Abstract Games are very curious mathematical objects. They tend to be are deprived of any significant cultural context to present what – in principle – really matters to another curious thing called a game player. This act of cultural removal is rather subjective, but anybody can sense it, when we see several people around the world play the same game and enjoying it the same way. Many games, like Go or Chess are played on several dozens countries at this very moment. Not even conjectural prohibitions based on Religion, Law or by political reasons, manage to destroy the memory of the rules that define those persistent and rather illusionary things…
Here in, an abstract game is: (a) A game for 2 players; (b) with no luck element and no hidden information; (c) where each game turn (except perhaps the first and the last one) consists of a move by the 1st player and another by the 2nd player; and (d) the set of rules agreed by both players do not leave any space to ambiguity.
This, in a way, restricts the field of study, but leaves an endless Ocean of possibilities and magical wonders! We can say, with no hesitation, that Humanity only scratched the surface of such great Sea of Games. Herein, the goal is to present a set of conceptual tools for those who like to design and test new abstract games, to inform people how to avoid common errors and pitfalls and so, in conclusion, to create better games.
There are two concepts that I find most relevant! The first one is Depth, or strategic complexity, meaning the capability of a certain game to have a certain number of degrees of skillfulness. The exact number of different skills is never exactly known, even because no one reached an precise definition of what is a degree of skill. A possible way is to say that a player is one skill above the another if he wins 2 out of 3 games. Even saying that, skill levels of different players are not disjoint, since the concept is not transitive. Different ways of playing work better on certain players than others. Just like Soccer! The more skill levels a game has the better, it means that a person can continuously learn about the game for a long time (even more than a single life or an entire civilization). A deep game also gives the players more chances to recover from crises (i.e., bad moves), or stating differently, if a player on a relatively bad position is replaced by a better player, this one may still be able to balance the game.
The other condition is Clarity. Clarity means that most board positions should be as close as possible to the way the Human mind sees things. This concept will surely be very different for a Martian, but since no ET was found yet, let’s stick to this human-centered vision. Tic-Tac-Toe and Hex are exceptionally clear. There is not, however, a direct correlation between clarity and the description of the rule set. Some simple games to describe tend to mess a lot when an actual game is played, but a difficult game to describe will possibly have some clarity problems as well. For instance, many Chess Variant designers find on clarity a merciless judge. People are used to the way a Knight moves, but some similar fairy pieces (with the same right to existence as any other) create a problem of lack of clarity that prevents players to be interested on such opaque game.
The joint combination of this two features give a glimpse on the quality of the game. Tic Tac Toe suffers due to limited strategic possibilities, Go scores highly but is penalized by subtle rules, Hex scores very highly (I dare to say that 19x19 Hex would approach Go in depth, while retaining a much better clarity). A computational approach of this subject would say that given a game tree with N nodes, complexity would be the total nodes required to formulate sensible strategies, and clarity would be the ability to search deeply inside the game tree in order to achieve them.
Well, but this are just general concerns that you should have in mind. What about the real and objective game´s ruleset? The next section will talk about some basic game mutators. That is, modular concepts that can be applied to almost any game, creating new games (not necessarily better ones).
Basic Mutators
As we all found by experience, there are many good ideas out there hidden on obscure games. The next list is not intended to be complete, but it tries to dissect as many basic concepts as possible, in order to provoke people to mix them in some strange, new and hopefully also in skillful ways.
Let’s state some extra principles to those already stated on the initial Abstract Game definition. The game may have a board, consisting of cells linked together in some specific ways (a square tiling, an hexagonal tiling, a rhombus, …). Each player has, at least, one set of stones of a certain color (let’s say, black stones for the first player, white stones for the second), where the possible playing options are stated by the rules defining the game.
Each mutator must be seen as a rule, or part of a rule, that needs some preconditions before execution (i.e., may only works on certain game states/positions), and may create, when executed, events that enables other mutators to work (even on the same player´s turn). On the following list, some mutators have glimpses of possible preconditions and events.
Pass A player does not affect the game state. It is the null mutator.
Drop This is, probably, the most applied rule on abstract games. A piece may be dropped into a certain board cell. The drop restrictions can be various. The most common is that the cell must be empty. Other options would restrict it to a certain area (e.g., must enter into the players initial zone), on local conditions (e.g., must be near a friendly stone), or global ones (e.g., the board must not have more than x stones).
