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Chess started in India as "chaturanga" around year 600 and spread to Asia as xiangqi.
Chess appeared in Europe as courier chess in 1200, which added the bishop. In around 1500, the queen was added and this finalized the rules of modern chess. The queen variation was called "Mad-queen chess", and the existence of the queen expanded the power of pawn promotion.
Shogi emerged in Japan in 1200 and added many new pieces. Dai shogi emerged in 1230 and added even more pieces. "Dai" means "large". A shogi board is 9x9 and a dai shogi board is 15x15. Fairy shogi was a fad.
The pieces of shogi and xiangqi have the same rule for motion and capture. The chess pawn is a rare piece with different rules. Fairy chess has many pieces with different rules for motion and capture.
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A goal for game design is depth, which can be defined as the difference between the world champion and an average human, measured by Elo ratings. The computer world champion can also be included.
Go and shogi have big depth. Chess has poor depth.
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Elo ratings:
"Human depth" is the difference between the world champion and an average player.
Human Computer Top-tier Average #1024 #128 #1 Computer Infinite Year that computer #1 human
depth depth depth human human human human computer beat the #1 human at the time
Go 3262 >5400 514 600 2400 3348 3862 5400 >6000 2016 Lee Sedol
Shogi 2200 >5000 700 600 1900 2800 4800 >5600 2013 Shinichi Sato
Xiangqi 1983 >3200 386 800 2397 2783 3950 >4500 2006 Xu Yinchuan
Chess, men 1631 >2800 211 1200 2453 2620 2831 3642 >4000 1997 Gary Kasparov
Chess, women 1550 335 1100 2085 2315 2650 >4000 1993 Judit Polgar
Scrabble 1450 >1700 800 2250 2500 >2500 2006 David Boys
Backgammon 1250 >2000 1500 2750 3250 >3250 1979 Hans Berliner
Checkers 1240 1600 208 1200 2000 2232 2440 2814 2814 1995 Don Lafferty Solved in 2007
Tic Tac Toe 0 0 0 0 0 0 0 0 0
Rock paper scissors 0 0 0 0 0 0 0 0 0
Tennis, men 600 -600 0
Tennis, women 500 -500 0
Billiards 438 2375 2813
Golf 2000 120
Soccer 2600 850 0 1750 2600
College football 400 -400 0
College bball 514 1387 1901
"Computer depth" is the difference between an infinite computer and an average player.
"Top-tier depth" is the difference between the human #1 and the human #128.
An Elo ratings difference of 200 corresponds to a 3/4 probability for the stronger player winning.
For soccer, we use the English soccer league system.
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Rules should be simple. Soccer rules are simple and football rules are complex.
Rules should yield a game with big depth, where depth is the difference between the world champion and an average player.
Doom chess has flexible rules. There are default rules and players may change them by gentleman's agreement. The default rules can be different for each tournament. Elements of Doom chess include:
There is a "draft", with a roster of pieces to choose from. Each piece has a value, and there is a value cap.
There is a "huddle". Each player decides his opening formation in secret.
The game ends when capture become impossible. The remaining pieces are totalled by points and the player with the most points wins.
The king is not sudden-death. Non-royal. It's okay for the king to be captured.
The game has blockers, which can't capture and can't be captured.
Balls can be added, which can be carried and passed. Each piece has a rule for passing and receiving. Yardage gains are part of the score function.
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A piece has a rule for motion, a rule for capture, and it can have special powers. Many combinations are possible.
Define "pure" to be a symmetric piece that has the same rule for motion and capture. They can be represented by 1 point on the chart.
Define "divergent" to be a symmetric piece with different rules for motion and capture. It can be represented by 2 points on the chart.
There are many versions of fairy shogi, and they collectively have most of the symmetric pieces. Fairy shogi uses the symmetry between rookwise and bishopwise motion.
The chart shows fairy chess space, where the X axis is rookwise range, the Y axis is bishopwise range, and the Z axis is knightwise range. The chart shows the Z=0 plane. A knight is {X,Y,Z} = {0,0,1}. An archknight has twice the range of a knight and is at {0,0,2}.
Go uses a zero piece that doesn't move.
Most of the natural symmetric pieces are in the Z=0 plane. The Z=1 plane has all fusions of Z=0 pieces with a knight.
More dimensions exist, such as the camel leaper (3,1) and zebra leaper (3,2).
A blocker has a capture range of zero. This weakness is balanced by making it uncapturable.
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Doom chess emphasizes pieces that are full-directional. Such pieces can move forward, backward, and to both sides. Furthermore, most pieces should be symmetric, where motion directions are symmetric and capture directions are symmetric.
A blank entry in the table indicates a value of 0.
