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Mapped Chess

Introduction

This game presents a new idea, which consists in mapping a complicated 8x8x8 levels chess game on two levels, using a unique set of standard pieces and two affordable boards.

The aim is to retain the feeling of 3D Chess while still being a 2D Game easily comprehensible. Indeed, the flaws usually attributed to 3D Chess are avoided: difficulty to visualise, difficulty to manage when dealing with too many pieces, difficulty to maintain pieces strength balance going from 2D to 3D, and most of all, difficulty to lead to an end by checkmating a constantly fleeing King.

In the following description, pieces keep their relative strength, while gaining more control squares (twice as much in fact), and the King is less mobile than in complete 3D Game.

Setup

The setup consists in two boards, one representing the odd levels and the other the even levels. The boards are put side by side, but oriented 90°, so that white squares on one board correspond to black's on the other. The initial Pieces positions are the usual ones, on one of the boards.

Pieces

The pieces are usual ones with the addition, in a second variant, of a set of white and black "Protective Pawns" (see below), possibly with some marks to distinguish them from normal Pawns, placed on the corresponding locations on the other board.

Rules

The rules are the traditional Chess Rules for en-passant capture, promotion, initial two-steps, castling, checks, mate, stalemate... The Objective is still to checkmate the oponent King. But the Pieces have extended movements coming from 3D liberty: First, the Knight: As in 3D it controls squares arranged on a spherical shell (respecting a 2 by 1 jump in any direction), when you decide to map this on two boards, one for odd levels and one for even ones, you first get additional controlling squares of four orthogonal steps on the current board, and four orthogonal jumps on the other. Next the Bishop: In 3D, it moves across the squares edges in 12 directions, remaining on the same colour. When you map this on the even and odd levels boards, you get additional orthogonal moves alternately on the two boards. The Bishop gets thus an additional truncated Rook movement ! Of course, any piece standing in its way on either board interrupts the move. Then the Rook: I chose to merge the usual Rook in 3D (orthogonal moves in 6 directions) with the so-called Unicorn triagonal movement (across the corners of the cubes). There are two reasons for this: One is that it appears natural for the rook to move along alternate colours. Second, the analysis reveals that the Rook needs exactly those additional movements to keep its relative strength. When mapped on two boards, the "super" Rook now gets additional diagonal moves alternatively upon them. Hence, it receives Bishop-like truncated movement. Like the Bishop, any piece placed in between hinders its way. It is interesting to note the symmetry between Rooks and Bishop about their mutual displacements. And finally, you'll not be surprised to find the Queen as a combination of Rook and Bishop (in fact, some movement being redundant, the Queen looses a bit of its relative strength) the King has got one step Queen movement and is able to castle (also it may not be justified) the Pawn get a complementary Bishop (for capture) and Rook (for advancing move) one way step movement. But it can ONLY move without capture when none of the controlled squares are occupied, and it can make double move initially, and promote. In the second variant (recommended), "Protective Pawns" placed on top of the others on the other board, can neither move nor capture, but can be captured by enemy: their role is to proect initially the King from direct attacks. Globally, each piece has twice as much squares under control for double space, so that their relative strength remains the same (according to ZOG, if the Pawn value is 1, the Queen gets about 9, the Rook 5, the Bishop 4 and the Knight 3.5. However, they control two to three times more squares on their current board compared to the other board, asymmetry that one should keep in mind when seeking a strategy.

Notes

We have checked that a bare King can be mated against the following combinations: (K+Q), (K+R+R), (K+R+N), (K+R+B), (K+B+N).

We can now proceed to show a simple test Games. The first one was (badly) played by Zillion of Game engine against itself, but gives a feeling of the Play. Capital letters correspond to the second board.

We can see the pressure of the black pieces building up around the exposed King until the final sad fate occurs.

