Game Systems - Part 4

Game systems (sets of components that function together in multiple games, such as decks of cards) are probably almost as old as games themselves. For thousands of years, humans have often had more intelligence and energy than are required to survive long enough to reproduce, so it is in our nature to game.

Humans play with what's available in our environment. H.J.R. Murray's History of Board-Games Other Than Chess (1951) shows that technologically primitive societies often play games on boards scratched in the dirt with sticks, using stones, seeds, or seashells for playing pieces. Also universal are games played aloud, such as guessing games, and games played with the body, such as Rock Paper Scissors. Therefore, I propose that humankind's First Game System was probably a combination of sticks, dirt, stones, body parts, and voice.

You might object that games, like art, arrive only with the leisure that civilisation produces, but some anthropologists think that members of hunting and gathering societies tend to have more leisure than members of agricultural or industrial civilisations. However, it's next to impossible to prove that our earliest human ancestors used the First Game System. As Murray writes, "So long as a people is content to mark out the board on the ground and to use any convenient object at hand for the pieces, there is very little chance of [the game's] survival" -- that is, its survival as an archaeological object. We know that Mancala is old because we have examples of carven boards from long ago, but the copies of the games that were played in the dust are long gone.

Of course, most people reading this article have readier access to office supplies and pocket change than to dirt and rocks. That's why I will focus on pens, paper, and coins - the contemporary urban equivalent of sticks, dirt, and stones, respectively. The human body and voice, which haven't changed much since the Stone Age, are also a part of this game system. Pens, paper, coins, body, and voice therefore form what I call the Urban Low-Tech Game System, or ULT.

The possibilities of both the ULT and the First Game System are overlooked by most contemporary gamers in developed countries. This is a shame, because the ULT is both extremely inexpensive and extremely portable. It consists of components many of us have with us all the time. Therefore, if you are prone to boredom, you might find it useful to memorise the rules to some of the games in this article, because you can play them almost anywhere.

Spoken Games

Spoken games are played with the voice, although they can be played in online chat rooms if they don't involve something only voices can do, such as singing.

There is much you can do with no equipment as such. For example, try games you had thought you were tired of, but try a higher level of play. Consider the 20 Questions FAQ, which codifies the rules of 20 Questions, giving strategy hints as well as instructions for online play.

Twenty questions aren't enough when you're trying to guess "the reflection of the full moon in the eye of the werewolf on a mountaintop of the Carpathians on Walpurgisnacht" or "the concept of justice in the mind of Felix Frankfurter when he wrote his analysis of the Sacco-Vanzetti case". Both of these targets are mentioned in the rules for Super-Categories in the book Games for the Superintelligent by James Fixx (1972). I played it with my friends in high school, although we called it 20,000 Questions. In fact, there is no limit to the number of questions you can ask in this game, and the clarifications in the (merely) 20 Questions FAQ should be useful.

Indeed, guessing games form a large sub-genre of spoken games. Another famous one is Botticelli, in which players attempt to guess an historical person or fictional character based on the initial of the figure's surname. One less-known example is Kolodny's Game, a peculiar little pastime, also from Games for the Superintelligent, that might best be described as verbal Eleusis or Zendo.

There is a whole class of Ghost games in which players add letters of the alphabet to a growing word and attempt not to complete it. Superghost allows players to add letters to the beginning of the word as well as the end. Anaghost, from David Parlett's book of word games Botticelli and Beyond (1982), forbids players to complete a set of letters that forms an anagram of any English word. I enjoy the Ghost family so much that I adapted Superghost to the Alpha Playing Cards game system.

Hand Games

The satirical British gaming webzine Critical Miss examines games you can play with body parts in Gaming With Nothing. The games listed run from Rock Paper Scissors to Sexual Intercourse, and the authors write, "For each game we've outlined the basic rules and then added a few variations, together with guides to playing the game solitaire." Warning: Memorizing games for dull moments does not apply here. The grocery isn't the place for solitaire Sexual Intercourse.

Now for more games you can play with your hands. Let's skip Thumb-Wrestling in favour of games with more strategy.

Rock Paper Scissors and Friends

World RPS Society logoI'm sure that this game doesn't need much introduction, although if you come from another culture, you may know it as something like Snake Frog Slug (Japan), Elephant Human Ant (Indonesia), or General, Gun, Hands Up! (Myanmar/Burma). Briefly, at a signal, two opponents show each other one of their hands, shaped like a rock, a piece of paper, or a pair of scissors. Rock smashes Scissors, Scissors cut Paper, Paper wraps Rock. Each "weapon" beats one other weapon and is beaten by one other weapon, in a "non-transitive relationship".

