Moves that determine all the previous moves

This page lists moves that determine all the previous moves uniquely. If the move ends with a checkmate symbol (#), then the move also determines the game. Most of the material on this page comes from an exhaustive computer search up to ply 10 that I completed in January 2004. There are three exceptions:

By "move" I mean its representation in Standard Algebraic Notation (SAN), except for disambiguation (a precision on the file or rank of the starting square). Be careful, details are important: If the problem says "4. Ra8", then the problem asks to move a rook to a8 without capture.

The following chess problems look like nothing, but they're often very beautiful, especially the checkmate problems. The first few plies are trivial and omitted. Click on a problem to see the solution.

ply 1

(all 20 moves of white)

ply 2

(nothing)

ply 3

(16 captures of black pawns on the 5th rank)

ply 4

(9 captures of white pawns on the 5th rank)

ply 5

3. Qd6+
3. Qe4+
3. Qe5+
3. Qxb8
3. Qxf8+

ply 6

3... Bf6+
3... Bxb3+
3... Rxe5+
3... Qd4#

ply 7

4. Ra8
4. Rh8 (mirror of Ra8)

ply 8

4... b5#
4... Re1+
4... Re2 (similar to Re1+)
4... Qb5#

ply 9

5. Ng3# (republished in Probleemblad 07-08/2004)
5. Qxe4# (republished in Probleemblad 07-08/2004)

ply 10

5... Rh1# (republished in Probleemblad 07-08/2004, and featured as ChessBase Christmas 2006 Puzzle 7!)

ply 11

6. gxf8=N# (found first by Peter Rösler)

ply 12

(no checkmate problem)

ply 13

7. Ka3# (found by Stuart Rachels in 2015)
7. Ka5# (similar to Ka3#, same author)

ply 14

7... Kxb7# (found by Alex Fishbein in 2016)

Additional problems

Computation updates

Ply 11

I thank Joost de Heer for computing ply 11 with my program on his computer, thereby confirming that gxf8=N# is the unique such problem at ply 11. The computation took about 3 months on a 1.6 GHz Pentium4 computer, and ended in July 2004.

Ply 12

In 2007, I verified that no checkmate problem exists at ply 12. This left the slim possibility of a non-checkmate problem at ply 12, or of a problem at ply 13 or beyond.

Ply 13

In November 2015, I computer-verified Stuart Rachels's two problems with a special program that narrowly targeted non-capturing king-to-a-file problems at ply 13.

Ply 14

In January 2016, I computer-verified Alex Fishbein's problem with a special program that only targeted the move ...Kxb7# at ply 14.

Shortest checkmates

One way to search for moves that determine the game is to search for the fastest way of checkmating with a particular move, and then hope that the solution is unique. There are 840 possible mating moves in SAN without disambiguation. The interactive table below shows the length (in plies) of the shortest known solution for each move by White. An even length means that Black mates faster using the mirror move. Lengths up to 12 plies come from my computer analysis and are guaranteed. Lengths of 13 plies or above come from Stuart Rachels who is working on this task with other chess players without using computers. Lengths of 14 plies or above are in general not guaranteed. Entries in bold indicate that there is a unique solution of that length.

8=N????????
8=B????????
8=R????????
8=Q????????
8????????
7????????
6????????
5????????
4????????
3????????
2????????
1????????
abcdefgh
pawn moves:
knight moves:
bishop moves:
rook moves:
queen moves:
king moves:

Rarity of unique solutions

Below is the fraction of mating moves whose shortest solution is unique (for plies 4-12 where the number of mating moves is guaranteed). The overall fraction is about 1.2%.

PlyFraction unique
40 / 1
50 / 4
61 / 12
70 / 13
82 / 42
92 / 121
101 / 165
111 / 182
120 / 121
13+3? / 179
all10? / 840

page created: January 2004
page last updated: January 4, 2017

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