Move The move mutator is also very widely used. A stone already on the board, can move from a cell A to a cell B. This movement may be subject to certain restrictions, like intrinsic ones (e.g., it can just move to an adjacent cell, to orthogonal/diagonal cells, …), contextual ones (e.g., it can move to an empty cell, a cell not attacked by the opponent, only moves if it has x adjacent friends, …), or global ones (e.g., the total number of stones define how each stone can move).
Capture A set of stones, either friendly and/or unfriendly, are removed from the board and those cells become empty. This usually is an action caused by the execution of another mutator (most cases, this is a consequence of moving). Capturing can be a consequence of a certain pattern, like custodian capture (like Hasami Shogi), simple jumping (Checkers), cannon capturing (like in Xiang-Qi), bombing (all adjacent enemy stones are captured). Capturing may provoke several lateral effects, like Suicide (the captured piece is destroyed like in The Way of Go), or Protean capturing (the piece inherits the captured stones abilities, like in Cannibal Chess).
Jump A jump is simply using another stone to move to another cell not in range otherwise. This not include the Chess Knight, since it does not need another stone or piece to make its move.
Merge Two or more stones occupying the same cell are transformed into a different piece. Bashke, Laska and Focus use this concept in the Checkers game world.
Pivot The pivot mutator is a generalization of the Jump mutator. Usually a jump uses the intermediate stone as the pivot to move on a straight line. General pivot moves have much more liberty. Other kinds of pivot moving are scaling (check Scalus for use of that concept), and rotation (check Kefren or Twirls of Action) also known as Twirls, named by Claude Chaunier. These are just two possible ways to explore Pivot moves.
Swap A stone (the swapper) can swap position with another stone (the swapped). Possibly, the swapper will be on moving range from the swapped.
Shift Shift also means push a set of stones into a specific direction (e.g., check Epaminondas or Abalone). This shifting may produce other events, like single or group capturing.
Pile Piling inserts an extra dimension to bidimensional boards. There are several ways to pile, namely Staking (the new stone is placed on the top) and Queuing (is placed on the bottom).
This may provoke a change event, meaning that the new stone merged the piled piece. This also implies possibly a splitting mechanism.
Change This means changing the stone status. After the application of such mutator, a stone acts and reacts differently to the same conditions. Some examples include: stone promotion (increase its power) and demotion (decrease it), freezing (cannot move), stoning (cannot move or be captured), make royal/unroyal, …
Local Interactions After a move is done, the actual cell interacts it some local neighbors (the adjacent stones, the nearest orthogonal neighbors, …) and affects them. For instance, there are gravity forces (attracts all by one or more cells), and magnetic forces (attracts opposite color, repels equal ones). Some games where this is applied are Magnetic Go and Magnetic Chess.
Momentum A momentum mutator creates multi move games. It works like this: A previous moved stone will repeat its behavior on the following turns while it’s valid. Until now, from our knowledge, this was only used on Chess Variants.
Progressive This mutator affects the way turns are defined. The typical progressive mutator adds an extra movement for each player’s new move (one move for Black, two for White, three for Black, …). Other progressions are possible, softer ones (1, 2, 2, 3, 3, 4, 4, …) and wilder ones (1, 3, 5, 7, …). This obviously reduces the game length, and for some games it is a nice way to play a fast variant (give it a try with 9x9 Go). The set of movements could be sequential or simultaneous, it depends on the context where it is applied.
Save It’s a kind of active passing. The player gives the turn to the other player, but it saves the move for later use, i.e., next turn it can move twice in a row. This is a very strong mutator, and should be used with extra restrictions, in order to keep the game interest.
The produced events can activate more than one mutator. For example, a multiple move/capture is an application of a certain capture mutator within itself.
Improving the Spark
There is no magical formula for making an abstract game with depth and clarity. That implies a little of luck, insight or something else that creates the ‘spark’. I will speak of the something else, and also about the fact that the spark, if not treated right, may be lost, transformed into a poor game that lacked the basic care of any newborn.
