cp's OEIS Frontend

This sequence is A048987 plus the cumulative sum of A079485. - Richard Bean, Jun 18 2003

The word "terminate" is inappropriate if only termination by checkmate is considered, since games can also end in a draw. The earliest possible draws occur by threefold or 5-fold repetition of the starting position through, e.g., twofold resp. 4-fold repetition of the moves 1.Nf3 Nf6 2.Ng1 Ng8, or an equivalent sequence. - M. F. Hasler, Mar 02 2022

Gives the number of possible chess games where both sides start without queens. Queens are still allowed to appear later in the game through promotion.

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

The total number of such games should be less than the total number of standard chess games, and it appears A285873(n) <= A048987(n) for n >= 7.

Initial terms computed using the Chesspresso engine.

Gives the number of possible chess games where both sides start without rooks. Rooks are still allowed to appear later in the game through promotion.

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

The total number of such games should be less than the total number of standard chess games, and it appears A285874(n) <= A048987(n) for all n.

Initial terms computed using the Chesspresso engine.

Gives the number of possible chess games where both sides start without knights. Knights are still allowed to appear later in the game through promotion.

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

The total number of such games should be less than the total number of standard chess games, and it appears A285875(n) <= A048987(n) for all n.

Initial terms computed using the Chesspresso engine.

Gives the number of possible chess games where both sides start without bishops.

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

The initial terms exceed the corresponding terms in A048987, but this should eventually reverse and we should have A285876(n) <= A048987(n) for large enough n.

Initial terms computed using the Chesspresso engine.

Gives the number of possible chess games where both sides start without pawns.

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

The initial terms exceed the corresponding terms in A048987, but this should eventually reverse and we should have A285877(n) <= A048987(n) for large enough n.

Initial terms computed using the Chesspresso engine.

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

a(6) was computed in 1897.

Gives the number of possible chess games where both sides start without queens, rooks, knights, and bishops.

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

Initial terms computed using the Chesspresso engine.

This differs from A057745 at 6 ply and above because where an en passant capture would be illegal, the position is essentially the same as where an en passant capture is not available. It is two less than A057745 at 6 ply because the positions after 1. f4 e6/e5 2. Kf2 Qf6 3. f5 g5 are considered to be the same as after 1. f4 g5 2. Kf2 e6/e5 3. f5 Qf6.

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

The sequence became finite on Jul 01 2014 with the introduction of a new draw rule which is automatic (the 75-move rule). - François Labelle, Apr 02 2015