What are Pentominoes?

A pentomino is a set of 5 contiguous squares in a grid. If reflections and rotations of a pentomino are considered equivalent, (as they are in this game,) there are 12 distinct pentominoes. For reference, here they are:

Pauli: a Game of Colorful Pentominoes

by Alexandre Muñiz, last modified August 2001

Pauli is a game for two players based on some explorations involving polyominoes that I made in 1999 and 2000. It is, to use some funky jargon, a game of panchromatic pentomino achievement.

Equipment:

You will need the following equipment to play Pauli:

Board:
A chessboard or other square 8 by 8 board.

Pieces (30):
Five sets of 6 pieces are required. Each set contains pieces of a different color. If you make your own pieces, I recommend blue, green, yellow, orange, and red as colors. The pieces should have a design that clearly points in a single direction. During the game, pieces will be placed pointing away from their owners to indicate their ownership.

Icehouse pieces, (available from Looney Labs,) work reasonably well; however, since orange pieces aren't available currently, you should replace yellow and orange above with clear and yellow respectively. (This does require the Black Ice expansion set.) Also, since the Icehouse set only contains 5 pieces of every color/size combination, you will have to use pieces of more than one size.

Pentomino Cards (12):
Each card depicts a different pentomino from the set of 12 shown in the "What are Pentominoes" section. On one side it should be grey to indicate that the pentomino is passive; on the other side the same pentomino should be a bright color to indicate that it is active. At the beginning of the game, the cards should be placed to the side of the board, passive side up and spread out so that all are visible. As the game progresses, cards may be given to one player or the other. When this occurs, these cards should be placed in front of the owner, next to his or her stash.

Objective:

You win the game by controlling 7 or more cards at the end of any player's turn. (You receive these cards by making panchromatic matches of pentominoes, as described below.) You can also immediately lose the game if you have no legal moves on your turn, or if you have no unplayed game pieces remaining in your stash when you are expected to play one.

Matching Pentominoes:

A set of pieces on the board is a panchromatic match of a pentomino if the squares they occupy form a copy of that pentomino, and exactly one piece of each color is present in that copy. Different matches may overlap. The player who owns the majority of the pieces within a match controls that match, and receives the corresponding pentomino card.

Starting the Game:

Determine which player has the lower body temperature. That player is known as Cool, and the other player is known as Hot. The two players receive the following pieces:

Cool: 5 blue, 4 green, 3 yellow, 2 orange, and 1 red.
Hot: 1 blue, 2 green, 3 yellow, 4 orange, and 5 red.

At the beginning of the game, the pieces are placed off of the board in front of their owners. The set of pieces off the board that a player owns is called that player's stash.

Players alternate turns, starting with Cool.

Recognising Matches
Recognising matches may require some practice, but it is a necessary part of learning to play Pauli well. While you are still learning the game, take as much time as necessary after each move to ensure that both players are satisfied that they see what new matches were formed. Here are some puzzles and solitaire activities which may help you recognise matches better:

Put out a bunch of pieces on the board at random, and look for matches.
Make as many matches as possible inside a 4 by 4 square.
Make a figure which contains exactly one match for each pentomino. Try to do it using as few pieces as possible.

The Steps of a Turn:

On your turn, perform the following steps:

Step 1: Play a Piece
Place a piece from your stash pointing away from you onto an unoccupied square on the chessboard, subject to the rules in the Exclusion Principle section, below. If it is impossible to place a piece, either because your stash is empty, or because there is no legal placement possible, the game ends, and your opponent wins.
The Exclusion Principle:
Wolfgang Pauli's Exclusion Principle states that no two electrons in an atom may share the same quantum state. Our Exclusion Principle is this: only one panchromatic match may exist on the board for each pentomino. The following rules serve to enforce this principle:
1. If no one has an active card for a given pentomino, you cannot make a move which would make two or more matches of that pentomino simultaneously.
2. If your opponent controls an active pentomino card, you cannot make a move that makes a second match for the same card.
3. You can make a move that makes a second match of an active pentomino card you already control, but this causes an "explosion" resulting in the new match being removed from the board. (see the next step).
Step 2: Resolve Explosions
If you control an active pentomino card and you make a move that forms a second match of that card, all of the pieces in the new match are immediately returned to their owners' stashes. This is called an explosion. It is possible for a move to create multiple explosions. If this occurs, the pieces from all explosions are returned simultaneously.
If any matches on the board were destroyed by removing pieces, turn the corresponding pentomino card(s) passive side up. These cards are still considered to be controlled by the same player as before.
Step 3: Check for New Matches
If there are any new matches on the board, (see the Matching Pentominoes section above,) the corresponding card is given, active side up, to the player who owns the majority of the pices in the match. (This may not be you, even if you completed the match.)
Note: if a match is formed but immediately destroyed in steps 1 and 2, the corresponding card remains where it was at the start of the turn.
Step 4: Check for a Winner
If either player has at least 7 cards, regardless of whether the cards are active or passive, the game immediately ends, and that player wins.

