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Probably a lot more than you care to know about...
The Game of Nim

• Nim is a simple game of finite possibilities (unlike chess, say, where the possibilities appear to border on the infinite). In fact, nim is not much more complex than a puzzle. But unlike that other great game of limited possibilities, tic-tac-toe, there exists tremendous variety both in nim's conception and implementation. In tic-tac-toe there are Xs and Os; in nim the objects of play can be stones, straws, apples, oranges, matches, toothpicks, coins, beans, sticks, marbles and even, as in Alain Resnais' 1962 movie "Last Year in Marienbad", playing cards. In tic-tac-toe, the field of play is three rows of three. Nim's playing field varies from one to at least a dozen rows, and the number of counters in a row can vary from one to as much as two dozen. Some versions require that the winner take the last object; others that the winner avoid taking the last object.

• Nim probably originated in China, but the name is thought to be German, from nimm the German word for "take". (The first existing European reference to a nim-type is from the 15th century.) Nim was evidently played with what ever counters were at hand. The wide varity of legacy-objects in the cyber version graphics would seem to attest to that. And the wide varity of these objects probably indicates that we're a lot closer to nim's illiterate origins than we are to tic-tac-toe's. (Tic-tac-toe very likely comes from that other great ancient civilization, Egypt). Tic-tac-toe's dependence on writing implements and something to write on seems obvious enough, while nim can as comfortably be played with toothpicks or pennies as with pencils and paper.

• The contemporary attraction of nim (aside from its intrinsic puzzle value) is the mathematics it can be used to illustrate. If you're interested in the math involved:
  •  there's a nim page from the math department at Swarthmore,
  • Eric Berry and Soon Chung's have a nice  mathematical secrets of nim site,
  • and an AltaVista search  for "+nim +math" reveals 1000 of sites.

 On-line Play

The Web offers a great variety of nim games that can be played on line. (You'll need a Java aware browser.)

• Yahoo's Nim Page by itself offers a variety of online nim games.
• Srdjan Susnic has a very fine Java implementation of nim (here you need a Java enabled browser to play on line).
• Alexander Bogomolny explains the math with his Javascript version. Click on the Theory button.
• Evan Glazer, on the introductory Web page to his Java nim game, sums up nim nicely as ... a strategic game with a secret order hidden within it by mathematics. Without mathematical logic, it is difficult to win. But, if you look for a pattern, you just might outsmart your opponent!
• Here is a version written in Pascal. It's colorful, but it's rigged so you can't win. Also, its "about" page gives away some of the "secrets" to nim (and, as we know, nobody appreciates what they've been given nearly as much as something they've hacked together for them self).
• Here is a bare bones nim game at the University of Chicago.

 Download for Off-line Play

If you don't have a Java or even a Javascript capable browser, there are plenty of nim games you can download and play off-line. As a general rule, these aren't as interesting as the implementations now available on the Web, but they're good enough. (How good does the virtual replacement of stick and pebbles have to be?)

• NIM.ZIP; 3,470 bytes, for DOS. The program itself, written by Marijke van Gans in assembler, is an incredibly compact 1k. Van Gans inclueds MARIEN.BAT to recreate the 7-5-3-1 layout used in "Last Year at Marienbad". Van Gans also provides his source code: ftp://ftp.silicon-alley.com/pub/DOS/nimsrc.zip).
  And the source code comments contains this gem:

  ; rejoice! silicon alley lives! the tree that scatters its catkins to the winds
  ; lives a thousand times! publish and be immortal...
  

• MAC versions: Friends of Nim has a Mac collection nim-1.0.sit.hqx that is usually available on the Net somewhere. Check: http://ftp.wustl.edu/systems/mac/amug/files/game/n-q/. There is also, for the Mac, MARIENBAD-42.HQX, a nim game named after Resnais' movie.

"Last Year in Marienbad" features three playings of nim. In the first of these scenes, Sascha Pitoëff's character introduces the game in this dialogue:

"I know a game I always win."
"If you can't lose, it's no game."
"I can lose, but I always win."

He always does win too ( which anyone familiar with nim will recognize as some of the film's more plausible events).

If you have a Mac, try downloading MARIENBAD-42.HQX from one of the sites listed at: http://www.gamesdomain.com/directd/mac/board/marienbad.html.

• Matches.exe An easy to learn Windows 95/NT version of nim in a 201K ZIP file, with a nice, clean interface.
• EINSTEIN.ZIP In 1986 I wrote a compiled BASIC version of Nim for DOS. It was a game I played as a kid. We called it "the match-stick game" because we didn't know any better. When I sent this version out into the ether I named it "Hey Einstein". My version is interesting because it's the only implementation I've run across with a dynamic row count. The game starts with 5 rows, but by removing counters in the rows' centers, the row count can reach, in effect, as many as 8. (I fully concede that the dynamic row count might be because our source for the rules just didn't know any better.)

Hey Einstein is still floating around out there. It got picked up and published on the first GIGA GAMES CD-ROM. (It's in the /games/dos/word/ directory. I was only interested in the game's logic at the time, so to save having to program graphics and pointing devices, I used the letters "A" through "S" in the interface. Apparently that satisfied the conditions for a word game. Now, Hey Einstein appears to be on a new GIGA GAMES 5 .) Several years later, when I was programming in "C", I tried to make a more compact program. In NIM.EXE I got the logic and a mouse interface down to 13k. But NIM.EXE (downloadable as NIM.ZIP ) has ONLY a mouse interface. It can't be played with a keyboard. It will run in a Windows DOS box, but it's a crude program.

 A Book of Stick Games with a Nim Chapter

• Pickup Sticks is a wire bound, 18 paged paperback from a small California publisher, that purports to be the definitive book of children's stick games. That's hard to believe. Nim rates 154 words. The interesting thing about the book, however, is that it treats nim as a children's stick game even though it's the only one of these games where the advantage goes not to the nimble fingers, but the nimble minds.
• A search through the Library of Congress Catalog reveals no titles that include "nim" the game. (None include "tic-tac-toe" either.) Title searches at Amazon.com and Powell's Books haven't until recently revealed any book titles related to the game either, but as of November 1997 Sherron Pfeiffer's 64 page paperback, Creating Nim Games, can be found in their databases. A thorough search, however, reveals nim chapters in a great many math books dating back to at least the turn of the century. .

That's it.

This page has been accessed times since 6/6/2000.

Frans GustafsonFrans@lafn.org
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