Move Capture Value Armor Caliber # for Doom Features
chess
King *1 *1 4 1 1
Archking *2 *2 6 1 1
Queen *7 *7 9 1
Knight (2,1) ~ ~ 3 1 2
Archknight (2,1) ~2 ~2 6 1
Camel (3,1) (3,1) (3,1) 2.5 1
Zebra (3,1) (3,2) (3,2) 3 1
Rook +7 +7 5 1 1
Rook3 (Wolf) +3 +3 3.5 1 1
Rook2 (Dog) +2 +2 2.5 1 1
Rook1 (Wazir) +1 +1 1.5 1 1
Puppy +2 +1 2 1
Antipuppy +1 +2 2 1
Bishop x7 x7 3.5 1 2
Bishop3 (Lynx) x3 x3 2.5 1
Bishop2 (Cat) x2 x2 2 1
Bishop1 (Ferz) x1 x1 1.5 1 2
Farz x1 +1 1.5 1
Kitten x2 x1 1.75 1
Antikitten x1 x2 1.75 1
Bishop3+ (Lynx+) x3 or +1 x3 3 1 Cardinal3
Bishop2+ (Cat+) x2 or +1 x2 2.5 1 1 Cardinal3
Bishop1+ (Ferz+) x1 or +1 x1 2 1 Cardinal3
Roship +7 x7 5
Bishook+ x7 or +1 +7 4.5
Blocker, king *1 Unable 1 2 0
Blocker, queen *7 Unable 2 2 0
Blocker, rook +7 Unable 1 2 0 1
Blocker, bishop+ x7 or +1 Unable 1 2 0 1
Blocker, knight ~ Unable 1 2 0 1
Archbishop x1 or ~ x1 or ~ 5 1
Honey badger *1 +1 2 1 1
Bull (enforcer) *1 +1 2 2
Stone .5 1 0
Joker +1 +1 2 1 Starts as a wazir. Can use its move to transform to any of {wazir, wazer, ferz, farz}
Forcer +1 Unable 2 0 Exerts a kingwise force on a piece in rook range. The piece can be friend or foe
Bomb +1 Unable 2 1 If detonated, destroys itself and all pieces within a radius of 1, kingwise. Friend and foe pieces are destroyed.
Mortar +1 +2 2 1 Doesn't move when capturing
Diagonal pieces come in pairs, one light and one dark.
Numbers indicate range. Symbols for motion directions:
+ Rook
x Bishop
* King
~ Knight
| Forward or backward
- Right or left
^ Forward
v Backward
d Diagonally forward, either to the left or right, like a pawn capturing
e The range is exact. No more, no less. The piece can leap.
"Armor" is the number of hits a piece can take without being captured.
"Caliber" is the number of armor points subtracted by a hit.
After the forcer has forced a piece, the forced piece may not return to its previous square on the next move.
The roster has pieces from the rook-bishop chart. The table lists the most natural combinations, but any combination is possible.
The names of fairy chess pieces are in a state of chaos and we ditch them. Mammals with short names are tapped, such as the dog, cat, wolf, lynx, fox, and lion.
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Weak pieces are "serfs", such as the wazir, wazer, and ferz.
"Cantor pieces" are intermediate in strength between serfs and nobility, such as the dog and cat.
Doom chess avoids excessively strong pieces. Queens are so strong that it's rare for there to be an odd number of queens on the board. Even a queen with range 3 is excessively strong. An archking is a queen with range 2, slightly stronger than a rook.
Excessively strong pieces diminish the importance of lesser pieces. They're fork monsters. Don't have a piece that combines the moves of a knight and another piece. Also avoid the knightrider, a knight with extended range. That being said, have such pieces available in case players choose them by gentleman's agreement.
If a piece has a superstrong ability, give it a weakness for balance.
The cat+ is a compromise. It's a bishop with reduced range in exchange for the ability to move one square rookwise, noncapture.
You want to encourage exchanges between different kinds of pieces, and having pieces with a range of strengths helps.
The strength of a piece tends to be reflected by how often it's moved. Computers can do simulations and calculate this.
Design pieces that synergize with other pieces. A good team is {rook, bishop, knight} for their diverse directions of motion, and it gives them forking power. A queen adds further diversity.
The camel and zebra add forking powor.
Mixed pieces like the roship and bishook add forking power.
A Cartesian board enables big directional diversity, and a hex board has less diversity.
Diagonal pieces cover only half the board. This can be mitigated by adding pieces like the bishop+, which moves and captures like a bishop and also moves like a wazir non-capture. It can also be mitigated by having several bishopwise pieces on each color. For example, have 2 each of bishop1, bishop2, and bishop7. Diagonal pieces should come in pairs, one light and one dark. Doom chess uses both of these measures.
A good team is {light bishop, dark bishop, bishop+}, because you can lose one of them and still have full board coverage.
The camel is colorbound and the zebra isn't.
Pawns are poor team players. It's hard to make good pawn structure, and if a pawn captures, it often disrupts the structure.
Most leapers have poor board coverage. Board coverage for leapers:
Vertical
5 1/16
4 1/16 1 Commuter
3 9/64 1 1/2 Tripper Antelope
2 1/4 1 1/4 1 Alfil Zebra Stag
1 1/2 1 1/2 1 1/2 Ferz Knight Camel Giraffe
0 1 1/4 9/64 1/16 1/16 1/16 Zero Wazir Dabbaba Threeleap Fourleap
1 2 3 4 5 6 Horizontal 0 1 2 3 4
An amphibian is (1,1)+(3,0) and it has full board coverage.
Define tribes by motion type. Rook, bishop, king, knight, bishop+. Each member of the tribe can have any range.
The bishop tribe has 2 subtribes, light and dark. Doom chess uses bishopwise pieces in pairs, one light and one dark.
Doom chess has 2 pieces from the king tribe and 2 pieces from the knight tribe. It has only one rook7 because rooks have full board coverage. Having only one rook7 makes room for more rookwise pieces and more diversity.
