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Original Random Variant Chess

On this page, the original form of Random Variant Chess, originally on the main page of this subsection, is preserved:

The Original Form of the Proposed Game

The following diagram:

shows the layout of a form of Chess which involves a far more modest augmentation of the board. The rules are as for regular Chess except that the stalemate rule is as for Leaping Bat Chess (the player forcing stalemate gets 3/5 of the point for the game, the other player getting 2/5), and the King moves four squares when castling to Kingside or Queenside, and the moves of the additional pieces used are as described in the rules of Leaping Bat Chess.

Since this was written, I have been inspired by the institution of komidashi in the game of Go to propose what I believe to be a superior scoring scheme, which is discussed at length on a previous page:

Game Outcome Points for White Points for Black
White forces checkmate. 100 0
White forces stalemate. 60 40
White bares Black's King 56 44
White gives perpetual check 52 48
Draw 50 50
Black gives perpetual check 43 57
Black bares White's King 41 59
Black forces stalemate. 39 61
Black forces checkmate. 0 100

Since this scoring scheme includes bare King as a victory condition, it should be noted that when the last of the opponent's pieces other than the King is captured, a player can say "Continue" if he intends to play for a checkmate - or a stalemate.

This variant retains the symmetry of the opening layout. As you can see in the diagram above, four squares in each player's back rank contain question marks.

Which pieces are to occupy those squares is what is chosen at random in this form of Chess, from the following list of possibilities:

 1) Giraffe, Camel; Camel, Giraffe
 2) Fers, Camel; Camel, Fers
 3) Wazir, Camel; Camel, Wazir
 4) Man, Camel; Camel, Man
 5) Alfil, Camel; Camel, Alfil
 6) Dabbaba, Camel; Camel, Dabbaba
 7) Walker, Camel; Camel, Walker
 8) Tiger, Camel; Camel, Tiger
 9) Rhinoceros, Camel; Camel, Griffin
10) Wazir, Fers; Fers, Wazir
11) Man, Fers; Fers, Man
12) Walker, Fers; Fers, Walker
13) Tiger, Fers; Fers, Tiger
14) Rhinoceros, Fers; Fers, Griffin
15) Man, Wazir; Wazir, Man
16) Walker, Wazir; Wazir, Walker
17) Tiger, Wazir; Wazir, Tiger
18) Rhinoceros, Wazir; Wazir, Griffin
19) Man, Alfil; Alfil, Man
20) Walker, Alfil; Alfil, Walker
21) Tiger, Alfil; Alfil, Tiger
22) Rhinoceros, Alfil; Alfil, Griffin
23) Man, Dabbaba; Dabbaba, Man
24) Walker, Dabbaba; Dabbaba, Walker
25) Tiger, Dabbaba; Dabbaba, Tiger
26) Rhinoceros, Dabbaba; Dabbaba, Griffin
27) Man, Walker; Walker, Man
28) Tiger, Walker; Walker, Tiger
29) Rhinoceros, Walker; Walker, Griffin
30) Tiger, Man; Man, Tiger
31) Rhinoceros, Man; Man, Griffin
32) Rhinoceros, Tiger; Tiger, Griffin
33) Zebra, Camel; Camel, Zebra
34) Zebra, Fers; Fers, Zebra
35) Zebra, Wazir; Wazir, Zebra
36) Zebra, Man; Man, Zebra
37) Zebra, Walker; Walker, Zebra
38) Tiger, Zebra; Zebra, Tiger
39) Rhinoceros, Zebra; Zebra, Griffin
40) Giraffe, Zebra; Zebra, Giraffe
41) Walker, Tiger; Tiger, Walker
42) Man, Tiger; Tiger, Man
43) Zebra, Tiger; Tiger, Zebra
44) Dabbaba, Alfil; Alfil, Dabbaba
45) Man, Fers; Fers, Wazir

Optionally, the first 32 alternatives in the list above can stand on their own as the pool from which to select a variant.

Schedules of Play

In addition to playing each form of Chess thus randomly selected twice, with one player and then the other as White, the schedule of games is also to be varied so that each player has an equal chance of being the first to play a variant.

Thus, four games between two players would proceed in the fashion:

Game  1: A: White  B: Black   random variant 1
Game  2: A: Black  B: White   random variant 2
Game  3: A: White  B: Black   random variant 2
Game  4: A: Black  B: White   random variant 1

This pattern, however, when repeated, does still lead to one asymmetry between the two players: A plays, as white, the variant first encountered as black in the next game, while B plays, as white, the variant first encountered as black three games later. As long as there is a pause between pairs of games, however, this asymmetry would not be significant.