The article in Critical Miss implies that Rock Paper Scissors is no more strategic than Stares, Slaps, or Brawling. In fact, a great deal of study has gone into the game by the World RPS Society and the International RoShamBo Programming Competition. (RoShamBo is another name for RPS, Eric Cartman of South Park notwithstanding.) As the rules for the second programming competition read;

The game is trivial from a game-theoretic point of view. The optimal mixed strategy is to choose an action uniformly at random (one-third probability of each). This will ensure a break-even result in the long run, regardless of how strong (or how weak!) the opponent is.

However, against predictable opponents, a player can attempt to detect patterns in the opponent's play, and exploit those tendencies with an appropriate counter-strategy.

In other words, if you play purely at random, you can expect to win 50% of the time over the long run. However, if your opponents are attempting to out-think you, and you're smart enough, you can win much more often. The Wikipedia notes:

...if the opponent is human or a non-random program, it is almost certain that he plays suboptimally and that a modified strategy can exploit that weakness. This is easily demonstrated by Roshambot, a computer program that easily defeats some human players (as does its author Perry Friedman, who won an $800 competition against seven opponents including former world poker champion Phil Hellmuth in August 2001).

Sometimes low-tech games require a high-tech touch. Chris Moneymaker, the 2003 world Poker champion, learned to play Poker online. He completely ignored the "tells", or body language, of his opponents, which can be faked at a high level of play anyway. He merely analyzed his opponents' past betting patterns and played the odds. In Rock Paper Scissors as in Poker, it may pay to play like a computer.

Rewind, Seattle public radio's answer to The Daily Show, interviewed one of the organisers of the 2002 International Rock Paper Scissors Championships in November 2002, then did a followup piece with World Champion Pete Lovering a week later. (RealAudio software required.) Be sure to listen past the main RPS piece in the second show for a plaintive attempt to sway public opinion:

Support for Rewind comes from Water, which, despite its ability to rust Scissors, erode Rock, and dissolve Paper, continues to be excluded from the International Rock Paper Scissors Championships...

Multi-Weapon RPS

Perhaps Water has finally had its big break, however, because Rock, Scissors, Paper Plus adds Water and three other weapons for a total of seven (Rock, Paper, Scissors, Water, Bird, Bomb, and Chopper). With 21 possible interactions among the different weapons - there are ((w^2 - w) / 2) interactions, where 'w' represents the number of different weapons - there are too many combinations for any but an experienced player to remember. However, RSP+ does have a nice scoring system that adds a little strategy to the game, for example, enabling a player to shout "MATCH!" as he shoots, gaining bonus points if both players shoot the same weapon.

I prefer Rock Paper Scissors Spock Lizard to RSP+, partly because it is simpler, and partly because the non-transitive relationships are illustrated in an elegant diagram. (Also, I like making the "Live long and prosper" sign from Star Trek.) Each weapon defeats two others and is defeated by two others, as explained in the ten basic rules. Notice that rules 1, 2, and 3 are the same as in regular RPS.;

  1. Rock crushes Scissors
  2. Scissors cut Paper
  3. Paper covers Rock
  4. Rock crushes Lizard
  5. Lizard poisons Spock
  6. Spock smashes Scissors (presumably in frustration over his haircut)
  7. Scissors decapitate Lizard
  8. Lizard eats Paper
  9. Paper disproves Spock
  10. Spock vaporizes Rock

Perhaps it would be interesting to combine the five weapons of Rock Paper Scissors Spock Lizard with the unique scoring rules of Rock, Scissors, Paper Plus to create a hybrid game that is better than either. Ultimately, any scoring rules you can add to an RPS variant, even "best two out of three", will make the game better, because "one-shot" games are simply too devoid of strategy.

I wonder how a computer program written to play an RPS variant with more than the traditional three weapons would look. My intuition is that it would be quantitatively different, not qualitatively different. One kind of pattern recognition in this domain is probably much like another.

Besides being a Pagan symbol, the pentagram of the five weapons in Rock Paper Scissors Spock Lizard is curiously reminiscent of the Daoist (also spelled "Taoist") diagram of the Five Elements:

In Chinese [Daoist] thought, things in nature can be classified in five types: metal, wood, water, fire, earth... These five elements... are not just the materials that the names refer to, but rather metaphors for describing how things interact and relate to each other.