1. Ke1 - E1 Rh8 - E5+

2. Pd2 - E3 Qd8 - A5+

3. Pb2 - C3 Nb8 - c6

4. Pa2 - c4 Pa7 - c5

5. Nb1 - B3 QA5 - D5

6. Ra1 - B2 Ph7 - G6

7. Bf1 x f7+ Ke8 x f7

8. RB2 - A2+ Kf7 - e8

9. Qd1 - C2 PG6 - G5

10. Ph2 - G3 Ng8 - f6

11. Rh1 - f3 QD5 - H1+

12. Bc1 - F1 QH1 - G1+

13. KE1 - E2 Nf6 - e4+

14. KE2 - D2 Nc6 - d4+

15. KD2 - D1 QG1 x F1+

16. KD1 - d1 QF1 x g1+

17. Kd1 - C1 Nd4 x f3

18. Pg2 x f3 Bf8 x f2

19. QC2 - f5 Ne4 - c3+

20. KC1 - D2 Qg1 - e1+

21. KD2 - D3 Qe1 - e3 mate

0-1

The second longer one I find more instructive:

We follow the white pieces building up a safe place for their King on the other board, then harass the enemy King from one side of the board to the other side by vicious checks that pick up a few pieces in passing, until finally the black King falls.

1. P a2 - a3 R h8 - d4

2. N g1 - f3 R d4 - a4

3. N f3 - e5 P d7 - f5

4. Q d1 - b3 R a4 - a5+

5. B c1 - c3 R a5 x c3

6. R a1 x c3 N g8 - h6

7. Q b3 - b5+ P c7 - c6

8. Q b5 - E5+ P e7 - e6

9. Q E5 - E6 Q d8 - h4

10. N e5 - f3 Q h4 - H4+

11. K e1 - D1 B f8 - f6

12. Q E6 - C8 B f6 x c3

13. N b1 x c3 Q H4 - H5+

14. P e2 - F3 Q H5 - B5

15. Q C8 - C2 R a8 - A8

16. R h1 - H1 N h6 - g4

17. N c3 - b3 R A8 - D8+

18. N b3 - D3 N b8 - d7

19. R H1 � H7 R D8 - G8

20. P h2 - G3 Q B5 - A6

21. R H7 - H5+ K e8 - D7

22. Q C2 - F2 N g4 - e5

23. N f3 x e5 N d7 x e5

24. Q F2 - D4+ K D7 - E7

25. Q D4 - E4+ K E7 - d7

26. Q E4 - d4+ K d7 - E7

27. R H5 - H7+ K E7 - F6

28. R H7 - H4+ K F6 - E7

29. Q d4 x e5 P g7 - F6

30. R H4 - E4+ K E7 - f8

31. B f1 - h1 K f8 - g8

32. B h1 - d1 Q A6 - B6

33. Q e5 - g5+ K g8 - F7

34. Q g5 - D5+ K F7 - g8

35. Q D5 - d8+ K g8 - G7

36. Q d8 - D7+ K G7 - h6

37. Q D7 x c8 Q B6 - B1+

38. K D1 - e2 K h6 - H7

39. Q c8 - D7+ K H7 - g8

40. R E4 x b7 R G8 - G7

41. B d1 - D8+ K g8 - G8

42. R b7 x f7+ K G8 x f7

43. B D8 - d7+ K f7 - f6

44. Q D7 x G7+ K f6 - e5

45. N D3 - E3+ K e5 - d6

46. Q G7 - C7+ K d6 - c5

47. Q C7 x c6+ K c5 - B4

48. B d7 - D6+ K B4 - A5

49. Q c6 - a6 mate

1-0

These Games let one imagine the wealth of new situations that can occur in the Game, with very strong threats from long range pieces which can now in some way jump over obstacles in the current board through the other board.

The Queen is especially dangerous, although being slightly less powerful than in 2D, when she approaches with support of the enemy King from the other board.

Finally, The Game was edited in the english "Variant Chess" Magazine Vol.7, issue 54



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By Stephane Burkhart.
Web page created: 2007-10-18. Web page last updated: 2007-10-18