"Attack asymmetry" is where a piece can attack another piece and the other piece can't attack back. This is part of the magic of chess and it leads to forking opportunities. "Fairy space" is the structure of attack diversity. Diversity can come from many sources:
*) Direction diversity, for example the {rook,bishop,knight} set. The queen adds further diversity by combining directions.
*) Range for capture.
*) Range for motion. Fast pieces outmaneuver slow pieces.
*) Divergent pieces, with different rules for motion and capture. For example, the wazer, which moves like a wazir and captures like a ferz.
*) Rank
*) Flavor. For example, rock paper scissors.
*) Motion that depends on terrain.
*) Pieces that capture without moving, like a mortar.
*) Creation. The ability to create a new piece and put it on the board.
*) 3D motion.
If two pieces are combined, the strength of the fusion tends to be equal to the sum of the parts, plus a small bit. For example, a queen is stronger than a rook + bishop.
For pieces with large range, rookwise range is stronger than bishopwise range.
For pieces with small range, rookwise range is weaker than bishopwise range. A wazir is weaker than a ferz because it needs 2 moves to make 1 ferz move.
The strength of a piece tends to scale with the number of squares it can reach in a move. This often depends on board location. Board coverage also matters. Bishopwize pieces cover only half the board.
Define a function for the strength of a piece as Sxyz, which can be measured with simulations. x is rookwise range, y is bishopwise range, and z is knightwise range.
Define a difference function Dxyz
Sxyz = Sx0z + S0yz + Dxyz
Define a knight function Kxy
Kxy = Sxy1 - Sxy0
A piece that moves rookwise with range i and captures rookwise with range j has strength Rij.
A piece that moves bishopwise with range i and captures bishopwise with range j has strength Bij.
There are two more functions for pieces with mixed ranges for motion and capture.
The precise strengths of the wazir and ferz are fundamental parameters to measure.
It's rare for a bishop to have a chance to move with range 7. It's from corner to corner, and bishops shouldn't be in corners. A bishop with range 5 is worth almost as much as a bishop with range 7.
The following table gives an estimate of value as a function of range.
Range Rook Bishop King Knight Bishop+ Camel Zebra Blocker Blocker Blocker Blocker
Rook Bishop King Knight
1 1.5 1.5 3.5 3 2 2 2.5 .5 .5 1 1
2 2.5 2.0 6 5.5 3 3 4 .7 .7 1.25 1.5
3 3.5 2.5 7.5 8 3.5 - - .8 .8 1.5 1.75
4 4.0 3.0 8 - 3.75 - - .9 .9 1.65 -
5 4.5 3.25 8.5 - 4.0 - - 1.0 .95 1.8 -
6 4.75 3.5 9 - 4.25 - - 1.1 .8 1.9 -
7 5 3.5 9.5 - 4.25 - - 1.2 1 2 -
Draft chess has a roster of pieces to choose from. Each piece has a price. Each player has a budget for buying pieces, like a salary cap.
Each player drafts in secret and then decides an initial formation in secret.
Players may add pieces to the roster by gentleman's agreement, and they can change the piece values.
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A triangle piece is full-directional and has full-board coverage.
Triangle pieces aren't symmetric. They can be made symmetric by giving them the ability to transform to a different kind of triangle. A transforming triangle is a "turret".
Avoid discontinuity of goals. For example, a sudden-death king is a discontinuity in that the value of a king is infinite compared to other pieces. It's an obstacle to balance among pieces. It diminishes the king's options and is an obstacle to complexity.
Chess pawns are a discontinuity because they're low strength but can become queens. Also, the fact that they're one-way diminishes complexity.
Castling is an awkward rule. Ditch it. Also ditch en passant.
Offense is hard to generate. Blockers and bombs help.
In classical chess, it's hard to generate offense with pawns because it's hard to pass a defensive line of opposing pawns.
Pawn battles are often boring because all pawns have the same powers.
You want to get your pieces into enemy territory, but there are hazards. The invading pieces should be weak pieces. They should have the ability to capture backwards and support the next wave of attackers.
Avoid leapers other than the knight. The {2,0} leaper covers only 1/4 of the board and the {2,2} leaper covers only 1/8. The {3,1} and {3,2} leapers cover the full board. They're unnatural but some players like them.
Design rules that discourage draws.
Classical chess has a rule that the game is a draw if any possible move results in self checkmate. Ditch this rule.
Draws can be lessened by disallowing repeat positions.
Grandmaster-level games draw around half the time. Among non-draws, white wins around 3/5 of the time. The higher the level of play, the more frequent the draws. Blitz has a lower fraction of draws than classical chess.
The fact that chess is prone to draws decreases game depth.
Find ways to equalize black and white. For example, declare that if the piece count at the end of the game is equal, then black wins. Clock times can also be unequal between players. This is analogous to "komi" in the game of go.
Draws can be lessened by eliminating the sudden-death of kings, and by tallying piece strengths at the end of the game.
Pieces can have rank, where you can only capture a piece with equal or lower rank.
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It can be expanded to 5 pieces by adding a spock and a lizard. It can be expanded to any set of pieces with odd number.
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Some of the fundamental powers are:
Motion
Capture Move to a square and capture the piece in it
Transform Can transform to a different kind of piece
Armor The ability to take multiple hits before being captured.
Caliber The ability to subtract more than one armor point in a hit
Armorer Add armor to pieces
Rank A capturing piece must be >= the rank of the captured piece
Mortar Can capture without having to move
Force Exerts a force on a piece within forcing range.