Daoism describes both a production chain and a control chain between the elements. In the production chain, wood produces fire; fire produces earth; earth produces metal; metal produces water; water produces wood. In the control chain, wood controls earth; earth controls water; water controls fire; fire controls metal; metal controls wood. The production chain outlines a pentagon and the control chain outlines a five pointed star.

In graph theory, this kind of graph, in which every point connects to every other, is called a "clique". Unfortunately for Qabalists everywhere, it's not possible to map the structure of Rock Paper Scissors Spock Lizard topologically onto the diagram of the Five Elements without equating items nonsensically, saying, for instance, that the weapon Rock maps onto the element Wood, or the weapon Paper is the element Water. Still, in a certain sense, Daoism posits that everything in the world is engaged in a constant game of five-weapon Rock Paper Scissors. Who knew the humble game of RPS was so important? Just don't go cyanotic waiting for your non-gamer (not to mention non-Daoist) friends to appreciate its beauty, charm, and significance.

Other Hand Games

Sadly, I wasn't able to find playtesters for the Co-Op Finger Game, a sort of cooperative RPS described in the book Co-Op Games Manual by Jim Deacove, one of the mavens of cooperative games at Family Pastimes. It will have to wait for another article.

A two-player hand game that will be familiar to many readers is Odds & Evens. One player is Odd and one player is Even. On a count, the players "throw" one or more fingers. If the sum is odd, the Odd player wins; if the sum is even, the Even player wins. As "11-Digit Boy" points out on the Rock Paper Scissors around the world site linked to earlier,

With 3 people, you can have Zeroes, Ones, and Twos, and take the remainder when the total number of fingers is divided by 3.

Of course, this can extend to any number of players. If you have eight players, divide by eight and calculate a remainder of 0 through 7. I suppose the generalized game can be called Remainders. As with RPS, adding virtually any scoring rules that track results over multiple turns will make the game more interesting.

Pen and Paper Games

By "pen and paper game" I mean a game that can be played with pens or pencils and an ordinary piece of blank paper or graph paper. Pen and paper games are also called "pencil and paper games", "paper and pencil games", and so on. Googling the various combinations of terms is instructive.

Pen and paper role-playing games are outside the scope of this article; so are Sid Sackson's series of "Beyond..." game books (Beyond Words, Beyond Solitaire, Beyond Tic Tac Toe, etc.), because, excellent though they are, you need copies of the game boards printed in the books to play the games. However, buckle in, because we are certainly going beyond Tic-Tac-Toe.

Waving Hands

Although Waving Hands, also known as Spellbinder, Spellcaster, Spellcast: Deathmatch, and Firetop Mountain, is sometimes thought of as a pen-and-paper-and-hands game, it can actually be played as a pure pen and paper game, a sort of written, two-handed Rock Paper Scissors with special powers for the gestures. On each turn, players write orders for their wizard character and any monsters they control. Orders, which designate hand gestures or knife stabs from the wizard, and targets for the wizards' and monsters' attacks, are revealed simultaneously, as in Diplomacy. A wizard's two hands can cast spells separately or together, and it may take a sequence of gestures over several turns to cast a spell, so that a skillful opponent can sometimes anticipate it. Bluffing is also possible.

Several computer versions of Waving Hands have been programmed. The Unix version by Andrew "Zarf" Plotkin is especially fine, and rumour has it that obsessive play nearly caused some Carnegie Mellon students to drop out of college. Zarf's version is now included in Debian GNU/Linux. The manual version can be found online at The Game Cabinet.

Richard Bartle, the designer of Waving Hands, wrote a rivets-and-sorcery novel based on the magic system in the game, called INsightflames. Out of respect for Bartle, who has taken the book offline for some reason, I won't cite the URL, but I will tell you that the Wayback Machine is your friend.

Two Classic Games

Two classic pen and paper games that you might have played already (perhaps during a boring lecture) are the traditional game Dots & Boxes and Sprouts, invented by John Conway and Michael Paterson.

Dots & BoxesIn Dots & Boxes, players alternately draw line segments on a grid of dots, attempting to enclose the most square boxes. When a player encloses a box, she writes her initial in it and goes again. This can lead to astonishing cascades of boxes; the player who can force the other player to cede her one or two long cascades usually wins.

In Sprouts, players draw curves from one preexisting dot to another on the page, adding another dot somewhere along the new curve from which yet another curve can sprout. A maximum of three curves can extend from any dot, and curves can't cross. The last player who can move wins.