Attempting to eliminate this particular asymmetry does not yield an obvious answer, because one player had to play white first; for example, the following scheme:

Game  1: A: White  B: Black   random variant 1
Game  2: A: Black  B: White   random variant 2
Game  3: A: White  B: Black   random variant 2
Game  4: A: Black  B: White   random variant 1
Game  5: A: White  B: Black   random variant 3
Game  6: A: Black  B: White   random variant 3
Game  7: A: White  B: Black   random variant 4
Game  8: A: Black  B: White   random variant 4
Game  9: A: White  B: Black   random variant 5
Game 10: A: Black  B: White   random variant 6
Game 11: A: White  B: Black   random variant 6
Game 12: A: Black  B: White   random variant 5

although it allows A and B both to play first as White with a new variant when it is played twice in succession an equal number of times, finds A playing first as White for both variants 1 and 5; changing from the first to the last of a group of three games does not change who plays first.

One way to solve the problem is for player A to play Black first for the last six games, so that player A would play: WBWBWBBWBWBW. But would that be fair?

And then I remembered how one way to minimize White's advantage from moving first would be to have white move once for the first turn, and then for each player to make two moves per turn afterwards. Thus, a very simple possibility exists:

Game  1: A: White  B: Black   random variant 1
Game  2: A: Black  B: White   random variant 1
Game  3: A: Black  B: White   random variant 2
Game  4: A: White  B: Black   random variant 2
Game  5: A: White  B: Black   random variant 3
Game  6: A: Black  B: White   random variant 3

and so on, with each player taking White for two games in a row, except that the players alternate colors after the first game.

General Extended Random Variant Chess

Should, however, 45 possibilities be deemed insufficient, another method of randomizing the variant in use is provided, which offers more variations. Extended Random Variant Chess requires that several more pieces be defined, as follows:

The Empress (also known as the Chancellor) moves as either the Rook or the Knight.

The Princess (also known as the Archbishop) moves as either the Bishop or the Knight.

The Cannon (also known as the Pao) moves as a Rook, but when capturing, must jump over exactly one piece of either color to reach the piece to be captured, on any square beyond it.

The Leo moves as a Queen, but follows the same rule for capturing as the Cannon. (That is, the rule about jumping over one piece to capture, but that rule is applied to it's own move along Queen lines.)

The Vao moves as a Bishop, but follows the same rule for capturing as the Cannon. (Again, although like the Cannon it captures by leaping over another piece, it still captures along Bishop lines, unlike the Cannon.)

The Grasshopper moves, and captures, on the square immediately beyond the nearest piece of either color in any of the eight directions in which a Queen moves. Thus, the eight spaces to which the white Grasshopper in the center of the board in this diagram can move to are those which contain black Grasshoppers.

The Archer moves, but does not capture, as a Man, and captures (and gives check), but does not move without capturing, as a Knight.

The Sprinter moves, but does not capture, as a Giraffe, and captures (and gives check), but does not move without capturing, as a Man: to any immediately adjacent square, diagonally or orthogonally.

The Star moves and captures as either a Wazir or an Alfil; that is, it can move one space orthogonally, or two spaces diagonally.

Given these extra pieces, the choice of a random variant from the larger pool for Extended Random Variant Chess may proceed in one of two ways:

The first method (yielding General Extended Random Variant Chess) begins with this step:

It is chosen at random for the Queen to be replaced by one of:

1) a Queen (that is, left alone)
2) a Griffin
3) a Rhinoceros
4) an Empress
5) a Leo

It is chosen at random for the two Bishops to both be replaced by a pair of:

1) Bishops (that is, left alone)
2) Tigers
3) Sprinters
4) Vaos

It is chosen at random for the two Rooks to both be replaced by a pair of:

1) Rooks (that is, left alone)
2) Princesses
3) Cannons

It is chosen at random for the two Knights to both be replaced by a pair of:

1) Knights (that is, left alone)
2) Men
3) Zebras
4) Archers
5) Stars
6) Grasshoppers

As an example of General Extended Random Variant Chess, here is what the array would become if the following random selection of a variant took place:

Queen:    5) Replaced by Leo
Bishops:  2) Replaced by Tigers
Rooks:    3) Replaced by Cannons
Knights:  1) Left as Knights
Variant: 32) Rhinoceros, Tiger; Tiger, Griffin

Since the Bishops were replaced by Tigers, the Tigers in the variant are replaced by Vaos, and the pieces on the back rank are:

Cannon, Rhinoceros, Vao, Knight, Tiger, Leo, King, Tiger, Knight, Vao, Griffin, Cannon

as shown in the diagram below:

Note that in this diagram, a circled G replaces the symbol used on the previous page for the Griffin; that makes that symbol available to represent the Leo, to correspond with analogous symbols representing the Vao and the Cannon.