The piece has a pattern for the force it can exert
Repel Exerts a repulsion on all pieces within repulsion range.
The opposing player must then move a piece within the repulsion zone out of the repulsion zone.
It is allowed to capture the repeller.
Bomb Explodes and destroys all pieces within bomb range. The bomb is also destroyed
xert
Banish Send a piece to a penalty box for N moves
Ambassador Protects nearby friendly pieces
Ball passing
Ball receiving
Ball interception
Terrain-based powers
Ability to change board terrain
Ability to change board connectivity or create new space
Coordinated moves between pieces, like castling
Piece drops
Simultaneous moves, where both players move simultaneously
A forcer exerts a force on other pieces. A forcer has a range of motion, a range for exerting force, and a range for the impact of the force. All ranges are independent and any combination can be chosen. A forcer can force its own pieces or an opponent's. A piece that was forced must wait at least 1 move to return to its former square. Repeat positions are disallowed, like in the game of go.
A bomb can't capture. It can detonate, whereupon it destroys itself and all pieces within a radius of 1, kingwise. This includes friendly pieces.
A stunner stuns a piece within stun range for N moves. A stunned piece may not move or capture.
Some games have terrain, such as inaccessible squares. Xiangqi is an example. One can give pieces powers or weaknesses that depend on terrain. A power can be to change terrain.
Armor points is the ability to take hits without being capture. Each hit subtracts an armor point.
Most pieces have 0 armor points, in the sense that they can be captured in one turn.
A piece that's uncapturable has infitinte armor points. A blocker.
Give squares the ability for multiple occupancy.
Add a 3rd dimension.
The properties of a piece can depend on terrain.
Pieces can have the power to change terrain.
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A ball can be on the ground or it can be carried by a piece. A piece can pick up and put down a ball.
A piece has a passing pattern and a receiving pattern. A piece may pass the ball to another piece that's within its passing pattern, and if the ball passes through the receiver's receiving pattern.
Some pieces have an interception pattern or a goalie pattern.
A piece has a pattern for kicking.
Each side starts with balls on their back row, and the goal is to move your ball as far forward as possible before the ball-carrier is captured (tackled). One point for each row forward. You must also defend against the enemy ball.
Alternately, the score can be based on the number of rows gained without being captured. If a piece advances and isn't captured on the next move, it gets credit for forward progress.
Give credit for forward progress. The score is the furthest the ball advanced during the game.
Each side can have multiple balls, and the total score is the total rows gained.
The game can start with balls on the ground.
Some pieces may have the power of inducing a fumble, or to strip a ball.
One can specify how many balls a piece may carry. The number could be zero. An ineligible receiver.
One can specify a move limit at which time the game ends and points are tallied. This promotes offense with the ball.
One can include columns in the scoring function. For example, reward being close to the center, like rugby.
One can include a goal zone. There can potentially be space behind the goal zone, like for hockey.
Have the option for arbitrary geometry and terrain. A piece's powers can depend on terrain.
Pieces can have more than one armor point. For example, it may take more than one tackle to capture a ball carrier.
If the score is tied at the end of the game, the winner is the first to achieve the score. Or, you could have overtime. Keep moving until one side has a better score.
Move Capture Pass Receive Web Armor Caliber Value
King1 King *1 *1 *1 U 1 3.5
King2 Archking *2 *2 *1 U 1 6
King3 *3 *3 *1 U 1 7.5
King7 Queen *7 *7 *1 U 1 9.5
Rook1 Wazir +1 +1 *1 U 1 1.5
Rook1H Wazir, heavy +1 +1 *1 U 1 2 2.0
Rook2 Dog +2 +2 *1 U 1 2.5
Rook3 Wolf +3 +3 *1 U 1 3.5
Rook7 Rook +7 +7 *1 U 1 5
Bishop1 Ferz x1 x1 *1 U 1 1.5
Bishop2 Cat x2 x2 *1 U 1 2.0
Bishop3 Lynx x3 x3 *1 U 1 2.5
Bishop7 Bishop x7 x7 *1 U 1 3.5
Knight1 Knight ~1 ~1 *1 U 1 3
Knight2 Archknight ~2 ~2 *1 U 1 6
Knight3 Knightrider ~3 ~3 *1 U 1 8
Bishop1+ Ferz+ x1,+1 x1 *1 U 1 2
Bishop2+ Cat+ x2,+1 x2 *1 U 1 3
Bishop3+ Lynx+ x3,+1 x3 *1 U 1 4
Blocker, rook +3 1 1.5 Ineligible to carry a ball
Blocker, rook, heavy +2 2 1.5 Ineligible to carry a ball
Blocker, bishop x3 1 1.5 Ineligible to carry a ball
Blocker, bishop, heavy x2 2 1.5 Ineligible to carry a ball
Blocker, knight ~1 1 1.5 Ineligible to carry a ball
Blocker, knight, heavy ~1 2 2.0 Ineligible to carry a ball
Running back *3 +1 *1 U 1 3
Fullback *2 +1 *1 U 1 1 3
Quarterback, slow +1 +1 *3 U 1 3
Quarterback, fast *2 +1 *2 U 1 3
Midfielder +1 +1 *2 U +1 1 3
Goalie *1 +1 *1 U *1 1 3
Receiver *2 +1 *1 U +1 1 3
Enforcer +2 *1 *1 U 1 1 3
Enforcer, high caliber +2 1 2 1.5 Ineligible to carry a ball
A blank entry means that the piece doesn't have the feature.
