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Many Rules in One Game

I was inspired by the thought of a game in which, for example, the rules of Cylindrical Chess might be valid on all the light squares, while on all the dark squares the rules of Alice Chess would be in effect; this seemed like a clever new idea which deserved more discussion because not only could you have different rule sets by geography, you could also have different ones by time, as in

List Chess -- Multiple Rules at Different Times

  1. A list of games is chosen by mutual agreement of the two players. For best results, there should be an odd number of games on the list, and the number of games should be less than one fourth of the expected number of turns in the game.
    A short and conservative list might be, for example, FIDE Chess, Nutty Knights versus the same army, and Clobberers (both sides use the Colorbound Clobberers).
  2. White chooses a game from the list; it will be the rules for his first move. Black chooses a set of rules that has not already been chosen. White makes a move and chooses one of the remaining rule sets. Repeat as needed.
  3. When each of the games has been used once, the players choose from games that have been chosen only once.
  4. There are two kinds of checkmate, pictorial and functional.
    Pictorial is when you are still in check at the end of your move, according to the current rules. It is checkmate, even if the rules change so that your King can't be captured.
    Functional checkmate is when you are not in check according to the current rules, but when the rules change the opponent will be able to capture your King.

Observations about List Chess

If there is just one game on the list, it is exactly as though you weren't playing List Chess at all. If there are two games on the list, the first player has a huge advantage. If there are three games on the list, the advantage of choosing first is evidently balanced -- on White's first move (when choosing the rule set for the second move) only one game is left to be chosen, and despite what Microsoft would have us believe, if you have only one choice you have no choice. If there are a thousand and one rule sets on the list, the first player has a marked advantage because the game will never last long enough to exhaust the list.

You can see more than one move ahead. However, the tactical complexity of seeing three ply when there are 64 rule sets to be chosen from is 249984 (64 times 63 times 62) times as large as the tactical complexity of FIDE Chess.

This game may be playable with a short and conservative list of rulesets.

By complete coincidence, I was going through some old stuff and found List Chess, which was mentioned in my NoST column in 1976 or 1977, and which makes such an excellent example here. It makes me want to design a game called Coincidence Chess, but I have no idea what the rules would be; and it shows that multiple rules may be a clever idea, but not a new one.

Metarules

The first three rules of List Chess are the specific rules that make this game fair and playable. The fourth rule is a meta rule, a rule that defines how to handle the transition from one rule set to the next, as they change at different times.

If you have multiple rule sets on the same board at the same time, for example one game's rules apply to light squares and another to dark, the required metarule is this:

  1. Movement is determined by the rules of the origin square; this also determines whether a capture can be attempted on the destination square.
  2. The effect of an attempt to capture is determined by the rules of the destination square.
An additional metarule is implied: when the rules change from FIDE Chess to Shatranj, the piece that started the game on d1 changes from being a Queen to being a Ferz, and so on. Descartes might know how best to phrase this metarule, but I can only give an example.

Too Many Rules

Now that we have a metarule that covers having different rules in space and another that covers having different rules in time, it's possible to specify a game that goes beyond sanity:
  1. start with a list of about 300 million rule sets
  2. Each turn, each player assigns a different rule to each of the 262144 squares of a 64x64x64 3D chessboard, and makes a move (just like List Chess).
You can see that the game is properly and fully defined, it is a fair game (both players have an equal chance), and that is playable (not by mere humans of course) as well as interesting (to those who can play it).

A more humble example of a game with rules that vary both in space and in time is Piazza San Marco Chess.

Exceptions to the Metarules

Not all games fit into the pattern.

In general, if a game expands the board, its effects in the multirule context are undefined; for example, if the rules of Alice Chess apply this turn, perhaps you can move your King onto the Looking Glass board and there find safety? Is the second level of a 3D chessboard equivalent to the lookingglass board of Alice?

Another example of an interesting situation not covered by the metarules is Relay Chess. In general, the idea of relay is that a piece defended by a friendly piece gains the powers of the defender; but when the rules are different on g1 and e2, the Pawn on e2 that is defended by the Knight on g1 gains what power?

It is probably best not to include such rulesets in the game.

Compass Chess

So far, multiple rules on the same board seems less interesting than multiple pieces on the same square; however, the interesting results I got from examining crowded squares came from examining the less obvious possibilities of rules for crowds.

As an example of an unobvious rule for multiple rules in the same game, let's try Compass Chess: different rulesets apply in different directions. For example, if you are moving North, the rules of FIDE Chess apply, and if you are moving South, the rules of Clobberer Chess (clobberers versus clobberers) apply.

This game doesn't really work well as an example, or perhaps as a game. You need to choose 16 (north by northwest, and so on) different rule sets, and in the end the result is the same as if you had defined one rule set with specific moves allowed for each of the pieces. (However, specifying it as the 16 rule sets is probably easier.)

It's a bit confusing to think about. If you try to move your Knight-thing (the piece that started on g1) to the Northeast, you might be able to make a Fibnif or a Waffle move (depending on what game is chosen for that direction); if you try to move North, perhaps you can make a WD move. In other words, the pieces may gain greatly in value, or in some cases they may lose value.

When choosing the 16 rule sets, you'd have to be careful to make a fair game -- North is always North, and forwards for W is North but forwards for Black is South.

Influence Chess

Influence Chess is another unobvious use of multiple rule sets on the same board.

Each piece type (R, N, B, Q) comes from a different game, and behaves according to the rules of that game. In addition, all adjacent pieces also have the option of using the rules of that game. Kings and pawns can't be influenced. However, enemy pieces (other than K and P) can be influenced. Maybe relay is better than adjacent. There's a certain strangeness to using the power of a Queen to relay the ability to make a Knight move. In that case, the name of the game should perhaps be Legal Relay Chess.

Depending on which games you choose the rulesets from, this could be extremely intriguing.

Summary

I have exhausted my own brain, but doubt that I have exhausted the possibilities of different rules on the same board. Please feel free to demonstrate that I failed to find the best new idea.


Written by Ralph Betza.
WWW page created: May 7, 2001.