Case Studies in Chess Variants

Since my previous posts on variants, why they work, and why they don't, I've been hearing from some inventors and designers of variants. A variant has been implemented based on my an idea of mine. Here I develop and sometimes revise the ideas in older posts, while considering variants I missed in those older posts.

1) Four Player Chess 

In Four Player, the board is shaped like a huge plus sign. 

1.1.) Free For All

In the free for all variant, each player plays against all of the others. One must balance good chess moves with wise strategic decisions. Hastiness can lead to a quick death, and passivity can lead to a slow death. In standard chess, you expect self-interest from your opponent, and if your opponent does not play with self-interest, this helps you. But there are many scenarios in 4 player where one player not acting in their own self-interest can hurt other players. Everything is in flux in this variant. Although an alliance of sorts naturally arises between the players across from one another. If Red is mated, Green and Blue are in a natural place to pincer Yellow. It is therefore in Yellow's interests to keep Red alive.

If you get too far ahead in points, you invite the revenge of the other players--they can not only see your name and rating, but even without this and without communication, they can see that if they do not work together, they will place third and fourth, so in teaming up they may achieve second and third, or first and second place. 

The most interesting result here is that there is in principle no winning strategy. Whatever a player's strategy is, the other players can figure it out. Perhaps Red plays cautiously to avoid provoking the other players. Yellow, Green, and Blue can realize that this Red's strategy.

It seems to me that free for all games in general have a lot in common with Prisoner's Dilemma scenarios. In the Prisoner's Dilemma, two players are asked by an investigator to confess to a crime. They are not able to communicate to one another. They can cooperate, hoping that the other will also cooperate. Or they can betray one another, hoping that the other will not also betray them. The worst outcome for the individual is to be trusting and to be betrayed by the other player. The best outcome for the individual is to betray the other while not being betrayed oneself. But mutual betrayal leads to a worse outcome for both players than mutual trust and co-operation. 

The values of the numbers players receive for each decision is part of the game's design, of course. And also, so is the absence of communication between the players. These numbers and assumptions are not immutable. 

It's easy to imagine a scenario where two players benefit by mutual cooperation, but fail if one or both of them opts for betrayal or defection. But perhaps the similarity ends there. In Four Player, there is no God-like prosecutor, but all participants are playing for points.

In this example, Yellow can capture the highlighted pawn, since the Red Queen pins the pawn that would recapture. Red could in principle take the other pawn, putting the Blue King in check by two Queens. Either Red or Yellow would quickly pick up 20 points for the Black King. But Yellow did not go in for this. Perhaps this was wise. Red could just move the Queen back, unpinning my pawn, and allowing me to take Yellow's Queen. Since that I am only one one point here, it probably didn't make much sense for Yellow to risk it all to finish me. Perhaps Red would not want to cooperate with Yellow, who is the highest rated player in the game. But the opportunity for Yellow and Red to both profit was right there--and they could have played against Green easily afterwards. Since I won this game with Green in second place, perhaps Yellow and Red should have killed me here. 

It also might seem as if I am taking issue with the variant--but I am not. I think that it's interesting. I also don't mind that what seems to be an essential element of chess (expecting other players to act to maximize their self-interest) is absent here--there are more radical examples--Judo chess for instance does not have turns. Free For All is to my mind, very fruitful. I can imagine a number of interesting tweaks to the game. 

1) Firstly, what would happen if the ratings and names were hidden? 

2) Secondly, what if there was some way of enforcing contracts? Suppose players lost points for defecting? 

3) Thirdly, what if betrayed players received some compensation--for instance, extra moves? If a player is attacked by two players, they may make two moves. Or three moves for three attackers.

Again, this is not criticizing the variant as it exists. In an older post, I discussed sibling variants, cousin variants, descendant variants, alien variants, and rival variants. I did not think to discuss parent variants. What is there to discuss after all? A lot, it turns out. Any variant which becomes a parent is probably a successful one. The Four Player Format on chess.com has dozens of sub-variants, which seems like a sign of its fertility as a game. 

I am not particularly good at FFA. If any strong FFA players happen across this post, I'd be very happy to hear from you. 

1.2.) Teams

In the teams variant, players opposite one another are allied. The division of each team into two armies allows fast, decisive attacks. It could be played between two players, with armies of the same color, but the clockwise movement of the turns is what makes it unique. 

But the logical problem which distinguishes Free for All is completely absent here.  

In this position, Red to move. Red takes Green's Bishop, and it seems that mate is inevitable. Yellow will sacrifice their own Queen to give check, and then Red will deliver mate with the Bishop. Blue is powerless to help. 