"U" means universal receiver. Can catch the ball from any direction.
"Armor" is the number of hits that a piece can survive without being captured.
"Web" means that the piece can catch or block balls that are within web range.
"Caliber" is the amount of damage inflicted in a hit. The amount of armor subtracted. Most pieces have a caliber of "1".
If a piece with a ball is tackled, the ball goes to the tackling team.
When the move count expires, the positions of the balls are measured.
A computer can vary the choice of pieces and formation and find choices with big depth.
The game of go hinges heavily on experience. A general property of a game is the degree to which experience matters, and it varies between games. It's a matter of taste. Some like games that emphasize experience and some like games that don't. The rules of Doom chess can be steered to either emphasize or de-emphasize experience.
A goal is to diminish the importance of computers. Imagine a tournament where players are sequestered so that they can't communicate with computers.
A game can be designed for a team of humans and computers. For example, a game can have goals for which there is no engine.
Wise tournament structure can promote drama and generate ticket revenue. Blitz games are exciting.
A computer can simulate a game and calculate piece strengths.
A computer can evaluate each piece's fraction of the total moves, and this tends to be proportional to the strength of a piece.
Let T be the time given to a computer per move, and S(T) be the ratings strength.
S will have an approximate form S ~ D(T) ln(T), where D(T) is game depth. D will be a weak function of T.
Rosters of pieces can be varied to study the effect on D, and strategic rosters can be identified to maximize D.
Let V be the value of a piece and let Vteam be the sum of piece values. Doom chess is a roster that maximizes D/Vteam.
Give each player a clock so that they can put it where they please. Connect them wirelessly. Such clocks help team chess.
An electronic board can sense piece movement, making clocks unnecessary. This increases the watchability of blitz chess.
Blitz chess could add timeouts. For example, give each player 3 timeouts of 30 seconds each. It gives the crowd a chance to catch up with the game.
In general, there can be a function that converts the physical time taken for a move to a time charged on the clock, and the function can be non-linear.
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Emanuel Lasker, Berthold Lasker, and Edward Lasker are all chess grandmasters and mathematicians, and they're all related and friends. They worked together to promote go and fairy chess.
Emanuel Lasker was the chess world champion and his mathematics PhD advisor was David Hilbert.
Edward Lasker: "While the Baroque rules of Chess could only have been created by humans, the rules of Go are so elegant, organic, and rigorously logical that if intelligent life forms exist elsewhere in the universe, they almost certainly play Go."
Triangle chess is a generalization of square chess. It has the pieces of square chess, plus triangle pieces.
Triangle chess adds new angles to square chess. Square chess has the angles of rook, bishop, and knight. Triangle chess adds angles for the badger and gopher.
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A beaver is a trishop with half steps.
The elements of square chess are the rook, bishop, and knight. Molecules are sums of elements, such as
Queen = Rook + Bishop
The chart shows the elements of triangle chess. The molecules are:
Tring = Badger + Gopher
Packer = Badger + Trishop
Viking = Gopher + Trishop
The first two beaver ranges are equivalent to other pieces.
Beaver1 = Badger1
Beaver2 = Packer1
Some triangle pieces are useful and some aren't.
A Badger1 is a subset of a Rook1. Ditch it.
A Badger2 is fundamentally different from square pieces and has full board coverage. Keep it.
Badgers with range larger than 2 are interesting. Use them. A Badger3 has 9 moves and isn't excessively powerful.
A Gopher1 covers only 1/4 of the board and has a poor turning radius. Ditch it.
A Gopher2 is fundamentally different from square pieces and has full board coverage. Keep it.
Gophers with range larger than 2 are interesting. Use them. A Gopher3 has 9 moves and isn't excessively powerful.
A trishop are similar to a bishop. Ditch it.
A Hawkeye1 is similar to a knight and more knightness is needed. It also has a 3-leap horizonal motion. It has 6 moves and is slightly weaker than a knight. Use it.
A Hawkeye2 is absurd. Ditch it.
A Wolverine1 is absurd. Ditch it.
A Tring1 is part rook and part knight. It has 6 moves. It's interesting because it's vulnerable to diagonal pieces. Keep it.
A Packer1 and Viking1 have 9 moves and are similar to a king. Ditch them.
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A piece that moves like a bishop covers 1/3 of the board.
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The chart shows pieces that are full-directional. More combinations are possible.
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One can define a set of standard rulesets, which players can change by gentlemen's agreement. Playtesting will lead to a good list of standard rulesets.
A tournament can define a ruleset that's released when the tournament begins.
Rules can be designed that flummox AI. Make the rules hard to program.
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Numbers indicte the approximate year that the game emerged.