Let’s start on the initial setup. First, the game designer should decide what shape will define the board and if it begins empty or not, if there is still the possibility to drop stones afterwards. A related point is to decide the total number of stones. A good rule is to see how stones are capable of moving (if they move at all). Board density (i.e., the average number of stones per cell) is relevant on this decision. A game with moving stones and growing density may face ‘traffic’ problems on the endgames. Usually if stone mobility is high, then density should be low, and vice versa.
If the designer chooses an initial setup, he must see if that setup does not go through another global pattern before the game really begins (i.e., both players found that to attack or defend, they should position their stones into a certain tactical pattern). In those cases, the designer should change the initial setup to that intermediate one. It will speed the initial phase, without decreasing its depth (this of course, may be risky, if the designer or the game testers are not able to see other potential good openings, on those cases, the game depth will suffer).
The number of moves of a typical game is an essential thing to note. Very short games are not very interesting, except for children, very long games take much time to be played and tend to be rather tedious. Perhaps if Go was presented today, it would suffer from this fate, many people would not be interested because it takes too long to finish a game, and they would miss its remarkable depth. Ralf Gering marks 20 turns (i.e., 20 moves for each player) has a minimal mark for a average game score, in order to have some interest. Of course, this also depends on the number of moving options, but too many options reduce clarity! This is a tight business! For maximal turns, an original game that takes more than 100–120 turns will need a good marketing!
An important subject is to avoid mirror tactics. This happens when one player can mimic the other, in order to achieve a draw (like in Halma) or even victory (like in Hip on even square boards). This can be done by using odd boards (that is with a center cell, usually called Tengen), allowing captures, or asymmetrical positions (i.e., that after a certain move, the other player cannot mimic it).
Two more things about the initial phase, Handicaps and Equalizers. Handicaps are always a good way for two players with different skills still manage to get some fun paying (ups, I mean playing) the game. This is done by creating a better position for the weaker player, by giving him some extra moves, extra material or easier winning goals.
Equalizing means to balance first (or even second) player’s advantage. This can be done, using an Handicap system; or by using the N-move equalizer: After N moves, the player on disadvantage may choose which side to play. When N is 2, this rule is also known has the PIE rule (i.e., you cut, I choose). There are other ways, like giving two moves per player, except for the first game move, but these are less general and may not work everywhere.
Besides the beginning, there is also the end! How the game should stop? What will be the winning goal? There are several classical concepts:
1. Territorial – wins the player with more controlled cells
2. Pattern – wins the player that first achieves a certain pattern of stones or cells: n-in-a-row, n-in-a-group, n-enclosed
3. Connecting – link two or more edges, link two or more special cells, link all friendly stones
4. Capturing – capture x enemy stones, capture some key stones (i.e., royal stones)
5. Reaching – reach a set of key cells, surround a certain stone or cell area
The designer should take special attention on one thing. On a typical endgame, the winning player has enough power to win? Is he able to decide the final outcome of the game? In Chess, we know that King + Bishop vs. King is a draw. If almost all Chess games would end on this position, then another winning rule would be needed (e.g., the Bare King rule – a player looses all other pieces are captured).
After the rule set is defined, the designer should look into each single rule and ask some questions: Is this rule necessary? Why is it so? Is it a logical consequence of some other rule(s)? If so, it should be placed on the notes section, not among the rules! Does the rule interacts with the other rules to create some more tactical possibilities? Or is it totally independent? If so, and if the rule decreases clarity without giving some to the game as an whole, then the designer should rethink about keeping the rule.
Combinatorial Game Theory talks about game temperature. A hot game state is one where the player has the advantage to move. Otherwise a cold game is one where the player does not want to move (in that sense, a game with a pass rule is never cold, since players may pass their turns). Some samples: Hex is hot and gets hotter. An extra move never hurts the player and usually puts them in a winning position, more so towards the end of the game. Go starts medium hot then cools down to lukewarm. Towards the end of the game moves become less effective until they are not worth making. Gonnect starts hot then suddenly turns freezing cold at the end. An extra move is good during the early and middle games, but can become a game-loser in the endgame. This does not give the designer a way to determine a level of quality, but can give him insights about how his own game reacts from the opening until the endgame.
Final Words
A really nice thought is to imagine that maybe some games invented in this century will be played in the year 3002 (perhaps one of your own games), where Hollywood, Microsoft, Intel, the Computer Game Industry, and so many other powerful businesses would already entered into oblivion…
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