Pencil and paper games: Improving Tic Tac Toe

Among the most well-known pencil and paper abstract games are Tic-Tac-Toe, Gomoku, and Dots'n'Boxes. Another famous game that can be played with a pen is Connect4 (but many families have bought this game anyway). 

Many connection games can be also played with pencil and paper, like Hex, TwixT or Bridgit. Of course, there are other famous games in this genre like Hangman or Battleship but, as usual, we'll stick here with the abstract ones.

In this post let's check some examples that improve the playability of Tic Tac Toe, one of the simplest abstract games.

An interesting version is Ultimate Tic Tac Toe and is played on a 9x9 grid of nine 3x3 areas (like in a Sudoku board). Each player makes a move on one of the nine mini-boards. But the next player must play at the board relative to the previous opponent's move. For eg, when a player plays at the upper-left corner, the next player must play at the upper-left 3x3 board. When a player makes a 3 in-a-row that mini-board belongs to her. If a move goes to again to that finished 3x3 board, the player can choose whatever open board she prefers. Wins the player that makes a 3 in-a-row of mini-boards (play online here). A similar game is 1976's Tri-o Tri-x.

The next variant is SOS. In this game, played on a square grid of size 3x3 or larger, players can write an S or a O on an empty square. Every time a player makes a orthogonal or diagonal row with the S-O-S sequence, he crosses it with his color and scores one point. The player with highest score wins.

Another variant is 3D Tic Tac Toe, played on a stack of four 4x4 boards (a 3x3x3 version is a trivial win for the first player). So, a player wins by making a 4 in-a-row using orthogonal or diagonal lines in all three dimensions. This can be represented in a page by drawing a line of four 4x4 boards, where the leftmost board is the bottom, and the rightmost is the top. This game was published in 1947 as Qubic:

One variant designed by Trevor Truran in 1981 for Games and Puzzles #81 is Knights and Crosses:

Here's another pen and pencil game called Order and Chaos by Stephen Sniderman that appeared on GAMES #25:

[addendum] Another 3D Tic-Tac-Toe is 1969's Stop Dot, published by Mattel.

Here the game is played on five faces of a 3x3x2 cube, and the goal is to make a 5 in-a-row with five different colors (at least over two faces):

These are the rules: 

Pencil and paper games: Dots and Bugs

Pencil and paper games all share the property that each grid cell can only be used a very limited number of times (usually once or twice). Walter Joris is probably the game designer that most contributed to this genre with his 2002 book 100 Strategic Games for Pen and Paper. There's more recent Joris fun on his pinterest page.

Here are two pencil and paper games played in the Eastern bloc.

Dots. Played on a grid of any size - traditionally on a 39x32 grid typical of a squared copybook in Russia [wikipedia].

Each player draws a dot of his color on an empty intersection. If the player closes a chain of his own dots (including diagonal connections) and the interior includes at least one enemy dot, then the player connects his dots with lines. Those dots, including the inner area, are out of the game (let's say the player captures the area). The player scores one point per surrounded enemy dot. If the inner area does not have an enemy dot, then the player cannot capture that area. Also, if there are more than one option to close chains, the player must select just one of those to close.

When the board is full, the player with more points wins.

Usually, the game starts by playing a limited number of moves in a central area to prevent players moving initially in the borders (since those dots cannot be captured). A nice way to solve this problem would be to make a toroidal board, but at a probably high cost in clarity.

The wikipedia page mentions a variant that allows for knight-like connections, which encourages more offensive play. 

Another variant prevents a chain from scoring if it gets surrounded by a larger enemy chain.

An extra rule is the idea of Houses. A House is a chain that surrounds an area with only empty spaces. If the adversary moves there, and does not close a chain himself, then the House becomes a closed chain. This rule seems to open a cold phase at the endgame, when dots must be placed in the remaining intersections that penalize the players (getting the game closer to a no-pass Go).