Restricted Extended Random Variant Chess

The second method (yielding Restricted Extended Random Variant Chess) proceeds as follows:

A piece substitution is chosen at random from the following list:

 1) No substitutions.
 2) Griffin replaces Queen.
 3) Rhinoceros replaces Queen.
 4) Empress replaces Queen.
 5) Leo replaces Queen.
 6) Tigers replace Bishops.
 7) Sprinters replace Bishops.
 8) Vaos replace Bishops.
 9) Princesses replace Rooks.
10) Cannons replace Rooks.
11) Men replace Knights.
12) Zebras replace Knights.
13) Archers replace Knights.
14) Stars replace Knights.
15) Grasshoppers replace Knights.

The difference between this and the method for General Extended Random Variant Chess, which uses the same set of substitutions, is now that at most one of the possible four substitutions is made, while before a substitute for the Queen, one for the Bishops, one for the Rooks, and one for the Knights were all chosen independently. In this way, the basic array of conventional Chess pieces, instead of being replaced by something chosen completely at random is left largely intact, with only one kind of piece usually replaced by something else.

Both methods now continue as follows:

Then, one of the 45 variations for the unallotted two positions on each side of the board is chosen. The variation may need to be modified, depending on the replacements chosen for the Queen, the Bishops, or the Knights, as follows:

The first method provides for 16,200 possible opening arrays, all of which largely retain the symmetry and balance of forces of the regular game of Chess. The second method provides only 675 variations.

The first method of producing a random chess variant all but ensures that the ordinary chessmen, other than the King and the Pawns, will not be present. As this is not necessarily desirable, even if more than 45 possibilities are felt to be needed, the second method, which has the advantage that most of the conventional chessmen will still be present was developed. With 675 possible opening arrays, it should still provide sufficient variety to preclude an excessive reliance upon book openings.

Also note that if the Rooks are replaced by Cannons, castling may still take place, with the Cannons functioning as the Rooks, but if the Rooks are replaced by Princesses, there is no castling.

Only one combination of substitutions is chosen, and it applies to both players, just as the variation chosen from among those in the list of 45 variations applies to both players.

Systematic Random Variant Chess

Examination of the possibilities offered by the two forms of Extended Random Variant Chess has suggested a third form, based on Restricted Extended Random Variant Chess. In this form, choosing the variant has three steps.

The first step is to choose a base array, from three possibilities involving related pieces:

1) Rook, ?, ?, Knight, Bishop, Queen, King, Bishop, Knight, ?, ?, Rook
2) Rook, ?, ?, Archer, Sprinter, Queen, King, Sprinter, Archer, ?, ?, Rook
3) Cannon, ?, ?, Knight, Vao, Leo, King, Vao, Knight, ?, ?, Cannon

The next step is to choose a substitution at random in the fashion of Restricted Extended Random Variant Chess. If General Extended Random Variant Chess were used, one could use the rule that "leaving the Knight alone" may mean "replacing the Archer by a Knight", and "replacing the Rook by a Cannon" may mean "leaving the Cannon alone". However, then the base array would be irrelevant. Since it is the substitution rule of Restricted Extended Random Variant Chess that is used, the substitutions have to be modified the opposite way to work: if Archers are present, "Replace Knights by Archers" must change to "Replace Archers by Knights", if Vaos are present, "Replace Bishops by Vaos" must change to "Replace Vaos by Bishops", so that all the possibilities of changing one piece in the base array selected remain available.

The third step is to choose one of the 45 variants for the positions noted by question marks.