Both of these games have been analysed extensively. Dots & Boxes is the subject of the book The Dots and Boxes Game: Sophisticated Child's Play, by Elwyn Berlekamp (2000). There is a World Game of Sprouts Association that publishes technical papers such as The Focardi and Luccio Analysis of 7+, and it even has its own fight song to the tune of "Old Rocky Top".

Other Pen and Paper Games

Invisible City Productions is an interesting site to explore in search of good low-tech games. They have been publishing a new game every month since 2000. One of their games is Abs-Trac-Toe. This is a fun game in which players first draw a board in a goofy "abstract" shape and subdivide it into spaces into which they take turns placing symbols such as the traditional 'X' and 'O'. Unlike Tic-Tac-Toe, however, more than two people can play, so players' initials are a good way of marking territory, and the use of coloured pencils is also recommended, as the board rapidly becomes tricky to decipher. Coloured pencils also add to the "abstract art" quality of the game.

The object of Abs-Trac-Toe is to score as many shared borders as possible -- that is, if two spaces marked with your symbol share a border, that counts as one point for you. It becomes clear very quickly that it is important to mark spaces that have as much "surface area" (that is, as many borders) as possible. As in life, size doesn't matter much; a small space may have many more borders than a larger one that might seem superficially attractive. Also, all else being equal, it is important to mark the more central spaces, as they allow you to form branching structures of connected spaces. In this way, Abs-Trac-Toe is a little more like Go than like Tic-Tac-Toe, and some of the same strategies apply. It is possible, for example, to make "thin moves" (loosely connecting chains of spaces you intend to fill in later) and "thick moves" (dense lumps of tightly-connected marks). Overall, Abs-Trac-Toe is a good introduction for newcomers to the world of complex and interesting pen and paper games, the more so because its name is so unprepossessing.

The Origami Game doesn't require a pen, just paper. It is essentially a paper-folding race. Though basically a sport rather than an abstract game, there is some strategy, as in most sports. The designer writes, "When folding these geometric shapes try to do 2 or 3 folds at the same time, and try to find the 'key' folds that allow quicker folding".

Middleman, by Eric Solomon, is a clean, simple simulation of the marketplace. Players buy wholesale and sell retail cans full of an unspecified commodity goop (our game group calls it Soylent Green). The winner is the player with the most money after 10 rounds of buying and selling. The symmetry of the game design is pleasing; the rules for selling cans are a simple inversion of the rules for buying them. The game of which Middleman reminds me the most is Sid Sackson's Executive Decision, but with the manufacturing phase abstracted out. Middleman is proof that pen and paper games can be engaging multi-player simulations, not just abstract strategy games.

Another unusual pen and paper game, Veptheca, by Jordan Tuzsuzov, is a good example of the cutting edge in pen and paper games. While it is somewhat similar to Nim, the "take the last matchstick" game played for drinks in bars, the main mechanic is based on vector addition, a mathematical operation that layfolk may remember from physics class. Unfortunately, except perhaps for people who use vectors every day, this game suffers from lack of clarity: it is difficult to see which move to make and why to make it. The Veptheca website includes animated diagrams of game moves, suggesting that a computer version of the game with auto-display of all possible moves from a given dot would be useful until players get the hang of the game. It might also make a toroidal game (with board wrap-around) practical. Whether it works or not, however, Veptheca is an interesting experiment, and the surest sign I've seen that pen and paper games still have a lot of potential.

Many of my readers will be familiar with the game Mafia, also known as Werewolf and many other names. In both games, roles for the players are often assigned by handing out playing cards: red for the good guys, black for the bad guys. Obviously, however, if you don't have a deck of cards handy, slips of paper are just as easy and far more flexible, and players are less likely to forget what, say, the Five of Hearts means. Hence, it seems to me that Mafia and Werewolf are best played as pen and paper games.

Mafia and Werewolf are mob rule and paranoia played for laughs. I will summarize the version I know best. About eight to ten players are given slips of paper on which one of the following three words is written: "Werewolf", "Villager", or "Seer". There are two Werewolves and one Seer; the rest of the players are Villagers. The game consists of a series of "day" and "night" phases. At night, all players close their eyes. The Referee, who isn't one of the players, says "Werewolves, awake!". The Werewolves open their eyes and silently designate one of the other players to be rent apart in the night (figuratively, of course). The Werewolves close their eyes and the Referee says, "Seer, awake!". The Seer opens his eyes and silently indicates one of the other players. If that player is a Werewolf, the Referee nods. The Seer then closes his eyes. The Referee says, "Everyone, it's morning. Wake up!" The Referee announces the player who was killed by the Werewolves. That player is out of the game. Now the players collectively decide whom to lynch from among the other players. The Villagers want to lynch a Werewolf. The Seer wants to help them without giving himself away, or he'll be the next midnight snack. The Werewolves want to divert suspicion from themselves and lynch a Villager, which also makes their job of killing the entire village easier. The game ends when both Werewolves are killed, in which case, the Villagers have won, or when the number of remaining Werewolves equals the number of remaining Villagers, including the Seer, in which case, the Werewolves have won.

