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Chess started in India as "chaturanga" around year 600 and spread to Asia as xianqi.
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 xianqi 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
Xianqi 1983 386 800 2397 2783
Chess 1631 >2800 211 1200 2453 2620 2831 3642 >4000 1997 Gary Kasparov
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
Billiards 438 2375 2813
Soccer 2600
Tennis 2400
Golf 2000
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.
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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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Most pieces should be full-directional. They should be able to move forward, backward, and to both sides. Furthermore, most pieces should be symmetric, where motion directions are symmetric and capture directions are symmetric.
A piece has a rule for motion, a rule for capture, and it can have special powers. Many combinations are possible. Doom chess chooses the most natural pieces.
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.
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There are many versions of fairy shogi, and they collectively have most of the symmetric pieces. The chart shows the pieces of fairy shogi. 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}.
A blocker has a capture range of zero. This weakness is balanced by making it uncapturable.
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).
Move Capture Value Armor # for Doom Features
chess
King *1 *1 4 0 1
Archking *2 *2 6 0 1
Queen *7 *7 9 0
Knight ~ ~ 3 0 2
Rook +7 +7 5 0 1
Rook3 (Wolf) +3 +3 3.5 0 1
Rook2 (Dog) +2 +2 2.5 0 1
Rook1 (Wazir) +1 +1 1.5 0 1
Wazer +1 x1 1.5 0 1
Puppy +2 +1 2 0
Antipuppy +1 +2 2 0
Bishop x7 x7 3.5 0 2
Bishop3 (Lynx) x3 x3 2.5 0
Bishop2 (Cat) x2 x2 2 0
Bishop1 (Ferz) x1 x1 1.5 0 2
Farz x1 +1 1.5 0
Kitten x2 x1 1.75 0
Antikitten x1 x2 1.75 0
Bishop3+ (Lynx+) x3 or +1 x3 3 0
Bishop2+ (Cat+) x2 or +1 x2 2.5 0 1
Bishop1+ (Ferz+) x1 or +1 x1 1.75 0
Fullback *1 +1 1.5 1
Blocker, king *1 Unable 1 2
Blocker, queen *7 Unable 2 2
Blocker, rook +7 Unable 1 2 1
Blocker, bishop+ x7 or +1 Unable 1 2 1
Blocker, knight ~ Unable 1 2 1
Joker +1 +1 2 Starts as a wazir. Can use its move to transform to any of {wazir, wazer, ferz, farz}
Forcer +1 Unable 2 Exerts a kingwise force on a piece in rook range. The piece can be friend or foe
Bomb +1 Unable 2 If detonated, destroys itself and all pieces within a radius of 1, kingwise. Friend and foe pieces are destroyed.
Mortar +1 +2 2 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.
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. More pieces from the chart are possible, such as the fox and lion.
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.
Direction diversity is possible because the board is Cartesian. A hexagonal board can't do this.
Bishopwise pieces cover only half the board. This can be mitigated by adding pieces like the cat+, which moves and captures like a cat 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 ferz, cat, and bishop. 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, archcat}, because you can lose one of them and still have full board coverage.
Pawns are poor team players. It's hard to make good pawn structure, and if a pawn captures, it often disrupts the structure.
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 2.0 2.5 2.5 .5 .5 1 1
2 2.5 2.0 6 5.5 3.0 5 5 .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 Transform Can transform to a different kind of piece Rank Armor The ability to take multiple hits before being captured. Damage The ability to subtract more than one armor point in a hit Healing Add hit points to pieces 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 Stun Stuns a piece for N moves Bomb Explodes and destroys all pieces within bomb range. The bomb is also destroyed Banish Send 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. Xianqi 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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Each side has a ball, which is carried by a piece. A piece may pass the ball to another piece that's within its passing range, and if the ball passes through the receiver's range.
Each piece has a rule for passing, receiving, and interception. Some pieces may be designated as ineligible to carry the ball.
Each side starts with a ball 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.
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 risk.
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 Value
King1 King *1 *1 *1 U 3.5
King2 Archking *2 *2 *1 U 6
King3 *3 *3 *1 U 7.5
King7 Queen *7 *7 *1 U 9.5
Rook1 Wazir +1 +1 *1 U 1.5
Rook2 Dog +2 +2 *1 U 2.5
Rook3 Wolf +3 +3 *1 U 3.5
Rook7 Rook +7 +7 *1 U 5
Bishop1 Ferz x1 x1 *1 U 1.5
Bishop2 Cat x2 x2 *1 U 2.0
Bishop3 Lynx x3 x3 *1 U 2.5
Bishop7 Bishop x7 x7 *1 U 3.5
Knight1 Knight ~1 ~1 *1 U 3
Knight2 Archknight ~2 ~2 *1 U 6
Knight3 Knightrider ~3 ~3 *1 U 9
Bishop1+ Ferz+ x1,+1 x1 *1 U 2
Bishop2+ Cat+ x2,+1 x2 *1 U 3
Bishop3+ Lynx+ x3,+1 x3 *1 U 4
Blocker +7 2 1.5 Ineligible to carry the ball
Running back *7 +1 *1 U 3
Fullback *2 +1 *1 U 1 3
Quarterback, slow +1 +1 *7 U 3
Quarterback, fast *2 +1 *2 U 3
Midfielder +1 +1 *2 U +1 3
Goalie *1 +1 *1 U *1 3
Receiver *2 +1 *1 U +1 3
Enforcer +1 *1 *1 U 1 3
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.
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.
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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
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.
Final move Capture frequency
Opening 16 1/3
Middle game 22 1/5
End game 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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