I read this: New Rules for Classic Games

New Rules for Classic Games, by R. Wayne Schmittberger, written in 1992, is exactly what it sounds like. "New Rules" contains possible amendments to rules for Risk, Monopoly, Poker, Bridge, Scrabble, Reversi/Othello*, Shogi, Go, and of course Chess.

Some assembly required, rules not included

In order to include as many variants as possible, often only the rules amendment and its justification are included. If you are unfamiliar with a particular game, I would recommend having either a copy of Hoyle's Book of Games, or Wikipedia available to consult. For example, a means to make Bridge a six-player game is included, but not the actual rules of Bridge, leaving someone unfamiliar with the orthodox game in the dark. A few of the more obscure games, as well as ones like Go that are played mostly in southeast Asia, are given cursory explanations.

Among the few completely described games in "New Rules" is Eleusis, which is a deduction game for four or more players, and played with two or more standard decks of cards. It's a rule-discovery game like Zendo. A similar one that is described fully is Haggle, a party game where 8 or more players are each given a starting set of playing cards, as well as 1 unique rule or hint about the relative value of the cards. (Each player is given a different rule about scoring. All the rules apply to all the players and it's each player's responsibility to negotiate for information about the other rules from other players)

Speaking of reference material, "New Rules" mentions several similar books that also warrant investigation, including "Discovering Old Board Games", "Winning Ways for Your Mathematical Plays", "A Gamut of Games", and "The Oxford Companion to Chess".

General principles of variants.

The first few chapters cover general principles that can be applied to many games, including a few ways to fairly balance two-player games with first-player advantages. Two methods get most of the coverage here: 

1) The bidding method, in which players bid for the right to go first with some resource or unit that's easily division within a game, such as points in Scrabble, or life in Magic: The Gathering.

2) The pie-cutting method, in which one player decides what the additional advantage (or disadvantage) for playing second will be, and the other player decides whether to go first or second based on this.

Both methods allow players to find a compromise that both will agree upon.

There is also a chapter on limitations of variations based on their emergent properties. These include the "petty diplomacy" problem inherit to symmetrical three-player games. The problem is that weaker two players usually have an incentive to work together against a stronger third player, and that starting badly is often an effective strategy for winning in the end. The author explains this as the reason why three-player versions of chess always fail to get widespread adoption.

As a counterpoint, many commercial games since the book's publication in 1992 are playable by three people through "snowball" mechanics where, unchecked, a player that is ahead can rapidly increase their advantage. Having these mechanics allows a game to remain balanced even when players have means to directly interfere and hinder each other. Modern example include Munchkin, Talisman, Smallworld, and Cosmic Encounter.

Some Novel Chess Variants

Fairy chess had a lot a support in the early 20th century, with thousands of puzzles involving fairy pieces being published. One fairy piece, the grasshopper, which moves like a queen, but MUST jump over a piece to move, is covered in detail in "New Rules". The jumping requirement becomes more restrictive as the game progresses to the endgame, and the estimated value of the piece reduces from about 3 (a knight or bishop) to less than 1 (less than a pawn).

Many iterations of Grand Chess have been developed before, with published examples being given as early as 1617. These are played on a 10x10 or 12x12 board with some additional pieces like rook-knight combinations or knight-like pieces that jump different distances than the usual 2-and-1. 

Chess variants in which pieces have one-time special powers are collectively referred to as "exotic" variants. The book gives a few examples, but spends the most on one called "missile chess". In missile chess, each piece has the exotic power to capture a piece that it could capture normally, but without needing to move to that piece. (In some fairy variants, there are 'medusa' pieces that can do this all the time). The modern commercial game Knightmare Chess, with its single-use cards that grant the pieces or the player temporary powers, might be considered an exotic variant.

An older book that I previously reviewed, "Chess Variations: Antient, Modern, and Regional" had some variants in which the abilities of the pieces changed with their location on the board. Most commonly, there were areas that protected pieces inside them as well as a central movement hinderance like a river.

"New Rules" has some of these that were new to me. There is Sputnik chess, which grants pieces more power if they are on the opponent's half of the board. There is also parallel worlds chess, which is played with two sets of pieces on three boards. In parallel worlds chess, the middle board starts unoccupied, and pieces which move to that middle board (in lieu of their normal move) are granted invulnerability and much greater movement until their leave that board.

The author also includes a variation of their own: Extinction chess. The setup and movesets of the pieces are the same as orthodox chess / queen's chess, but the first player to lose all of any kind of piece loses the game. To balance this, pawns can also promote to an additional king, which makes the original king non-unique, and therefore able to be captured without losing the game.

There was also some coverage of variants of Shogi. Notable amongst these was Tai Shogi (Great Emperor Chess), a 25x25 game with 361 pieces and an emperor that could teleport-kill exists just to show that people have been letting complexity get out of hand for centuries. Tai Shogi was not described in detail, but the full rules for Chu Shogi (Middle Shogi) were given. Chu Shogi was played for centuries in Japan, and had a low-mobility, high-attack piece called a lion.

An oversight of stone-placing games?

There is substantial coverage of variants of Pente and Othello/Reversi, but no mention of ways to play these games with three or more players. From personal experimentation, both can games can be played with three or more provided that you have a full set of coloured glass stones for each player. These stones are available for cheap at craft stores, as well as pet stores with a fish section.

 In Pente, a capture occurs only in an ABBA configuration. For 3+ players, a third player can block a capture on Player B's behalf by forming a line of ABBC. A player who captures five pairs in total, regardless of from who, wins.

In 3+ Reversi, all opponents' stones get captured in a 'sandwich', regardless of the arrangement of the opposing pieces. So, if A place places a stone at

the end of ABBCCB,

it becomes ABBCCBA,

and then AAAAAAAA.

*Reversi and Othello are nearly, but not exactly the same game. The commercial version, Othello, has a slightly different starting state than the much older, public domain version, Reversi.

This review a continuation of an ongoing exploration from the reviews of
Chess Variants and Games for Intellectual Development and Amusement and

Chess Variants - Ancient, Regional and Modern

There's an endless library of games to explore!