Werewolf was originally named Mafia, with the Werewolves originally Mafia hit men. The Graduate Mafia Brotherhood of Princeton University plays an elaborate form of the original game, with many more types of role than the three given in the summary above. They even have source code available in C for a computer program that will generate a random Mafia variant and act as moderator. A highly recommended site.

Books on Pen and Paper Games

100 Strategic Games for Pen and Paper (2002), by Walter Joris, is probably the finest book of pen and pencil games to appear in the past decade. Almost all of its games are original, or original adaptations of board games. There is such a wealth of games in the book that I have played only a fraction, but to my eye, there's hardly a bad game there. Even if fully half of them were bad, it would be worthwhile to buy the book for the 50 good ones. My only complaint is that Joris doesn't always adequately credit the designers of the board games from which some of his pen and paper games are derived.

Super Sharp Pencil & Paper Games by Andrea Angiolino (1995) is a more eclectic collection. While Joris's games tend towards abstract strategy, Angiolino's book includes word games, two-player mazes, math games, even a Sid Sackson game (Poe, from Beyond Words) that Angiolino adapted for use without the special printed board. In sum, this is a fine collection. It was reprinted in 2003 as Mind-Sharpening Logic Games, unfortunately without the author's errata.

The Joris and Angiolino books are readily available. Not only can they be ordered from major online booksellers, but I have spotted both on the shelves of my local independent bookstore.

New Rules for Classic Games by jack-of-all-games R. Wayne Schmittberger (1992) contains a chapter entitled "Paper & Pencil and No-Equipment Games". Besides numerous pen and paper games and the full rules to Lewis Carroll's game Arithmetical Croquet, this chapter contains the rules to a hand game called Finger Baseball. This is an indispensable book for any gamer who likes not only to play games, but to play with games.

The book Games with Pencil and Paper (1973, 1993) contains a number of interesting games and even adapts the excellent vintage board game Conspiracy to pen and paper. The pen and paper version is called Subterfuge, and is such a dead-on adaptation that I was outraged the rules didn't credit the designer of the original game, Eric Solomon. Eric Solomon's Black Box Then I remembered that Solomon was the author of the book. Solomon's game Middleman (described above) comes from this book. It's a pity that Solomon's games aren't better known. Actually, one of his games, Black Box, is famous; it has been programmed for just about every computer ever made, but usually without credit to him. Parker Brothers stopped manufacturing its board game version of Black Box decades ago, but a pen and paper version is available in Andrea Angiolino's book.

Mathematical studies of pen and paper games are the subject of the books Winning Ways for Your Mathematical Plays by John Conway and collaborators (including Berlekamp). A new set of the Winning Ways volumes costs about $200, but if you are more interested in in playing games than in combinatorial analysis, the website Games that interest John Conway is worth your attention, since it collects the rules to some Winning Ways games. So does the Mathematical Games site from Madras College in the UK.

Paper Games and Board Games: Differences

This section and the following one will be of interest primarily to game designers. If you don't have aspirations of that sort, you may want to skip to the section titled "Coin Games", below.

Just as the strengths of radio, as compared to television, enabled comedian Stan Freberg to aurally drain Lake Michigan, fill it with hot chocolate and whipped cream, and fly in the Royal Canadian Air Force to drop a ten-ton cherry on top "to the cheering of 25,000 extras", so pen and paper games have their own strengths, compared to board games, that should be extended as far as possible. This sums up the thesis of Walter Joris's paper The Difference Between Board Games and Pen and Paper Games, delivered in April 2003 at the conference Board Games Studies VI , According to Joris, with pen and paper games, 

  • players can easily fill the board with "pieces". 
  • occupied spaces can form a barrier, since the pieces can't be removed. 
  • games are flexible and interactive; characteristics of the "board" and pieces are easily changed, and this may lead players to develop variants or new games. 
  • players can use many more kinds of piece than with a board game, since the pieces are just symbols on paper. 
  • games can be played nearly anywhere at any time. 
  • games often have an elegant, abstract beauty.