Finally, as with Restricted Extended Random Variant Chess, since the Rhinoceros, Griffin, Tiger, Man, and Zebra are present in both the 45 variants and in the piece substitutions, duplication is to be dealt with by having the substitution take precedence, and modifying the variant chosen as follows:

This version, Systematic Random Variant Chess, allows the most interesting possibilities reachable by the General Extended version to be available, but retains the advantage of the Restricted Extended version of a less haphazard layout. It provides 1,935 possible opening layouts. (The number would be 2,025, except for two duplicate cases; as the second base array differs from the first base array in only two pieces, the combination with a Bishop and an Archer, or a Sprinter and a Knight, can be obtained with either array, and a different substitution in each case.)

Note that if it is considered a problem that some reachable arrangements are more probable than others, this can be solved as follows: consider the arrangements where an Archer or a Sprinter are substituted in from base array 1 as the original, and those where a Knight or a Bishop are substituted in from base array 2 as the duplicate, and make the duplicate arrangements unique by making the additional substitution of a Griffin for the Queen in that case.

Alternate Pawn Promotion Rules

In addition to the conventional promotion rule, that Pawns only promote to pieces found in the initial array for the particular game being played, two alternative promotion rules are advanced as possible options:

Pawns could be allowed to promote only to pieces which, while part of the pool of possible pieces from which a variant could be constructed, were not part of the initial array, subject also to the further restriction that only pieces of types not previously promoted to may be used.

This rule has two results: like promotion to captured pieces, it conserves physical chess pieces, and it further increases the variety of pieces potentially on the board. (Incidentally, note that neither the Bat, nor the Nightrider, two especially "troublesome" pieces, are included in the pool of those used for this variation.)

Alternatively, pawns could be, regardless of the specific variant in use, allowed only to promote to pieces found in the 'base' version of the array: Queen, Rook, Bishop, Knight, Camel, and Giraffe.

This would reduce the confusion that the large variety of possible initial arrays could potentially cause for promotion.

The Grasshopper, originally invented by T. R. Dawson, is one of the most popular Fairy pieces used in problems. I have given names to the Archer, Sprinter, and Star, but these are all such trivial combined pieces that they are unlikely to be original. The other pieces introduced on this page are well-established pieces used in Fairy Chess problems.

Progressive Random Variant Chess

In surveying the many enlarged forms of Chess that have been proposed through the ages, from the earliest varieties of Decimal Chess and Great Chess down to modern innovations such as Ciccolini's Game and Capablanca's Chess, I have found that the type of array I have proposed as the basis for Random Variant Chess has been used very rarely, and another type of array has been much more common. This appears to be because it has been considered highly desirable to keep the ability to place the castled King in this secure corner arrangement:

 | N |   |   |
 | P | P | P |
 | R | K |   |

Thus, instead of new pieces being added between the Knight and the Rook, as I thought to do so that the base array Rook, Giraffe, Camel; Knight, Bishop, King, Queen, Camel, Giraffe, Rook would concentrate the attacks of four pieces on each side on the squares in front of the Queen and the King, it seems to be the historical consensus of the chess world that new pieces ought to be added between the Queen and King and their flanking Bishops. Some versions instead added new pieces between the Bishops and Knights, so I suppose that is an alternate possibility that could be considered.

Interestingly enough, the one historical exception I have been able to find to this tendency, where the new pieces were placed in the place I was originally inclined to put them, between the Knights and the Rooks, was devised by Carrera in 1617. It is not only referred to in the book Chess Eccentricities by Major George Hope Verney, but it is also mentioned in the book introducing Chancellor Chess. It placed a Princess (that is, a piece with the moves of a Bishop and a Knight, but called a Centaur in this game) on the Queenside, and an Empress. (that is, a piece with the moves of a Rook and a Knight, called a Campione in this game) on the Kingside. Much later, in 1874, H. E. Bird devised a game with the same complement of pieces, but different names, where the two new pieces were between the two Bishops and the Queen and King (with the Empress called an Equerry, and placed next to the Queen, and the Princess called a Guard, and placed next to the King), and then, several years later, in 1921 or shortly thereafter, Capablanca placed the new pieces (the Princess called an Archbishop, and the Empress the Chancellor) between the Bishops and Knights on the two sides, this time with the Princess again on the Queenside. Surprisingly enough, all three games were designed for a board with 8 ranks and 10 files, rather than a 10 by 10 board; while this is more sensible, most enlarged Chess variants have tended to use a square board rather than following the example of Courier Chess. Capablanca, at least, did also consider the 10 by 10 board.