Optional Rules:

Adjusting the Balance Between Players:

Although the game hasn't been tested enough to prove it, I suspect that the first player has a very real advantage. Here's a rule that should balance things out:

Before starting the game, one player picks any card or combination of cards. The other player must then decide whether to be Cool and take the first turn, or be Hot and receive these cards, passive side up.

Likewise, in order to play a game at a handicap, the better player can offer cards and the first turn to the weaker.

Shorter Games:

For a shorter game, make the winning condition 5 or 6 cards instead of 7. Since it is possible for both player to achieve the goal simultaneously, the winning condition should be rephrased as "If a player has at least n cards, and has more cards than his or her opponent, he or she wins the game."

Note that what little playtesting this game has received was done with a 6 card goal, (although cards were not used at the time.) My instinct is that playing to 7 cards should work just as well, and as it allows the rules to be simpler by one phrase, I'm going with it. However, if further playtesting shows the game tending to stagnate with neither player getting the 7th match, I can change it back.

Strategy:

Clumping Pieces vs. Scattering:

Be careful about clumping your pieces together, because if your opponent causes an explosion that includes them, you will be at a material disadvantage in terms of pieces on the board. Where your pieces are well mixed with your opponent's you can take advantage of your opponent's pieces in creating matches that you own, but your opponent can do the same thing to you. However, careful choice of colors can make it so that you can use some of your opponent's pieces without your opponent being able to use yours.

Color Considerations:

The distribution of the colors of pieces is an important factor when considering a move. If you run out of a color, your options become more limited. For colors you have few pieces of, you should try to make use of your opponent's pieces on the board of that color. Likewise, you should hoard your own pieces where your opponent is low on or out of a color, and use them only where your opponent cannot easily borrow them. The middle colors are therefore often the safest, but still, where it is necessary to use the other colors to form matches, go for it! Also, when planning explosions, try to get your own pieces of colors you are out of back.

Easy vs. Hard Pentominoes:

Some pentominoes are easier to form than others. "Easy" pentominoes are useful offensively when active, as it will be easier to form the second copy that causes an explosion. However, once the match is destroyed and the card is passive, "hard" pentominoes are prefered, because it will be harder for one's opponent to form a new copy of the same pentomino and steal the card.

History:

The initial idea for this game occured to me some time in the early spring of 2000. Although I did not originally consider it an Icehouse game, realising that it could be played with Icehouse pieces gave me the impetus to work on it until I had a complete set of rules, which I posted to the Icehouse mailing list on May 6, 2000. The initial name of the game was Wolf Gangs, which was a pretty obscure pun. The name Pentominice was suggested instead, and I didn't complain. This version of the game had a stagnation problem: since there was no concept of a passive pentomino in it, the board could repeatedly be cleared by explosions without any progress toward the end of the game occuring.

The night before I went to Columbus for Origins 2001, I made a board with depictions of the pentominoes on it, and on the plane ride to Columbus I worked on a different pentomino game using icehouse pieces, which turned out to be hideously complex and unplayable. I was bummed out that I would have no playable game to show off the board with, but then I got the idea for passive pentominoes, which fixed the stagnation problem of the original game.

Since then the only substantive change to the rules has been to increase the winning condition by one pentomino. Replacing the board with cards is a cosmetic change, but one which I think will make it easier to keep track of matches. Finally, the game now has a new name. Pauli is a nice short cryptic name of the sort that is popular with abstract games, and which immediately suggests the exclusion principle. And since it doesn't have "Ice" or "Martian" in the name, one can, in theory, play it without Icehouse pieces without feeling like one is doing something wrong.

Acknowledgements:

Thanks to Liam Bryan for being my first playtest guinea pig, Ryan McGuire for inspiring the card idea, and Alison Frane for being confused by my confusing original writeup of the rules, and giving me some direction in attempting to make the rules clearer. Thanks bunches to Kevin Wilson, who gave me a lot of great suggestions for editing this page. If the rules are still confusing, it is nobody's fault but my own, but if they are confusing enough, you can tell me how and see your own name here.

Also deserving of recognition are Andrew Looney, John Cooper, and everyone else who made little pyramids such a fun thing to play with, Samuel Golomb, Martin Gardner, and everyone else who made pentominoes such a fun thing to play with, and, of course, Wolfgang Pauli, without whom this game would be called something else.

My theme song while writing this page has been "Puzzle" by Vivian's Keeper. While it is true that the Music from the Edge of Heaven album by Wham! has a Hot Side and a Cool Side, I refuse to admit that this had any influence in the terminology used in this game.

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