I agree with all of these points.

Paper Games and Board Games: Similarities

It is peculiar that Joris focuses only on the differences between board games and pen and paper games, because there are many similarities between them, enough so that many commercial games were once pen and paper folk games. Guggenheim is the folk original for the commercial games Facts in Five and Scattergories. Battleship was a pen and paper game as early as World War I. Mastermind was once a pen and paper game called Bulls & Cows, and the version played with valid English words instead of random sequences of letters or numbers is called Jotto. I have read that even the classic commercial abstract strategy game Twixt was once a pen and paper game, although I have yet to confirm this. (Anyone who can is invited to email me.)

Not only is it often possible to translate pen and paper games to board games, but also to move in the opposite direction. By studying the books described above, I was able to discern some techniques that designers can use for converting board games to pen and paper games. Note: The notation "Joris #22" means that the game is number 22 in Joris's 100-game collection.

  1. Board games in which pieces are placed and never moved, such as Gomoku, are easily converted to pen and paper games. Example: Supermill (Joris #22), an adaptation of the ancient game Nine Men's Morris.
  2. If the board is small enough, the board and all its pieces can be redrawn each turn. Example: Paper Neutron (Joris #74), Joris's adaptation of Neutron.
  3. Mancala variants can be played with pen and paper by drawing the basins as large as possible and the stones as small dots. To add a stone to a basin, draw a dot; to remove a stone, cross one out. Example: Awele (Joris #86).
  4. Dominoes can be played on paper by drawing a box around two squares of a piece of graph paper. Write a number at each end of the "domino" to indicate the number of spots. Example: Paper Dominoes (Joris #63). Other polyominoes, such as pentominoes, which have five squares rather than two, can be simulated too.
  5. Simply accept that pieces will leave "clones" behind as they move across the board. Adapt the game rules as necessary to account for this fact. Example: Paper Halma (Joris #12). Also see Column (Joris #81), which seems to be a paper adaptation of Robert Abbott's Epaminondas, and Grupo (Joris #9), which seems to be a paper version of Claude Soucie's Lines of Action.
  6. Convert board games (such as Go) in which captures form an important part to lighter, more tactical pen and paper versions by adding the rule that the game ends with the first capture. Example: Single Take Go (Joris #53). This excellent game is also found in Schmittberger as One-Capture Go.
  7. Treat spaces as already containing pieces with certain attributes. Example: Subterfuge, Eric Solomon's adaptation of his board game Conspiracy. Rather than secretly bribe a pawn representing a secret agent and move it around the board with the secret papers, as in the board game, players treat every space as already containing a pawn. A player then writes a bribe for the agent who is notionally at, say, square 57 right onto that square on her private copy of the board, or states that that the agent at square 57 is handing off the papers to the agent on an adjacent square.
  8. Even dice can be emulated with pen and paper techniques. If you print the chart below, you will have a set of "paper dice". It is easy to improvise the chart on the spur of the moment as well.

1-1 1-2 1-3 1-4 1-5 1-6
2-1 2-2 2-3 2-4 2-5 2-6
3-1 3-2 3-3 3-4 3-5 3-6
4-1 4-2 4-3 4-4 4-5 4-6
5-1 5-2 5-3 5-4 5-5 5-6
6-1 6-2 6-3 6-4 6-5 6-6

This gadget from Schmittberger represents all possible dice rolls with two six-sided dice. Each player receives one table and chooses one of the rolls on her turn, crossing them off as she plays them. Of course, these paper dice are different from ordinary dice, since you can't make the same roll more often than once per 36 turns. This can be a good thing; paper dice can introduce strategy where there was none before, enabling players to save "good" rolls for situations where it matters, and dumping "bad" rolls in situations where the roll is less important.

  1. Another way to eliminate dice in a pen and paper game by having the players pick somewhat smaller numbers secretly, then sum them publicly to form the "random" number. Middleman, described above, uses this technique to simulate the vagaries of supply and demand.

Coin Games

I won't describe drinking games such as Quarters here, because you need a pitcher of beer as well as coins, and the beer is far more important, being penalty, prize, and the object of the game, all in one.

Change Change is a solitaire game, in effect a sliding-block puzzle like the 15 Puzzle that you play with coins. It was designed by Sid Sackson and appears in his book A Gamut of Games. Players take four coins of one denomination, four of a second, two of a third, and one of a fourth (for example, four pennies, four nickels, two quarters, and one dollar). They are placed randomly in three rows of four, with the "hole" in the lower-right corner. The player tries to form a pattern with the coins that shows mirror symmetry around the middle row. Since in this case, there are only one dollar and one hole, both must be in the middle row to attain symmetry. Here is a diagram representing one valid solution to a round of Change Change.