Given that the three basic moves in the modern game of Chess are those of the Rook, the Bishop, and the Knight, and that the Queen represents the combination of two of them, those of the Rook and Bishop, it should not be too surprising that the other combinations were thought of as obvious pieces to add to the layout.

Adding a Knight's move to the abilities of the Queen, giving rise to the Amazon, is another popular possibility; among the games which included this piece were the Emperor's Chess and the Sultan's Chess, both devised by L, Tressau in 1840.

Perhaps the most sensible arrangement would be to follow the location used for Bird's variant, but to put the Princess back on the Queenside to better balance the locations of the pieces by their power. That version probably has been thought up by someone historically as well.

One of the things I tried to do with Random Variant Chess was to avoid changing the power of the pieces in the array. Thus, the Empress, a Rook and Knight combined, was used as a replacement for the Queen, and not as one of the possible added pieces, and the Princess, a Bishop and Knight combined, or a Pao, the Cannon from Chinese Chess, could replace the Rook.

Yet, the Griffin, a very powerful piece indeed, is allowed as an added piece. So the goal of limiting the change in power of the pieces, while allowed to limit the number of variations, was not consistently met.

Thus, another factor incorporated in this revision of the game is to allow an increased variety in the piece substitutions and added pieces, and to use the Shatranj pieces as another alternative base array.

The diagram below shows the various forms of the basic layout that are intended to be provided in this form of the game:

If both the Camel and the Giraffe are added to the complement of chess pieces, arrangement A is used. If only the Camel is added, either arrangement B1 or B2 is used. But if neither the Camel nor the Giraffe are added, then the Knight is kept next to the Rook, so as to preserve the castled position shown above, and either arrangement C1, C2, or C3 is used.

Some additional pieces, beyond those defined for Leaping Bat Chess on the previous page, and the additional ones defined above, will be provided here. The Counsellor combines the moves of the Man (or the King) and the Knight, and the Duke can move as a Rook or Bishop, but only one or two spaces, and the Count can move as a Rook, but only three spaces.

As a two-space move by the Duke is not a jump, this is not the Squire from RennChess, also used as the Mammoth or Mastodon by Mats Winther. It should be noted that RennChess, or Renniassance Chess, by Eric V. Greenwood, also has a piece called the Duke with a different move. The piece used here was called the Duke in Greater Chess, a game from 1942 invented by W. Day.

The Squirrel, on the other hand, combines the Dabbaba, the Alfil, and the Knight, and does jump to a square two steps away from it.

Thus, the added pieces are now chosen from this list:

With arrangement A
 1) (Giraffe, Camel); (Camel, Giraffe)

With arrangements B1 and B2:
 2,  3) (Camel), Fers; Fers, (Camel)
 4,  5) (Camel), Wazir; Wazir, (Camel)
 6,  7) (Camel), Man; Man, (Camel)
 8,  9) (Camel), Alfil; Alfil, (Camel)
10, 11) (Camel), Dabbaba; Dabbaba, (Camel)
12, 13) (Camel), Man; Counsellor, (Camel)
14, 15) (Camel), Squirrel; Squirrel, (Camel)
16, 17) (Camel), Duke; Squirrel, (Camel)
18, 19) (Camel), Duke; Duke, (Camel)
20, 21) (Camel), Duke; Counsellor, (Camel)
22, 23) (Camel), Count; Count, (Camel)
24, 25) (Camel), Count; Counsellor, (Camel)
26, 27) (Camel), Count; Duke, (Camel)
28, 29) (Camel), Walker; Walker, (Camel)
30, 31) (Camel), Tiger; Tiger, (Camel)
32, 33) (Camel), Cannon; Cannon, (Camel)
33, 34) (Camel), Princess; Empress, (Camel)
35, 36) (Camel), Rhinoceros; Griffin, (Camel)

