagram) includes the information on whether en passant is available (i.e., pseudolegal), not whether it is legal. [Depending on the variant of chess that is played, it may be allowed to make otherwise "illegal" moves which expose one's king to a capture.] - M. F. Hasler, Mar 02 2022

Does not include games which end in fewer than n plies.

According to the laws of chess, the "50-move rule" and "draw by 3-fold repetition" do not prevent infinite games because they require an appeal by one of the players, but the "75-move rule" introduced on Jul 01 2014 is automatic and makes chess finite. - François Labelle, Mar 30 2015

Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.

Even though the sequence may be infinite (if none of the rules for draw is ever invoked by any of the players), the sequence becomes constant from a given rank n on, since it is increasing (I conjecture - even though some positions available at the n-th move might not be available on the (1+n)-th move) and bounded, thus it has a limit. The challenge is now to find this limit (or at least nontrivial upper bounds) and the rank from which on the sequence becomes constant. - M. F. Hasler, Feb 15 2008

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). About Hasler's second challenge, a chess problem by L. Ceriani and K. Fabel shows that at least one position is visited for the first time at ply 366. - François Labelle, Apr 01 2015

Definition: position = position with castling and en passant information, diagram = position without castling and en passant information.

The positions are taken from the sets that are counted in A083276.

In view of the 75-moves rule any chess game is finite.

The largest value appearing in the sequence is thought to be 218. - François Labelle, Dec 01 2016