Green's Queen is pinned here. The weird-looking Queen move by Red and Yellow is as I understand it, one of the better openings. 

You can play 4 Player Chess here: 

https://www.chess.com/4-player-chess?t=play 

2.) Shogun Chess

I have some personal stake in this variant, since it is based on an idea of mine. I was talking with my friend, the graphic designer and Shogi (Japanese chess) enthusiast Couch Tomato. In Shogi, all pieces may promote once they enter the promotion zone. What if, I wondered, pieces in chess could promote, like they do in Shogi?

A Shogi position

In the diagrammed position, the Rook will capture the Gold General, and promote to a Rook+King. The Bishop can promote to a Bishop-King, and the other pieces promote to Gold Generals. Promoting pieces has historically been unique to Shogi.

Couch Tomato liked my idea, and all of the details are his decisions. There are piece drops, as in Shogi, and there are Fairy Pieces (nonstandard pieces). Pieces may not be dropped in the promotion zone--only in a player's own 1st to 5th ranks. 

Pawns promote to Captains, which move like Kings. 

Knights promote to Generals, which moves like a Knight+King.

Bishops promote to Archbishops, which move like a Bishop+Knight

Rooks promote to Mortars, which move like a Rook+Knight.

Queens demote to the Duchess--this moves like the Ferz from shatranj--one square diagonally. When the Queen is captured, it is reintroduced as a Duchess. It begins in promoted form.

Players may have as many captains as they want, but they may only have one promoted piece of a kind. So there may not be two promoted Bishops per side, or two promoted Knights per side, two Rooks, or two Queens. 

In this position I blundered mate brilliantly. 

White is mated, since the Bishop on g6 and the Knight-King cover all of the squares White could move to. 

In this position, White has dropped the Duchess on e3 for defence. Black drops the Duchess on f4, forcing White's position open. White dies shortly after. 

The result of these rules is a nice blend of Chess with Fairy Pieces, and Shogi. The game rewards patient maneuvering--since drops in the opponent's camp are forbidden. Players must vie for control of the center. Hanging b, c, or g pawns is often fatal. Crazyhouse players are naturally good at it, but sometimes a bit skeptical of it, since many of the usual knockout sequences are forbidden. Since the Queen is demoted upon reintroduction, it is more frequently sacrificed. Often the Duchess is dropped on the fifth rank, threatening to promote to a Queen.

Much of the opening wisdom could have been lifted from crazyhouse--but of course they deviate sharply. The engine likes 1.d4 with White, and with Black, it responds to 1.e4 with 1.d5, and runs its Queen around, capitalizing on the fact that it does not hurt so much to lose this piece. Against 1.d4, it responds with 1.d5. The e6/d6 setup, commonly used in crazyhouse and bughouse, remains playable. The French is playable, and so is the Sicilian, which is perhaps only barely playable in crazyhouse and bughouse. The a6/b5 Bb7 defence for Black is perhaps playable. The engine seems to assess the game as roughly balanced, with White enjoying on average a pawn advantage--this is more balanced than in crazyhouse.

At first I did not like the Duchess. But I have come around on this. Players must be flexible in their thinking, since the same piece has a radically changing value. The main changes I would make might just be based on the imagery of the pieces--perhaps I would have taken more cues from the medieval period of Japan, when the country was actually united under a Shogun. But the imagery and symbolism of chess is perhaps too tangential an issue to pursue here. The game is highly playable, and that's what matters most. It is neither chess, nor crazyhouse, but integrates them both. I would like to see a 10x10 variant, or at the very least, Shogun 960. 

3.) File Sharing Chess

Invented by Jeffrey T. Kubach, This variant involves nothing but the most imperceptible adjustment to chess. The variants above are like baroque fugues in all of their messy complication, but this one is like a sonatina.

The simple premise is this: where pawns are blocking each other, players may switch them out. 

Here Black can swap the e4 and e5 pawns. 

Pawns may be swapped in this manner, unless the enemy pawn is attacking one of your own pieces. Interestingly, one does not see very many pawn swaps per game. In appearance, it is very minimal. 

Under my classification, this is a rival variant, since it is designed to reduce the drawishness of Chess. I think it succeeds in this aim. Whether or not it is "chessy" enough is an open question. I think it's a better solution to the drawishness of Chess than for instance, no-castling Chess. 

4.) 8 Piece Chess

Also by Jeff T. Kubach, this is one of my favorite variants on an 8x8 board. Here I will not list all of the rules. I will just summarize.