With arrangements C1, C2 and C3:
                             ?L: Dabbaba     Cannon         Rhinoceros     Zebra          Princess
                             ?R: Dabbaba     Cannon         Griffin        Zebra          Empress
?L, Fers; Fers, ?R               37, 38, 39   87,  88,  89  134. 135. 136  179, 180, 181  233, 234, 235
?L, Wazir; Wazir, ?R             40, 41, 42   90,  91,  92  137, 138, 139  182, 183, 184  236, 237, 238
?L, Man; Man, ?R                 43, 44, 45   93,  94,  95  140, 141, 142  185, 186, 187  239, 240, 241
?L, Alfil; Alfil, ?R             46, 47, 48   96,  97,  98  143, 144, 145  188, 189, 190  242, 243, 244
?L, Dabbaba; Dabbaba, ?R                                                   191, 192, 193
?L, Man; Counsellor, ?R          49, 50, 51   99, 100, 101  146, 147, 148  194, 195, 196  245, 246, 247 
?L, Squirrel; Squirrel, ?R       51, 52, 53  101, 102, 103  149, 150, 151  197, 198, 199  248, 249, 250
?L, Duke; Squirrel, ?R           54, 55, 56  104, 105, 106  152, 153, 154  200, 201, 202  251, 252, 253
?L, Duke; Duke, ?R               57, 58, 59  107, 108, 109  155, 156, 157  203, 204, 205  254, 255, 256
?L, Duke; Counsellor, ?R         60, 61, 62  110, 111, 112  158, 159, 160  206, 207, 208  257, 258, 259
?L, Count; Count, ?R             63, 64, 65  113, 114, 115  161, 162, 163  209, 210, 211  260, 261, 262
?L, Count; Counsellor, ?R        66, 67, 68  116, 117, 118  164, 165, 166  212, 213, 214  263, 264, 265
?L, Count; Duke, ?R              69, 70, 71  119, 120, 121  167, 168, 169  215, 216, 217  266, 267, 268
?L, Walker; Walker, ?R           72, 73, 74  122, 123, 124  170, 171, 172  218, 219, 220  269, 270, 271
?L, Tiger; Tiger, ?R             75, 76, 77  125, 126, 127  173, 174, 175  221, 222, 223  272, 273, 274
?L, Cannon; Cannon, ?R           78, 79, 80                                224, 225, 226
?L, Princess; Empress, ?R        81, 82, 83  128, 129, 130  176, 177, 178  227, 228, 229
?L, Rhinoceros; Griffin, ?R      84, 85, 86  131, 132, 133                 230, 231, 232

Once an arrangement of the regular pieces and the added pieces is chosen from the 274 possibilities, the next step is to choose a base array and piece substitutions.

There are four possible base arrays. The first one has the forms as shown in the diagram above:

 A) Rook, Giraffe, Camel, Knight, Bishop, Queen, King, Bishop, Knight, Camel, Giraffe, Rook
B1) Rook, Camel, Knight, Bishop, ?, Queen, King, ?, Bishop, Knight, Camel, Rook
B2) Rook, Camel, Knight, ?, Bishop, Queen, King, Bishop, ?, Knight, Camel, Rook
C1) Rook, Knight, Bishop, ?, ?, Queen, King, ?, ?, Bishop, Knight, Rook
C2) Rook, Knight, ?, Bishop, ?, Queen, King, ?, Bishop, ?, Knight, Rook
C3) Rook, Knight, ?, ?, Bishop, Queen, King, Bishop, ?, ?, Knight, Rook

and the correspondence between the various base arrays is:

1       2      3      4
Rook    Rook   Cannon Rook
Knight  Knight Knight Archer
Bishop  Alfil  Vao    Sprinter
Queen   Fers   Leo    Queen

Either one base array, followed by one piece substitution, can be chosen, for Progressive Systematic Random Variant Chess, or the step of choosing a base array can be ignored, and a piece substitution for every piece can be chosen, giving Progressive Extended Random Variant Chess. It might also be desired to use just one piece substitution, but also to use either just one of the possible base arrays, or two or three of them selected to taste.

 1/*) No substitutions.

 */1) No substitution for the Queen.
 2/2) Fers replaces Queen.
 3/3) Griffin replaces Queen.
 4/4) Rhinoceros replaces Queen.
 5/5) Nightrider replaces Queen.
 6/6) Empress replaces Queen.
 7/7) Leo replaces Queen.
 8/*) Princess replaces Queen.

 */1) No substitution for Bishops.

 9/2) Tigers replace Bishops.
10/3) Sprinters replace Bishops.
11/4) Vaos replace Bishops.
12/5) Alfils replace Bishops.

 */1) No substitution for Rooks.

13/2) Princesses replace Rooks.
14/3) Cannons replace Rooks.

 */1) No substitution for Knights.
15/2) Men replace Knights.
16/3) Zebras replace Knights.
17/4) Archers replace Knights.
18/5) Stars replace Knights.
19/6) Grasshoppers replace Knights.

