Set Quarto

This game plays the same as the commercially-available game Quarto, except that you can do it with SET® cards. This fact was discovered by Greg Morrison.

Uwe Wilhelm brought the game to our attention after he found a posting in rec.games.board, or maybe rec.games.abstract. Not owning Quarto ourselves, we've paraphrased that posting's description for SET® cards, plagiarizing liberally at times.

Requirements

Part of a deck of SET® cards. In particular, choose all the cards that have only two of the three values of each property. E.g., remove all cards with threes, opens, purples, or diamonds. You'll be left with 16 cards, which is the deck for this game.

Setup

Lay out 16 of the unused cards face down in a 4x4 grid. These cards are merely placeholders marking the playing surface. Lay out the 16 cards in the deck face up.

How To Play

Players take turns placing one card each on one of these 16 spaces. The twist is that a player has to place the card that his opponent gives him.

The game begins when one player gives a card of his choice to the other. The second player places that card anywhere on the board, then chooses another card to give to the first player. The first player places that card, chooses another to give to the second player, and so on.

How To Win

The goal is to place four cards, all with a common attribute, either in a line of four or together forming a 2x2 square anywhere on the board. (NOTE: I think I recall that the Quarto rules call only for having 4 cards in a line; the 2x2-square version is mentioned as an alternative.)

It is possible for a game to end in a draw, at least in the simple, line-of-4-only version. It happened to us, once, like this. We don't know if it's possible to end in a draw using the 2x2-square variant, or any of the variants below.

Comments

The difficulty in the game lies in the fact that there are so many attributes to keep track of that it makes your head spin. The game ends up having two part turns -- deciding where to play the card given to you, then deciding what piece to give to your opponent. The game is short but it requires a lot of concentration.

Variants, part 1

It can be interesting to play with different rules for what combinations of four positions are "wins" (i.e., different than the usual rows, columns, diagonals, and 2x2 squares). On the regular 4x4 grid here are some possibilities for additional "wins" to use:

Other squares: Use the corners of any other squares you can find, besides the 2x2 ones. (Unless I'm miscounting), there are six 3x3 squares, one 4x4 square, four 1x1 "slanty" squares, and two "knight's move" squares. Here are examples of each of these types of squares:
```
- X - X    X - - X    - X - -    - X - -
- - - -    - - - -    X - X -    - - - X
- X - X    - - - -    - X - -    X - - -
- - - -    X - - X    - - - -    - - X -
```
Wraparound diagonals: There are six of these in all. Three of them are shown here; the other three are mirror images of these.
```
- X - -    - - X -    - - - X
- - X -    - - - X    X - - -
- - - X    X - - -    - X - -
X - - -    - X - -    - - X -
```
Wraparound 2x2 squares: There are seven of these in all. Three of them are shown here. Three others are similar. The seventh is the one with X's in the four corners, which is mentioned in a different guise above under "Other squares".
```
X X - -   - X X -   X - - X
- - - -   - - - -   X - - X
- - - -   - - - -   - - - -
X X - -   - X X -   - - - -
```

Another possibility is to try entirely different topological arrangements for the playing surface, instead of the standard 4x4 grid. This can lead to some very different relationships between the available positions. One arrangement that we have tried is the "starburst" pattern:

                       |
                   \   |   /
                     \   /
                 -  -     -  -
                     /   \
                   /   |   \
                       |

With this arrangement we used the following "winning positions". It is relatively easy to see others that might be used.

Rows - four cards in a row (4 total)
Inner half-circles - four consecutive cards in an arc of the inner ring (8 total)
Outer half-circles - same, except outer ring (8 total)
Wedges - two adjacent "half-rows" (8 total)

Variants, part 1

A completely different type of variant was suggested by Chris Jachimowicz: Instead of using cards to mark the territory of the board, allow the placement of the cards to dictate it. So the first card played might become either a corner piece or an inside piece as dictated by the placement of the following cards. Likewise, until more cards are placed, you won't be sure that the first card played is an outside row/column, or an inside piece.

mag and judd