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The second game is Клоподавка (Bug Supression) aka Virus War. Again, the game is played on a large grid. The players decide on a move budget (say N usually between 3 and 6) relative to the size of the grid.

Each player has a home base, each on opposite corners. On his turn, each player marks N squares on the grid. Markings can be on empty squares, or by shading a square marked by the adversary (let's call it a wall). A wall becomes unplayable. However, players can only mark or shade squares that have a connected path from their home bases. 

A player that cannot complete his move, loses the game.

In the following example (with N=6) Blue answered Red's early and over-extended attack by making four walls, cutting red walls from the rest of their army. Now, if Red wants to reconnect, he must spend four markings to get to his three walls.

play this game here

Virus is a very underrated game, I find it quite fun to play and surprisingly tactical. Perhaps the game is too decisive, being hard to counter an early advantage, but who knows what good players could make of it?

Games and their times

All classifications are arbitrary, but some are more useful than others (to paraphrase George Box).

When thinking about the origins of abstract games, I visualize three broad categories:

• Ancient/Traditional Games. These are games within the culture of a particular people or region. Their exact origins are often unknown; we only estimate their age by their first written references. These games usually lack a fixed rule set (if any), having several regional variations. It is often more accurate to think of them as families of related variants rather than single, fixed games.
• Old Games. These appeared after the commercialization of play. They were either published or patented by their creators. While variants of these games may exist, they generally arise due to the game's popularity and how players engage with their core ludemes.
• Modern Games. Most abstract games published online today fall into this category. Although their creators retain authorship, many have relinquished commercial rights, effectively placing these games in the public commons. Much like open-source software, they embody the spirit of freedom and collaboration that characterized the early internet. 
  

These categories are, of course, not rigid. There are still modern commercial abstract games (e.g., the GIPF project) and older games that were always intended to be public (e.g., Laska). However, I find these distinctions useful for understanding games in their historical context.

Even though the boundaries between these categories are not perfectly defined, it is possible to identify their temporal limits.

The era of old games began around the mid-19th century, when commercialization led to the emergence of the first game publishers. This period also saw the introduction of the patent system, which allowed some types of game rules and physical board designs to be removed from the public commons and be privately owned.

In my opinion, the era of modern games began with the rise of the video games industry, a transformation that took place between 1980 and 1990. This shift is particularly evident in board game magazines such as GAMES and Jeux et Stratégie, as well as in the game's sections of popular science magazines like Science et Vie. During this period, columns devoted to computer games gradually occupied more and more space. One consequence of this shift was the decline — and, in some cases, the disappearance — of these magazines in their original formats, as they struggled to compete with publications specialized in video games and software. Another outcome, in my view, was a decrease in the commercial value of abstract games. This reduced the pressures of commercialization and, coupled with the advent of the internet, opened the era of modern abstract games that continue to this day.

Most abstract game designers align with the era in which they live. Designers from the old era typically created commercial games — for example, Alex Randolph, Sid Sackson, Eric Solomon, and Robert Abbott. Meanwhile, modern designers tend to create games for the public domain, with early examples including Christian Freeling, Wayne Schmittberger, Fred Horn, and Ralph Betza.

However, there are exceptions. Some designers from the old era (approximately 1850–1980) adopted a modern, non-commercial approach to game design. Notable examples include V.R. Parton, Joseph Boyer, Martin Gardner, Sid Sackson (again!), and George Dekle. Conversely, some modern designers still produce commercial abstract games. Perhaps the most famous are Reiner Knizia and Kris Burm.

The commercialization of abstract games appears to be on the decline, even as the global board game market continues to thrive, with its popularity steadily increasing over the past twenty, thirty years. But every category remains alive today. Interestingly, traditional games still appear to be the strongest link. Cultural traditions are very resilient to change, with few dependencies that could threaten their continuity. It seems unlikely that Chess, Go, or Backgammon will lose their public in the medium, long term. In a way, this reflects the Lindy effect at work, with the longevity of traditional games correlating with their cultural significance and resiliency.

