A game of chess is called a "massacre" if almost every move is a capture. When only the final diagram and the number of moves are given, deducing the game is a chess problem called a "massacre proof game".

Let x be the number of non-captures. The case x=2 is uninteresting because at most 4 halfmoves can be played. The table below contains information about the cases x=3,4,5. The number of pieces left on the board is of course simply 32+x-ply.

Toward the end of the table you will find some links to the corresponding chess problems. The fields inside each list of problems are:

**solutions:**The number of solutions to the problem.**w/o DR:**The number of solutions without "Dead Reckoning" (= Article 1.3 of the Laws of Chess, repeated in 5.2b and 9.7). This gives the status of the problem prior to July 1, 1997, when the article was introduced. See this Dead Reckoning Tutorial to learn about the amazing effect of A1.3 on chess retrograde analysis.**(w+b):**The number of white pieces and black pieces.**diagram:**The location of each piece, white pieces first.**problem ID:**A link to the problem on the Chess Problem Database Server when it's there.

x=3 | x=4 | x=5 | |
---|---|---|---|

ply 0 | 0 | 0 | 0 |

ply 1 | 0 | 0 | 0 |

ply 2 | 0 | 0 | 0 |

ply 3 | 5330 | 0 | 0 |

ply 4 | 1579 | 70476 | 0 |

ply 5 | 1848 | 49758 | 770912 |

ply 6 | 1948 | 79313 | 1002112 |

ply 7 | 1572 | 112297 | 2324252 |

ply 8 | 1859 | 166847 | 4079067 |

ply 9 | 2243 | 235082 | 7456474 |

ply 10 | 3718 | 351119 | 13322408 |

ply 11 | 5749 | 581588 | 23181085 |

ply 12 | 9463 | 967742 | 40867572 |

ply 13 | 14123 | 1589381 | 71471685 |

ply 14 | 20787 | 2530833 | 123150384 |

ply 15 | 29323 | 3808155 | 202209472 |

ply 16 | 43978 | 5739797 | 324453946 |

ply 17 | 64134 | 8420818 | 500029995 |

ply 18 | 90659 | 12289682 | 760082705 |

ply 19 | 121380 | 16981034 | 1099990237 |

ply 20 | 143938 | 22302528 | 1543092047 |

ply 21 | 160061 | 27038573 | 2012263317 |

ply 22 | 149259 | 29971375 | 2469906062 |

ply 23 | 133316 | 30457039 | 2761290606 |

ply 24 | 98315 | 27518641 | 2829524382 |

ply 25 | 72997 | 22702677 | 2599742382 |

ply 26 | 41924 | 16157621 | 2124497143 |

ply 27 | 23453 | 10355382 | 1522979675 |

ply 28 | 9721 | 5498926 | 928366242 |

ply 29 | 3902 | 2501639 | 473870909 |

ply 30 | 890 | 873024 | 189297438 |

ply 31 | 161 | 229895 | 56139054 |

ply 32 | 17 | 38842 | 10835051 |

ply 33 | 2 | 3516 | 1141076 |

ply 34 | 0 | 90 | 46697 |

ply 35 | 0 | 0 | 416 |

ply 36 | 0 | 0 | 0 |

To show the similarities, I'm scaling the x=3,4 graphs to the level of the x=5 graph by using some fudge factors.

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