There are many other valid solutions, of course.

Change Change may sound like an easy game, but good old Sid set the bar high. In order to win a game of Change Change, you must complete seven successive rounds in 100 moves or fewer. That means each round must take you about 14 moves. I happen to be good at sliding-block puzzles�I co-authored one for the piecepack game system�but I wasn't able to come anywhere near this figure. Perhaps it is the uniqueness of the goal that Sackson designed into the game. Unlike the 15 Puzzle, which has a definite configuration of blocks towards which you can rocket almost unconsciously, mirror symmetry is an amorphous, open-ended goal with many possible solutions that can leave you puzzled as to which is the best to achieve, creating a more tactical than strategic game. In sum, Change Change may frustrate you, but it won't bore you for a long time. (Offer valid only if you like sliding-block puzzles. Definition of "long time" may vary from state to state (of consciousness).)

Coin-Moving Puzzles describes another set of solitaire games, or puzzles, if you like, involving sliding coins from one spatial configuration to another, such that each is touching at least two other coins. These games are challenging; my playtesters and I were unable to solve the first puzzle (turn the rhombus of six pennies into a hexagon) in less than five moves, although the authors state there are no less than 24 ways to do it in three moves. Just as with sliding-block puzzles, coin-moving puzzles will cause your brain's dendrites to branch and blossom as you discover and internalize new strategies and tactics; we discovered a move we called "scaffolding" in which two pennies are alternately slid ahead in a circular motion, each providing a "toe-hold" for the other. Although this is a mathematical paper, lay readers should be able to extract enough puzzles and strategies from it to make perusal worthwhile.

A brief digression: perhaps my readers think that puzzles are out of place in an article about game systems and the games you can play with them. I would disagree. Any puzzle, or solitaire game, can be turned into a multi-player game by making a contest out of solving it. For example, Change Change can be made a multi-player game if you add the rule that the winner is the player who solves a series of seven layouts in the fewest moves. Similarly, players can compete to solve coin-moving puzzles in the fewest moves. Low-tech game systems are especially suited to this sort of contest, because it is easy and inexpensive to produce as many sets of game equipment as are needed.

Moving on to more orthodox multi-player games, Seven Pennies, also by Invisible City Productions, is a luck-oriented game of penny-pitching for two or more players. At first it seems to be primarily an exercise in bad taste: the game uses Lincoln pennies on a game board consisting of a theatre and a balcony. Pennies are cast from the balcony into the theatre, presumably squeaking "Sic semper tyrannis!". Matched pairs of heads and tails are returned to the balcony; when you do this, you are said to Booth the pennies. (Please suppress that groan.) The main strategy consists of deciding whether to "Gather" the remaining pennies in order to add them to your score, or return them to the balcony, in order to "Cancel" the pennies of the player who has Gathered the most pennies with the opposite facing (if heads, then tails, and vice versa). Naturally, this leader-bashing mechanic is fairly unexciting in a two-player game, so I would recommend you try this game with at least three or four players. There are also several variants in the rules that add strategy; one variant adds nickels to the game, and another substitutes dice for pennies.

The Games Coins Play site collects a series of Nim-like games of increasing difficulty in which players compete to flip a line of 15 coins from all heads, in most cases, to all tails. The site contains a Java application that will let you play one of the six variants on the page against your computer. Madras College's Mathematical Games page also describes some games of this type. The games are simple, sometimes to the point of being insipid, as with the Trivial Game and the Baby's Game. It would not surprise me to learn that all of them have been completely solved. Nevertheless, the game they most remind me of is the much more complex Fight!.

Fight! is a numismatic confection, the rules to which Cheapass Games gives away on its business cards. (You can't get much cheaper than that.) Yes, the rules to this game and its variants fit onto an ordinary business card, yet it is deep enough that it could keep you entertained for hours. In short, all players start with the same set of coins, then take turns pushing a coin toward the center of the table and withdrawing up to a penny less in change. The last player with any coins wins.

One final hint: "AlphaTim" Schutz, designer of Alpha Playing Cards and former maintainer of the Penny Games site, spray-paints pennies on one side, making it easier to play Reversi and similar games. Gamers like to brag that they buy their glass stones cheap at craft or home and garden stores instead of at game stores, but at a mere one cent apiece, pennies are highly economical gaming tokens.