              2                              3                              4
    ------------------------------ ------------------------------ ------------------------------
 1) No substitutions.              No substitutions.              No substitutions.
 2) Queen replaces Fers.           Fers replaces Leo.             Fers replaces Queen.
 3) Griffin replaces Fers.         Griffin replaces Leo.          Griffin replaces Queen.
 4) Rhinoceros replaces Fers.      Rhinoceros replaces Leo.       Rhinoceros replaces Queen.
 5) Nightrider replaces Fers.      Nightrider replaces Leo.       Nightrider replaces Queen.
 6) Empress replaces Fers.         Empress replaces Leo.          Empress replaces Queen.
 7) Leo replaces Fers.             Queen replaces Leo.            Leo replaces Queen.
 8) Princess replaces Fers.        Princess replaces Leo.         Princess replaces Queen.
 9) Tigers replace Alfils.         Tigers replace Vaos.           Tigers replace Sprinters.
10) Sprinters replace Alfils.      Sprinters replace Vaos.        Bishops replace Sprinters.
11) Vaos replace Alfils.           Bishops replace Vaos.          Vaos replace Sprinters.
12) Bishops replace Alfils.        Alfils replace Vaos.           Alfils replace Sprinters.
13) Princesses replace Rooks.      Princesses replace Cannons.    Princesses replace Rooks.
14) Cannons replace Rooks.         Rooks replace Cannons.         Cannons replace Rooks.
15) Men replace Knights.           Men replace Knights.           Men replace Archers.
16) Zebras replace Knights.        Zebras replace Knights.        Zebras replace Archers.
17) Archers replace Knights.       Archers replace Knights.       Knights replace Archers.
18) Stars replace Knights.         Stars replace Knights.         Stars replace Archers.
19) Grasshoppers replace Knights.  Grasshoppers replace Knights.  Grasshoppers replace Archers.

Note that Princesses may only replace Rooks, and not the Queen, if substitutions are chosen for individual pieces.

Then the final step is to avoid excessive numbers of certain Fairy pieces due to their possible occurrence in both the piece substitution and in the variant (that is, the group of two or four added pieces) above:

The number of different variants provided by Progressive Systematic Random Variant Chess is 274 variants times 4 base arrays times 19 piece substitutions, giving 20,824 possibilities, and the number of different variants provided by Progressive Extended Random Variant Chess is 274 variants times 7*5*3*6 (or 630) piece substitutions, giving 172,620 possibilities.

A Slight Addition

It has occurred to me that there is another reasonable family of variants that could be added to the 274 basic possibilities above.

For the two additional forms of the base array shown below:

with which the correspondences with the four base arrays remain:

1       2      3      4
Rook    Rook   Cannon Rook
Knight  Knight Knight Archer
Bishop  Alfil  Vao    Sprinter
Queen   Fers   Leo    Queen

with arrangements D1 and D2, we add to the 274 possibilities above:

                          ?L: Tiger    Cannon   Princess Empress  Zebra
                          ?R: Tiger    Cannon   Princess Princess Zebra
?L, Man; Cannon, ?R           275 276           359 360  407 408  443 444
?L, Man; Griffin, ?R          277 278  323 324  361 362  409 410  445 446
?L, Man; Rhinoceros, ?R       279 280  325 326  363 364  411 412  447 448
?L, Man; Empress, ?R          281 282  327 328  365 366           449 450
?L, Fers; Cannon, ?R          283 284           367 368  413 414  451 452
?L, Fers; Griffin, ?R         285 286  329 330  369 370  415 416  453 454
?L; Fers; Rhinoceros, ?R      287 288  331 332  371 372  417 418  455 456
?L; Fers; Empress, ?R         289 290  333 334  373 374           457 458
?L, Wazir; Cannon, ?R         291 292           375 376  419 420  459 460
?L, Wazir; Griffin, ?R        293 294  335 336  377 378  421 422  461 462
?L; Wazir; Rhinoceros, ?R     295 296  337 338  379 380  423 424  463 464
?L; Wazir; Empress, ?R        297 298  339 340  381 382           465 466
?L, Walker; Cannon, ?R        299 300           383 384  425 426  467 468
?L, Walker; Griffin, ?R       301 302  341 342  385 386  427 428  469 470
?L; Walker; Rhinoceros, ?R    303 304  343 344  387 388  429 430  471 472
?L; Walker; Empress, ?R       305 306  345 346  389 390           473 474
?L, Duke; Cannon, ?R          307 308           391 392  431 432  475 476
?L, Duke; Griffin, ?R         309 310  347 348  393 394  433 434  477 478
?L, Duke; Rhinoceros, ?R      311 312  349 350  395 396  435 436  479 480
?L, Duke; Empress, ?R         313 314  351 352  397 398           481 482
?L, Count; Cannon, ?R         315 316           399 400  437 438  483 484
?L, Count; Griffin, ?R        317 318  353 354  401 402  439 440  485 486
?L; Count; Rhinoceros, ?R     319 320  355 356  403 404  441 442  487 488
?L; Count; Empress, ?R        321 322  357 358  405 406           489 490