Rookwise Bishopwise Modern Chaturanga Courier Xianqi Seven Shogi Dai shogi Tai shogi Ko shogi
range range chess chess Kingdoms
1500 600 1200 600 1200 1200 1230 1400 1700
1 1 King Raja King King King King General
7 7 Queen General Queen Queen Millenary
7 0 Rook Ratha Rook Chariot Chancellor Rook Rook Rook Chariot
0 7 Bishop Bishop Diplomat Bishop Bishop Bishop Elephant
- - Knight Ashva Knight Horse Cavalryman
- - Shogi knight Shogi knight Shogi knight
- - Pawn Padati Pawn
- - Shogi pawn Shogi pawn Shogi pawn Shogi pawn
1 0 Wazir General Sword Angry boar Angry boar Pawn
0 1 Mantri Ferz Advisor Dagger Cat sword Cat sword Longbow
0 2e Gaja Alfil Elephant
2 0 Violent ox Violent ox
0 2 Flying dragon Flying dragon
7 1 Dragon king Dragon king Dragon king Quartermaster
1 7 Dragon horse Dragon horse Dragon horse Centuria
7 2 Tiger wing
2 7 War hawk
2 2 Mastodon
3 3 Lion dog
4 4 Archer
5 5 Crossbowman
5 0 Flag waver
0 5
5 2 She-devil
2 5 Dove
- - Gold gen Gold gen Gold gen Gold gen
- - Silver gen Silver gen Silver gen Silver gen
- - Copper gen Copper gen Copper gen
Board Piece types Pieces Year
Chaturanga 8x8 6 16 1200
Modern chess 8x8 6 16 1500
Carrera chess 10x8 8 20 1627
Courier chess 12x8 10 24 1200
Shogi 9x9 8 16 1200
Xianqi 9x10 7 16 1200
Dai shogi 15x15 29 65 1230
Dai dai shogi 17x17 64 96 1400
Ko shogi 19x19 34 90 1700
Tai shogi 25x25 93 177 1400
Taiyoku shogi 36x36 207 402 1550
Go 19x19 1 170 -500
Probabilities in percent:
White wins Black wins Draw Fraction of white wins
among non-draws
Tournaments, 1851-1878 45.5 40.4 14.1 53.0
Tournaments, 1881-1914 36.9 31.4 31.8 54.0
Tournaments, 1919-1932 37.0 26.0 37.0 58.7
World championships, 2000-24 20.0 9.3 71.0 68.3
Chess engines, 2009 34.7 24.0 41.3 59.1
World Blitz Championships, 2009 39.0 34.6 26.4 53.0
For classical chess, the fraction of moves for an individual piece is:
Fraction of moves Total moves Value Fraction/value
Queen .237 3.53 9 .026
Rook .155 2.31 5 .031
King .217 3.23 4 .054
Knight .174 2.58 3 .058
Bishop .151 2.25 3 .050
Pawn .065 .97 1 .065
Total 28.8
Rooks are more likely to move long-range than queens or bishops. Queens and bishops are have similar probabilities for long-range moves. The fraction of moves of a given range is:
Range Rook Bishop Queen Queen Queen
total rook-wise bishop-wise
1 .25 .32 .30 .19 .11
2 .20 .24 .20 .11 .09
3 .18 .18 .15 .08 .07
4 .15 .12 .11 .06 .05
5 .10 .07 .08 .04 .04
6 .07 .04 .06 .03 .03
7 .05 .03 .04 .02 .02
A game has an optimal capture frequency. Too large or too small is bad for depth.
The modern capture frequency is 1/5, and in 1850 it was 1/4.
Master games tend to have a lower capture frequency than amateur games.
A game averages 16 captures upon conclusion.
Move range Capture frequency
Opening 1-16 1/3
Middle game 17-22 1/5
End game 23-32 1/7
Initial time Time added per move Time per move
minutes seconds seconds
Classical 90 30 165
Rapid 15 10 32.5
Blitz 5 3 10.5
Bullet 1 0 1.5
"Time per move" assumes 40 moves for each player.
Columns Rows Year Pieces
Capablanca 10 8 ~1925 Rook+Knight Bishop+Knight Classical pieces
Shako 10 8 Elephant Cannon Classical pieces
Grand 10 10 Rook+Knight Bishop+Knight Classical pieces
Fairy chess names are in a state of chaos. These are the names.
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More options for flavor:
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Number of people in the top 20:
Men Women Men U21 Women U21
India 4 4 6 4
USA 6 2 3
China 2 5 2
FIDE 2 2 1
France 2 1 1
Kazakhstan 1 3
Ukraine 3
Uzbekistan 1 1 1
Russia 1 1 1
Norway 1 1
Netherlands 1 1
Switzerland 1 1
Azerbaijan 1 1
Turkey 2
Hungary 1
Bulgaria 1
Slovenia 1
Poland 1
Belgium 1
Serbia 1
Mongolia 1
Georgia 1
Belarus 1
Iran 1
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Define "depth" as the difference in rank between the #4 and the #64 ranked players, divided by 4.