The game is just chess, except the Queen's Rook, Queen's Knight, and Queen's Bishop have all been replaced. The diagrams are taken from Tabletopia. (I guess it's hard to code this variant!) 

In this diagram, from a1 to h1, the pieces are Jailer, Lancer, Sentry, Queen, King, Bishop, Knight, Rook.

The Queen's Rook is replaced by a Jailer. The Jailer is a non-capturing piece. It paralyzes or "holds" any and all enemy pieces it touches orthogonally. The Queen's Knight is replaced by a Lancer. The Lancer is a capturing piece which moves in the direction that it is pointing. It may jump over any number of friendly pieces. And it may turn when it moves, but may not turn without moving. The Queen's Bishop is replaced by a non-capturing piece, the Sentry. The Sentry moves like a Bishop, but instead of capturing, it pushes enemy pieces according to the movements of the pushed piece. 

In this position, the White Jailer on c4 is holding Black's Queen on c5. White will probably win the Black Queen soon. 

In this position, Black's Lancer defends e5, so 1.e4 e5 2.Nf3 is not a threat for White. 

In this position, White is in check, since the Sentry is threatening to push the White Knight to e1, where the King is. White can't move the Knight to get out of check because Black would push the White Queen into the White King. White therefore must move the King, perhaps to f1. This is not only a good way to illustrate the movement of the Sentry but also a good thing to avoid. 

If you want to see some games of this, I did record myself playing with Jeff, the inventor of 8 Piece Chess. 

The game is fun. At first, it seems as if the Sentry is too powerful. But with a little practice, you learn to avoid the traps, and the games tend to be very well balanced, with Black managing to equalize. The Jailers tend not to emerge until the endgame. They immobilize every piece they touch orthogonally as long as they are touching them, including pieces which would be giving check, and including the enemy King. The variant makes you realize how much you can do with just one Bishop, or just one Knight. (I can't think right off the top of my head how many variants have just one of each piece type.) 

I tend to enjoy variants with larger boards, but this game seems deep enough, and fun enough. It's not as simple as File Sharing--if File Sharing is a Sonatina, I would think of this variant as one of Eric Satie's Gymnopédies. 

There are some important sub-clauses in the rules, which you can read here: https://www.chessvariants.com/rules/8-piece-chess 

5) Hidden Queen Chess

A simple yet clever idea. Before any moves are made, each player selects a pawn to be a hidden Queen. As the name would suggest, the players do not know which pawn is the opponent's hidden Queen. One must try to deduce the location of the Queen, and take or avoid risks accordingly. The Queen is only revealed as a Queen when it moves like a Queen. Until then it appears as a pawn. 

Here OkeiZH and I take turns against IM Opperwezen.

The game works--it has a Stratego-like element in trying to deduce the location of the Queen. Sometimes it is worth sacrificing material in order to discover the location of the piece. (I estimate it's worth two pawns to know where your opponent's Queen is.) 

I'd like to see a variant where the entire armies of both players are similarly hidden. A Knight would be revealed in one move. Other pieces would be revealed over several moves.

Although I imagine this would extremely difficult to code. 

Conclusion 

Since I wrote Why Do(n't) Variants Work? and The Problem With Sequels, I learned more about variants, and wanted to share some of my findings. Perhaps in earlier posts I was too fixated on the properties of successful variants as though there were fixed laws--when it may simply be relative to what kind of play the variant is supposed to reward. I noted that some variants were continuous with Chess, adding pieces around the original starting position on expanded boards. But of course, not every addition of a fairy piece to the standard chess configuration will work. One variant does nothing more than add all of my favorite pieces on a 10x10 board, but I could never blame anyone for not wanting to play it. 

Eventually I would like to design a variant. Rather than just being a critic who does not compose his own works. But most of my ideas are terrible, and would leave the Chess player feeling like they were stuck in a battle scene from Star Wars: Attack of the Clones. "Too many notes!" Of course, having an interesting idea for a variant is only part of creating a playable game. I think it is important not to get so creative in the design of the game that there is nothing left for the player to do. 

I also wondered if I overemphasized simplicity as a criterion of playability. Simplicity is of course, relative to what the player knows. Four Player is very messy for someone unfamiliar with Chess. Shogun Chess might overwhelm players lacking familiarity with Shogi, crazyhouse, and fairy pieces--but as someone with a bit of familiarity with all of these, I got reasonably strong fairly quickly, and even managed a win against the engine at the strongest setting. 

Anyway, happy playing and creating. Feel free to send me any variants you find interesting--although I am not likely to write any more posts like this one.