increasing the number of starting arrays, before piece substitutions, from 274 to 490, and thus increasing the total number of combinations from 20,824 to 37,420 for Progressive Systematic Random Variant Chess. and from 172,620 to 308,700 for Progressive Extended Random Variant Chess.

Equipment for the Game

Of course, normally, people playing the game would simply improvise equipment for it, should this game become popular, there would arise a demand for sets for the game. How could a set for a game like this be made without requiring an inordinate number of pieces, of wildly varied shapes, impossible to memorize?

The obvious improvised solution for a game like this would be to use multiple chess sets different in appearance or size. This suggests to me that a set specifically designed for this game could consist of the following, for each of White and Black:

This kind of piece would provide both an inexpensive indication of the exact type of the piece, and a differentiation of form comparable to what is normally expected from Chess pieces. For example, the shape could be that of a chessman on a square pedestal, with the pedestal being surrounded on its four corners by L-shaped posts a small distance from the pedestal to hold the piece's label.

Smaller, not Bigger

But the problem may be that this is simply too complicated.

Perhaps the goal should be to have as little change from normal Chess as possible while still allowing a fair amount of variation.

How about this, then:

1) R ? N B Q K B N ? R
2) R N ? B Q K B ? N R
3) R N B ? Q K ? B N R

on a 10 by 8 chessboard, with six possibilities for replacing the Queen:

1) Queen (R+B)
2) Princess (B+N)
3) Empress (R+N)
4) Amazon (R+B+N)
5) Griffin
6) Leo

and the extra two pieces could be drawn from a fairly short list of alternatives:

 1) Camel, Camel
 2) Squirrel, Squirrel
 3) Duke, Squirrel
 4) Princess, Empress
 5) Cannon, Cannon
 6) Tiger, Tiger
 7) Man, Counsellor
 8) Duke, Duke
 9) Duke, Counsellor
10) Count, Count
11) Count, Counsellor
12) Count, Duke

Then, the variation to be played could be chosen by rolling three dice of different colors, giving 216 possibilities. That might be as much variation as people would want, and as much as would be needed to achieve a game with more variety.

When the Princess and Empress are chosen as the additional two pieces, and either the Princess or the Empress is chosen to replace the Queen, instead two Cannons are used as the additional pieces,

Something Different With Almost Existing Equipment

If one keeps moving downwards, from a 12 by 8 board to a 10 by 8 board, the next step is the original 8 by 8 board.

Fischerrandom, sometimes also termed Chess 960, was an attempt to limit the amount of change to Chess caused by arranging the pieces randomly on the back rank. As noted, I've tried to avoid messy arrangements of pieces, and yet have a large number of possibilities, by adding extra pieces so that a much more restricted set of arrangements, mostly consisting of choosing pieces to add, would still lead to many possibilities.

If one were more restrictive than Fischerrandom, and insisted that the two Rooks and the King remained on their original squares, so that Castling would be completely unaffected, as well as insisting the Bishops be on squares of opposite color, the number of possible combinations would not be enough to make the game very random; if we added the restriction that one Bishop and one Knight had to be on each side of the King, there would be only six combinations:


but if one used a four-player Chess board, then there would be thirty-six combinations:

with one player using the white and yellow pieces, and the other the black and red pieces.

One could then go further; since the two groups of pieces each player controls are distinguished by color, they could be given other roles:

King   -> Man
Queen  -> Empress
Rook   -> Princess
Knight -> Giraffe
Bishop -> Zebra

This way, each side has only one King. And, thus, the pieces could be left as they are for a game of Chess with extra pieces played on the four-player board, or the regular Chess pieces could be randomly placed in one of the six arrangements noted above - and the arrangement for the red and yellow pieces could be completely random, so the number of possible arrangements would be 5,020 times 6, or 30,120.

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