Elo rating by rank:
Depth Matches #1 #2 #4 #8 #16 #32 #64 #128 #256 #512 #1024 #2048 #3072 Comp- Strat- Luck Commun- # of rated
million plexity egy ication players
Logic ~130 .58 2319 2173 2103 1872 1752 1660 1537 1 5 1 0 72 Cards. Speed
Shogi World 129 2800 1900
Spot It! ~100 .89 2149 2064 1962 1893 1734 1648 1520 1 1 0 4 71 Pattern recognition speed
Hive BS ~100 2098 1928 1736 1548 1504 1436 49 Hex tiles
Hand and Foot 87 .53 1650 1643 1626 1602 1588 1570 1539 1493 3 3 3 1 178
Hive ~80 1.04 1797 1774 1700 1627 1538 3 5 0 0 24 No board. Hex tiles
Ticket to Ride: Map 76 .23 2115 2094 1933 1823 1775 1706 1627 1582 1485 Not rated 344
Tennis, Men World 74 2297 2272 2068 1980 1927 1850 1772 1667 1513 515
Railroad Inc 73 2.6 2016 1984 1972 1928 1858 1768 1679 1573 2 3 3 0 185 Deep Blue Edition
Distilled 70 .17 1949 1860 1808 1716 1646 1570 1505 3 4 2 1 82 Cards and coins
Sushi Go 69 3.8 2046 2018 1936 1860 1813 1758 1661 1603 2 3 2 2 251
Welcome Perfect Home 67 2.8 2083 2036 2024 1940 1904 1848 1755 1683 1555 2 4 1 1 325
Splendor 65 9.9 2223 2220 2135 2109 2004 1955 1876 1798 1716 1634 1512 3 3 2 2 1288 Cards and coins
Castles of Burgundy 63 3.9 2041 2024 2018 1928 1878 1823 1765 1711 1640 1526 3 4 2 1 1222 Hex board size 4. Tokens and dice. No battle
Patchwork 62 3.0 2047 2025 2002 1932 1904 1838 1752 1685 1447 3 3 3 3 256 Square board 9x9, tokens
Seasons 62 10.2 1928 1907 1870 1825 1778 1667 1621 1530 3 4 2 1 239
Feast of Odin 62 .45 1965 1965 1857 1831 1776 1647 1528 5 4 1 1 84 Economic
Go World 59 3852 3733 3692 3664 3622 3553 3457 3359 3230 3006 893
Ticket Ride: Europe 58 2.7 2050 2043 1998 1980 1930 1852 1765 1696 1630 1543 2 3 3 2 812
Jaipur 58 2.9 1903 1899 1849 1813 1759 1675 1591 2 2 2 0 77
Ticket to Ride 54 15.9 2157 2103 2082 2060 2011 1948 1867 1810 1735 1669 1595 1475 2 3 3 2 2678 Topology
Bubblee Pop 52 2.3 1869 1866 1817 1754 1720 1665 1610 1520 1 2 3 0 187
Through the Ages 50 1.14 2014 1916 1887 1822 1744 1667 1503 4.42 4 2 3 72 Cards
Kingdom Builder 50 2.8 1917 1902 1854 1801 1746 1709 1654 1604 1541 2 3 2 3 421
Stone Age 50 5.7 1998 1918 1891 1870 1820 1760 1691 1624 1524 3 3 3 3 349
Gaia Project 50 .43 1870 1753 1736 1651 1590 1557 4.37 4 1 2 55 Hex board tokens, money, battle
The Vale of Eternity 48 .27 1910 1891 1764 1740 1680 1632 1571 1507 3 4 2 2 188
Kingdomino 47 6.8 1991 1988 1928 1902 1846 1797 1740 1674 1596 1 3 4 1 385
Puerto Rico 47 2.8 1998 1765 1743 1731 1699 1628 1556 4 4 1 1 101
Chess, Blitz World 45 2869 2838 2796 2765 2722 2676 2616 2554 2479 2391 2289 2174 2105 46000
7 Wonders Duel 45 13.1 1974 1948 1923 1887 1838 1790 1743 1708 1659 1609 1522 3 4 2 3 1492
Potion Explosion 44 3.0 1881 1859 1828 1792 1760 1704 1654 1599 1530 1 2 3 1 354
Terraforming Mars 43 4.2 2113 2053 2040 1994 1958 1916 1867 1821 1761 1675 1544 4 4 3 1 1347
Chakra 41 4.0 1922 1842 1827 1808 1732 1702 1663 1616 1546 2 4 2 2 514
Space Base 39 3.6 1917 1916 1862 1835 1773 1737 1706 1656 1614 1559 1458 2 2 3 1 1269
Captain Flip 39 2.2 1857 1843 1817 1760 1722 1696 1660 1631 1593 1546 1428 2 2 4 0 1095
Agricola 39 1.68 1828 1812 1800 1761 1732 1690 1643 1587 3 5 1 2 233 Simple board. Cards
Race for the Galaxy 38 13.8 1889 1853 1829 1815 1775 1720 1679 1613 1531 4 3 2 1 444 Cards
CuBirds 38 7.4 1829 1828 1795 1751 1712 1673 1645 1611 1572 1503 1 3 3 1 706
Ark Nova 37 11.0 2157 2150 2077 2056 2004 1969 1930 1885 1828 1769 1688 1585 1436 3.74 5 1 2 3298 Board, tokens, and cards
7 Wonders 37 11.8 1872 1869 1861 1830 1799 1753 1712 1679 1638 1593 1514 3 3 2 2 1305 Cards
Xiangqi World 37 2783 2754 2624 2610 2577 2524 2476 2397 206 Square board
Carcassonne 36 9.5 2045 2022 1999 1969 1936 1896 1853 1792 1734 1647 1509 1 3 3 3 1365
Yahtzee 36 10.9 1943 1918 1864 1842 1792 1758 1720 1679 1631 1530 0 1 5 0 678 Dice