In contrast, commercial abstract games appear to be losing relevance, especially when compared to highly competitive industries like video games and social media. And modern games are deeply dependent on the free flow of communication — a privilege we must not take for granted in the decades to come.

Catch

Catch is a 1995 game by Reiner Knizia, published in Spielbox magazine.

The game is played on an 8x8 board, initially empty.

Each player has twenty pieces, and there are twenty domino-like tiles shared by both players.

Rules:

• One player drops tiles vertically, and other player drops tiles horizontally
• On his turn, the player drops one tile on two empty squares
• For any enclosed area (either by tiles and/or board edges) with less than four squares, the player drops one friendly piece on each one of those squares
• When there is no valid moves left, the game ends. Wins the player with more friendly stones

The next board shows a final position where the game ended in a 13-13 draw.

This is a pencil & paper game. There's no need for a board to enjoy this game.

I would suggest using an odd-size square board, like 9x9. These boards have an odd number of squares. Since any group of tiles only removes an even number of squares, the remaining pieces will amount to an odd number, making draws impossible.

Take it Away

Take it Away is a 1969 game by Sid Sackson, published at Dover.

It is played on a 8x8 board with 34 white, 20 red and 10 blue stones (for a total of 64 stones).

• The game begins by players randomly placing every stone on the board, one per square.
• The first player starts by removing a white (which he keeps)
• On each remaining turn, the current player must pick one stone on the board and execute with it a sequence of checker-like jumps (orthogonal and/or diagonal). The sequence cannot stop while there are jumps to be made. Every jumped stone is captured.
• When there are no more jumps available, the player with highest score wins the game.
• blue stones value three points, red stones two points, and white stones one point
• There is an optional way to end the game: any player at any time can say "Take it Away" meaning he removes himself from playing. The other player continues making jumps while possible. When he ends, the remaining stones on the board will count as negative points for the last player (which the rules call the patsy).
  

The 'take it away' rule is what makes this game interesting. It is an auction-like rule that adds a very nice tension to the game. The rules especially shines if the game is played with three or four players.

The game appeared in Sackson's book A Gamut of Games.

Here's its description on Jeux et Strategie #45, where it was called Butin (booty):

Nevo

Nevo, aka 2-5-8, is a 1979 game by Michael Vonderheid, published by ArtDeco Games.

The game is played in a 7x12 grid, and each player has twelve pieces. 

The initial setup,

The rules:

• On her turn, the player moves one friendly piece to an adjacent (orthogonal or diagonal) empty space.
• Any piece that becomes isolated, i.e., not adjacent to another friendly piece, is removed from the board.
• Pieces that move to the adversary area score points. In the first enemy row, the player gets two points; in the second row, five points; and in the last row, eight points.
• for a piece to score the previous rows in its column (in the adversary area) must be occupied by friendly pieces, 
• for each one of these columns, only the furthest piece scores (eg, three pieces in the same column only score eight points)
• The player that first achieves a position worth sixteen points wins the game, but with three different pieces (so, two pieces scoring eight points each is not enough).
  

Some notes:

• Since isolated pieces are removed, it means that a piece movement must be thought in tandem with the group it belongs
• The original rules state that it is a decision of the adversary to remove these isolated pieces. I'm not sure if there is any board position where it would be advisable to keep these enemy pieces on board.
• If a column (in the adversary area) is not entirely occupied, the more advanced pieces don't score points
  
• Notice that there are no jumps or captures. This is a race and blocking game.

Here are the original rules:

Perhaps it's not needed, but since pieces can move backwards, there should be a rule about repeating positions. A Ko-like rule would not be easy to implement. It could result in a draw after three repetitions, just like in Chess, or end with a win for the player with the current highest score.

 

The game had a brief review on Jeux et Strategie #2:

And an even briefer mention in GAMES magazine #20,

 

 

Oh, and here's Omar Sharif, well-known actor and less-known game tutor: