Justification of the Rules of ST3d Chess, Kobayashi Maru Variant by L. Lynn Smith Several readers have asked me to explain my decision for applying particular conditions for this game. This paper will attempt to demonstrate the reasoning of each decision. It is hoped that this will enlighten those who continue to have questions. ------------------------------------------------------------------------------------------------- EVALUATION OF THE PLAYING FIELD The ST3D playing field offers one of the most unique and interesting game boards for 3D Chess. It maintains the standard number of 64 cells of the 8x8 field, yet expands the area of play beyond the mere cubic space of the 4x4x4 field. Each 2x2 attack platform will be considered to be one cell above or below the adjacent fixed board. Therefore the fixed boards are considered two cells apart. So, in order to connect two of these 4x4 playing areas, an attack platform must be positioned so that both share access to its cells. There would need to be specific rules for movement of pieces between these seperate areas, attack platforms and fixed boards, in addition to rules for the movement of the attack platforms. The first rule was to restrict all pieces moving between fixed boards, predicating such movement upon the specific placement of the attack platforms. This would influence the development, control and placement of each of these 2x2 fields. JUSTIFICATION OF PIECE MOVEMENT The ST3D playing field offers one of the most restrictive environments for the average chess piece. With the 4x4 fixed areas and the 2x2 attack platforms, most pieces have very little chance of mobility and suffer from the close quarter combat. So, the rules for the movement of pieces should not only offer freedom of development but also certain strategic restrictions which can be used to the benefit of the opponent. TYPES OF MOVEMENT In 2D chess, there are three basic type of moves; step, slide and leap. The step is a translation from one cell to an adjacent cell. The slide is a translation through directly adjacent cells. The leap is a translation from one cell to another which is neither adjacent nor directly adjacent. On the 2D playing field, there are available to the step and slide moves eight different directions. In the 3D playing field, the number of directions is twenty-six. In 2D, the directions are divided into two categories, orthogonal and diagonal. In 3D, there are three categories of directions, orthogonal, diagonal and triagonal. Orthogonal movement is translation along one axis. Diagonal movement is equal translation along two axes. Triagonal movement is equal translation along three axes. Basicly, each chess piece would keep their 2D moves. The 3D movement of the piece should continue to reflect these. In a cubic field, a solid 3D space of cells, those 2D moves would be simple to transpose. But the ST3D field, with both its shifting areas of cells and its staggered array, offers limited opportunies for direct translation. PAWN In 2D chess, the Pawn is the most restricted piece on the playing field. On the ST3D field, even more so. There was the basic attempt to maintain the 2D move restriction, forward movement only. Since the players begin the game on opposite sides of the playing field and upon seperate levels, this forward movement would also apply to changes in levels. Allowing the initial two-step move was a great help with the opening game. Pawns on the fixed level could quickly secure attack platform points, deterring the opponent from an early direct assault. Since the Pawns involved in the movement of an attack platform were not responsible for their displacement within the field, they were allowed to maintain this initial two-step option. This would allow such a Pawn to quickly occupy orthogonal-adjacent attack platforms, either horizontally and vertically. Such a two-step move, should pass vertically through two specific cells because the opponent should be allowed the opportunity of en passant capture. The capture move of the 2D Pawn is a simple forward diagonal step. The 3D Pawn should also have such a capture move. So, in addition to the normal capture move, there would be a 3D capture move. If the 3D capture move, which would involve a change in level, was to only a forward diagonal, a change in two axes, several of the Pawns would be denied the opportunity to exercise such a capture. Specifically, the Pawns located initially on the second and third file of the fixed boards. There should be parity among this particular piece. The diagonal change of level would be discarded in favor of the triagonal step. The use of the triagonal step allows for, not only the full exploitation of the 3D field, but it give every Pawn the same opportunity for such a capture move. This also allows for potential capture to the outside cells of the attack platform and the potential capture from the attack platform to the central files of the fixed boards. A great improvement over the simple diagonal. With the option of the initial two-step move, the opponent will have the option of the en passant capture. There will be numerous opportunities for such. There are the obvious potentials on the fixed boards, but the significant en passant captures can occur with the Pawns moving on the attack boards. Those which take their two-step option horizontally can occur adjacent each of the fixed boards. Those that occur vertically may occur through each of the fixed boards. Granted that such a Pawn was located initially triagonal from its opponent and open to capture, the single step vertically would place it on a diagonal and again be open to capture. With the two-step option, the player will attempt to avoid this second potential capture, thus denying the opponent and necessitating the en passant. As in 2D chess, the player would be allowed to freely promote the Pawn upon reaching the farthest rank of the opponent's fixed board. This would encourage aggressive development. But the attack platforms offered a unique opportunity for promotion. Allowing promotion of Pawn located on the far rank of an attack platform which reach one of the opponent's initial attack platform points, would encourage aggressive attack platform development and the necessity to protect those particular points on the playing field. Another interesting condition, particular to 3D Chess where the Pawn able to change levels without capturing, is that there are little or no opportunities for the creation of 'backward' Pawns. With the rules of this game, there are several positions in which the Pawn can be prevented from both moving and capturing. (Example: A White Pawn located on the second rank of an attack platform which is located at Ba1u.) BISHOP The 2D Bishop has only the diagonal slide and this will be maintained for playing upon the individual areas of the ST3D playing field. If allowed to continue this type of slide, the equal change of two axes, the Bishop would only be allowed to preform a single step from the fixed board or the attack platform. But since in 2D Chess, the Bishop usually compliments the Pawn by either defending or being defended, the diagonal change of level was discarded in favor of the triagonal. Combining both the diagonal and triagoanl change of level was discarded as this would result in this piece gaining access to the entire field, whereas in 2D Chess, it only has access to half. With the triagonal change of level, it continues to only have access to half of the playing field. Like with the Pawn, that vertical diagonal blindspot would offer some interesting strategic considerations within the game, just as the orthogonal blindspot in 2D Chess. ROOK The 2D Rook has only the orthogonal slide and this will be maintained. This is the most simplest of the sliders to visualize since it involves only the orthogonal direction. In most 3D playing fields, the Rook often loses significant influence, usually easily supplanted by the Bishop. Not so with the ST3D field, with the ability to slide vertically up to four cells, the Rook greatly out-manuevers the Bishop. QUEEN As in 2D Chess, the Queen would combine the powers of both the Rook and Bishop. This piece would also be denied the vertical diagonal for strategic reasons. KING As in 2D Chess, like the Queen but only able to step. It was also denied the vertical diagonal. This allows for the piece to be pinned and opens the possibility of the stalemate condition. KNIGHT On the 2D field, the Knight is the only piece which operates 'above' the board by leaping from cell to cell without regard to the condition of the intervening cells. This Knight is able to leap to any cell two away which are not directly orthogonal or diagonal connected. This is usually described as a translocation along two orthogonal cells followed by a 90 degree turn to an adjacent cell. This results in the familiar 'L' pattern of move. This 'L' pattern would be maintained with the application of the 3D Knight. There are other leap patterns for the 3D field but this one is the easiest for most players to visualize. The restriction that pieces are not allowed to move from fixed board to fixed board except from or through an attack platform will also be maintained with this piece. But its ability to leap from fixed board to attack platform, from attack platform to fixed board and between attack platforms will make for interesting gameplay. In fact, the mobility of this particular piece will place it in value just below that of the Queen, supplanting the Rook. The virtual freedom of the Knight while translating from and to attacks board was to make up for the obvious restriction that the piece suffers in the 4x4 area of the fixed boards, and the absolute impossible movement within the 2x2 areas of the attack platforms. It also allows this piece to occupy those attack platforms which are located one cell away from a fixed board. (Example: The Knight at Na4 is able to leap to the b1 cell of an attack platform located at Ba4d, and vice versa.) JUSTIFICATION OF ATTACK PLATFORM MOVEMENT With the attack platform movement completely dependent upon occupying pieces, this results in diminishing control as the game developed. Restricting movement of particular attack platforms to their particular side of the playing field would create points of contention between the players. Theoretically, there could result in the position where both players have lost all their power pieces and subsequent possesion of the attack platforms, and their Kings are stranded on seperate fixed boards. But this would be extremely rare and could basicly be judged a draw. As the game progresses, control and positioning of the attack platform plays a vital part of the game. As it should, since these unique features are what distinguish this 3D playing field from others. Utilizing the power pieces to determine the exact movement of the attack platforms creates interesting strategies, both offensive and defensive. It also allows for quick development in the opening game. Basicly, the attack platforms now become another piece within the game, neutral and dependent. JUSTIFICATION OF THE INITIAL SET-UP Since the attack platforms were to be commanded by the power pieces, it was determined that they should be balanced from the start. The standard start pattern of 2D chess would translate very well for this condition. Placing White attack platforms in their 'down' position was to mirror Black attack platfrom position. It was both logical and necessary, so that both players would begin the game on equal footing. SUMMARY Most want to know what was that "Eureka Moment" which lead to the development of the rules for the Kobayashi Maru Variant. While I was attempting to create a bitmap for the use of keeping track of both e-mail and snail-mail games, I noticed that the attack platform points on each side of the playing field create an interesting pattern. I could easily see those orthogonal and diagonal slides through this pattern but what ultimately established my path was when I realized that a Knight move could translate within the pattern. And even cover all the points. The fact that the diagonal moves resulted in two identical patterns further cemented the rules that power pieces could command the attack platforms. All the other rules seem to just fall into place. Having attack platforms remain on their particular side of the playing field was just a logical extension of their movement. Allowing Pawn promotion on the attack platforms which reach the farthest point of the field was to compensate for the weakness of the outside Pawns, and actually created a very nice point of early contention between the players. The triagonal capture move was to help the two central Pawns on the fixed board remain in play throughout the game. The decision to have only orthogonal and triagonal changes in levels was both so the Bishop would remain bound to half of the playing field and to ease the players' visualization of offensive and defensive patterns. All in all, I believe that the 3D chess player will find this game a definite challenge. ------------------------------------------------- Send all comments to: llsmith@ev1.net -------------------------------------------------- FOOL'S MATE IN THE KOBAYASHI MARU VARIANT OF ST3D CHESS 1. WQA-Wa4u BQA-Ba1d 2. WQA-Ba4d++ --------------------------------------------------