Lost Cities 34 5.0 1830 1780 1759 1731 1699 1659 1622 1589 1552 1742 1 4 2 2 617
Backgammon 34 5.9 1836 1830 1775 1737 1717 1674 1639 1591 1504 1 2 4 0 341 Tokens and dice
Chess, Class. World 34 2840 2810 2780 2754 2731 2695 2642 2591 2524 2446 2369 2279 2219 3.64 5 0 0 95000
Chess, Rapid World 31 2832 2755 2741 2727 2694 2663 2616 2574 2500 2425 2340 2237 2174 65000
Chess engines World 31 3651 3649 3628 3626 3617 3584 3503 3320 2917 2228 674
Wingspan 31 8.7 1903 1893 1866 1822 1793 1772 1743 1707 1671 1624 1563 1342 3 3 3 3 2037
Lucky Numbers 26 11.7 1797 1785 1768 1739 1728 1694 1664 1641 1611 1578 1522 1 2 4 1 1554
Hearts 25 2.54 1765 1762 1733 1718 1688 1671 1633 1609 1570 1530 1413 2 2 3 1 1078
Take 5 23 8.3 1762 1754 1737 1706 1691 1669 1644 1620 1594 1561 1492 1 1 4 3 1131 Cards
Azul 22 12.5 2224 2201 2120 2096 2061 1994 1931 1874 1813 1748 1676 1582 1499 1 3 3 3 4140 Tokens and patterns
Can't Stop 21 15.2 1775 1775 1746 1725 1698 1675 1663 1642 1615 1588 1547 1455 0 1 5 0 2307 Tokens and dice
7 Wonders: Architect 21 4.1 1753 1713 1703 1682 1664 1640 1619 1596 1563 1515 1 3 1 1 818
Catan 20 7.4 1812 1773 1761 1747 1720 1698 1680 1657 1630 1603 1569 1518 1449 2 3 3 4 3379 Hex board and tokens
Texas Hold'em 20 .32 1723 1698 1694 1673 1657 1636 1616 1593 1568 1528 3 4 2 0 870 Cards and bluffing
King of Tokyo 20 2.8 1765 1685 1679 1658 1631 1600 1568 1529 2 2 3 3 492
Solo 18 4.9 1670 1669 1643 1631 1608 1593 1572 1549 1510 1 2 4 2 462 Cards
Terra Mystica 12 1.14 1793 1751 1733 1722 1636 1599 3.97 5 1 1 52 Hex board
Taknoko 8 2.7 1851 1849 1786 1750 1693 1628 1752 2 3 2 1 92
Hearts WCG - 1691 1603 1575 1553 1528 1494 1446 100
Canasta - .74 1857 1833 1811 1712 1611 1541 2 2 4 3 57
Connect 4 - 4.4 2024 2010 1945 1830 1802 1726 1 5 0 0 59 Square board and tokens
Great Western Trail - .38 1869 1860 1828 1865 1604 1560 3 3 3 3 60
Barrage - .28 1832 1730 1660 1628 1598 1560 3 5 2 1 41 Board and tokens
Age of Innovation - .19 1880 1809 1727 1682 1649 1572 4 5 1 1 42 Hex board and tokens
Darwin's Journey - .87 1793 1751 1745 1702 1638 1598 4 5 1 1 52 Hex board and tokens
Barrage - .28 1836 1730 1660 1628 1598 1562 3 5 2 1 41
Obsession - .29 2082 2056 1808 1761 1669 1550 3 5 1 1 33 Tokens and cards
Dice Forge - 2.6 1939 1832 1785 1750 1673 1604 2 2 4 0 56
Warchest - .50 1761 1752 1737 1687 1604 2 3 2 0 24 Hex board, tokens, cards
Beyond the Sun - .23 1751 1708 1659 1619 1597 3 4 1 2 23
Xianqi World - 2783 2754 2624 2610 2577
Checkers World - 2433 2430 2403 2377 2351
Reflection - .27 2000 1960 1865 1787 1573 3 3 0 0 24 Square board and pieces
Chinese Checkers - .15 1683 1635 1609 1562 1 5 0 2 11 Hex board and tokens
Scrabble World - 2174 2162 2108 2077
Dungeon Twister - .047 1629 1621 1606 1471 3 4 1 3 9 Board, tokens, and cards
Galactic Cruise - .067 1836 1789 1740 1652 4 4 1 2 8 Ship design
Barca BS - <.0001 1704 1547 1317 Square board. Fairy chess. 110 rated games
Checkers - .44 1738 1598 1 4 1 0 2 Square board
Scythe - .79 1712 1696 3 4 2 3 2
Tumbleweed - 1615 1601 3 5 0 0 Hex board
Hanabi - 10.5 2 3 3 4 0 Cards
Bandito - 2.9 1 3 3 4 0
Turing Machine - .78 2 5 1 0 0
Trench - .002 0 Square board and pieces
King's Color - 0 0 Hex chess. Pieces change
Day and Night - 0 0 Square board. Row and diagonal building
Push Fight - 0 0 Square board. Pieces exert forces
Tablut - 0 0 Square board and pieces. Ancient.
Mahjong - .004 4 3 4 3
Depth Matches #1 #2 #4 #8 #16 #32 #64 #128 #256 #512 #1024 #2048 #3072 Comp- Strat- Luck Commun- # of rated
million plexity egy ication players
Ratings are from boardgamearena.org unless denoted otherwise. "World" means world ratings, "BS" means boardspace.com, and WCG means worldofcardgames.com.
Chess ratings are from FIDE.
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