# Massacre Proof Games

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 0 0 0 0 0 0 0 0 0 5330 0 0 1579 70476 0 1848 49758 770912 1948 79313 1002112 1572 112297 2324252 1859 166847 4079067 2243 235082 7456474 3718 351119 13322408 5749 581588 23181085 9463 967742 40867572 14123 1589381 71471685 20787 2530833 123150384 29323 3808155 202209472 43978 5739797 324453946 64134 8420818 500029995 90659 12289682 760082705 121380 16981034 1099990237 143938 22302528 1543092047 160061 27038573 2012263317 149259 29971375 2469906062 133316 30457039 2761290606 98315 27518641 2829524382 72997 22702677 2599742382 41924 16157621 2124497143 23453 10355382 1522979675 9721 5498926 928366242 3902 2501639 473870909 890 873024 189297438 161 229895 56139054 17 38842 10835051 2 3516 1141076 0 90 46697 0 0 416 0 0 0

## Plot of the table entries

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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