Pen and Paper and Coin Games

The number of games you can play with low-tech equipment approaches infinity when you add coins to pen and paper. With just these three items, you can play most of the hundreds of games at Jo�o Pedro Neto's World of Abstract Games, in all three of his main categories: Games of Soldiers (played with one kind of piece per side), Games of Kings and Soldiers (played with two kinds of piece per side), and Games of Towers (played with stackable pieces). In fact, I am not going to describe any games at all in this section, because I believe Jo�o's site is the definitive resource. I'll simply list a few of the games to which Jo�o has succinctly set out the rules: Amazons, Ataxx, Breakthrough, Camelot, Epaminondas, Focus, Lines of Action, Teeko, and Tempo. Of these, I have played all but Tempo (a "lost" Sid Sackson game) and Amazons. The games I have played are excellent, and I look forward to playing the others.


The conclusion to Walter Joris's paper reads:

I am not an historian, but as far as I know [no] "history" or bibliography is written about pen and paper games... But since there are a number of authors, and the number of games is increasing, maybe it is about time to undertake this...

Paper games are not commercial, since they are too little [as] an "object". They are in fact unsaleable. Because of that, and also because of their small number, they stay a bit in the shadow. But it is certainly my wish that a "culture" will arise of pen and paper games. Also I hope that, just as with board games a fertilization and a selection will take place. So that finally something like the "chess" [or] the "Go" of paper arises. For games do change of course, and grow slowly towards perfection.

To this I can add little but an amen, and my wish that all forms of low-tech games, not just pen and paper ones, will grow and spread. Wouldn't it be wonderful if more game designers took time to create good games that could be played almost anywhere with equipment that costs almost nothing? Not everyone can afford $75 for an Icehouse set or even $10 for a cheap Chess set, and even people who can may still need recreation and mental refreshment when they're stuck in some gameless dystopian nowhere.

In Other News

Speaking of gameless dystopian nowheres, consider the contemporary hospital. What if, instead of dripping cable television in with the morphine IV, hospitals offered their patients and visitors a variety of great games? Enter Games to the Rescue. We plan to give away a highly flexible game system and a book of rules for classic games to as many hospitals as possible, starting with the Seattle area. Please visit our web page and see if you want to help.

The present long-delayed Game Systems installment was originally intended to be about dice game systems, but I have been unable to obtain a couple of important systems:

  • Zap Dice look like a terrific, innovative game system, but I have not been sent a review copy although the designer has been promising me one for about two years. I'd buy a copy, but the fact that the company no longer responds to email isn't encouraging.
  • Dice Deck: No mysteries here; it's simply out of print and hard to find.

If you have information on how to obtain either of these, please let me know. I am willing to buy them, borrow them, or trade for them, within reason.

This just in: Rules of Play, by Katie Salen and Eric Zimmerman, is a new textbook on game design, meant for an academic setting. It not only includes a section on game systems, but also a suggested classroom exercise in which students design their own "open source" game systems. How many entirely new game systems do you suppose will suddenly emerge if this textbook is ever in wide use?

In other breaking news, the Rock Paper Scissors International World Championships are now sponsored by a major brand of Canadian beer. The 2003 competition was held on 25 October in Toronto. The new world champion is Rob Krueger, also of Toronto, who beat competitors from Canada, the US, and the UK for a gold medal and a $5,000 prize. For more details, see this press release.

Stick around for further articles in this series. Besides an article on dice game systems, future pieces in the planning stage include the counterpart of this article, high-tech game systems (not Nintendo or Xbox - think Merlin, Simon, and pocket calculators); game systems and intellectual "property" issues; the Island of Misfit Game Systems; and a game systems roundup, in which I'll discuss miscellaneous games and game systems that came to my attention after I wrote about their categories (card game systems, board game systems, etc.).

Finally, if you would like to see a list of links I used while researching this article, including many fine games and websites that did not make it into the final draft, visit my low-tech game systems bookmarks.


Thanks to my wife and frequent collaborator Marty Hale-Evans for her developmental edit of this article, her playtesting, and her comments and criticism, especially her key insight that sticks, dirt, and stones are isomorphic to pen, paper, and coins. She hasn't had bylines for this series, but she contributes far more to the articles than most people understand.

Thanks also to Walter Joris for sending me his paper and for his correspondence. Thanks to Andrea Angiolino for his correspondence and his directing me to the errata for his book. Thanks to my game group Seattle Cosmic, especially Ava Jarvis, for helping me playtest the games in this article, and for their comments.

-Ron Hale-Evans