A285877 -id:A285877 - cp's OEIS frontend

A048987 Number of possible chess games at the end of the n-th ply.

1, 20, 400, 8902, 197281, 4865609, 119060324, 3195901860, 84998978956, 2439530234167, 69352859712417, 2097651003696806, 62854969236701747, 1981066775000396239, 61885021521585529237, 2015099950053364471960

Offset: 0

S. J. Edwards

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

A. Bertilsson, Distributed Perft Project [also found a(11)]
James Grime and Brady Haran, How many chess games are possible? (Numberphile video), 2015.
Jakub Kowalski, Marek Szykuła, Experimental Studies in General Game Playing: An Experience Report, University of Wrocław, (Poland, 2020).
F. Labelle, Statistics on chess games
T. Sillke, number of legal chess positions
R. P. Stanley, Extremal [Chess] Problems
Wikipedia, Shannon number
Index entries for sequences related to number of chess games

Cf. A006494, A079485, A083276, A019319, A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

a(10) from Richard Bean, Jun 02 2003
a(11) from François Labelle, Jul 25 2004, who thanks Joost de Heer for providing computer time
a(12) from Paul Byrne on Oct 24 2006, verified by S. J. Edwards on Apr 25 2011
a(13) from Paul Byrne on Nov 08 2011, verified by S. J. Edwards on Oct 03 2012
a(14) from Richard Bean on Jul 24 2018, value from Peter Osterlund and Ankan Banerjee
a(15) from Paul Barnett on Jul 04 2022, value from wikipedia page "Shannon number"

A285873 Number of possible chess games at the end of the n-th ply starting without queens.

Original entry on oeis.org

1, 21, 441, 9872, 220447, 5247292, 124278971, 3113440755, 77520962327, 2024021927610

Offset: 0

Sean A. Irvine, Apr 28 2017

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.

			a(1) = 21 because there are 20 usual opening moves plus the additional move of moving the king into the vacant square where the queen would usually be.

Chesspresso^TM.

Cf. A048987 (standard), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

A285874 Number of possible chess games at the end of the n-th ply starting without rooks.

Original entry on oeis.org

1, 20, 400, 8702, 188473, 4505624, 106770421, 2770746488, 71151220765, 1969755500063

Offset: 0

Sean A. Irvine, Apr 28 2017

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.

Bernhard Seybold, Chesspresso.

Cf. A048987 (standard), A285873 (no queens), A285875 (no knights), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

a(9) from Sean A. Irvine, May 04 2017

A285875 Number of possible chess games at the end of the n-th ply starting without knights.

Original entry on oeis.org

1, 18, 324, 6572, 132640, 3030492, 68633066, 1733220521, 43321058602, 1182486223832

Offset: 0

Sean A. Irvine, Apr 28 2017

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.

			a(1) = 18 because each pawn can move forward 1 or 2 squares (16 moves) and each rook can move into the square where the knight would have been (2 moves).

Chesspresso^TM.

Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285876 (no bishops), A285877 (no pawns), A285878 (pawns and king).

A285876 Number of possible chess games at the end of the n-th ply starting without bishops.

Original entry on oeis.org

1, 22, 484, 11248, 260904, 6434922, 158069690, 4126252938, 107097735673, 2940365284820

Offset: 0

Sean A. Irvine, Apr 28 2017

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.

			a(1) = 22 because we have the standard 20 opening moves, plus the queen and king can each move into the squares that would normally contain the bishops.

Chesspresso^TM.

Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285877 (no pawns), A285878 (pawns and king).

A285878 Number of possible chess games at the end of the n-th ply starting with just pawns and king.

Original entry on oeis.org

1, 18, 324, 5658, 98766, 1683597, 28677387, 479763588, 8014917042, 132060434889, 2170519816231

Offset: 0

Sean A. Irvine, Apr 28 2017

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.

			a(1) = 18 since each pawn can move forward 1 or 2 squares (16 moves) or the king can move left or right (2 moves).

Bernhard Seybold, Chesspresso.

Cf. A048987 (standard), A285873 (no queens), A285874 (no rooks), A285875 (no knights), A285876 (no bishops), A285877 (no pawns).

a(10) from Sean A. Irvine, May 04 2017

cp's OEIS Frontend

A048987 Number of possible chess games at the end of the n-th ply.

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A285873 Number of possible chess games at the end of the n-th ply starting without queens.

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A285874 Number of possible chess games at the end of the n-th ply starting without rooks.

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A285875 Number of possible chess games at the end of the n-th ply starting without knights.

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A285876 Number of possible chess games at the end of the n-th ply starting without bishops.

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A285878 Number of possible chess games at the end of the n-th ply starting with just pawns and king.

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