2. The optimal version of Globe – chess
The game flows on annular ranks, annular diagonals and annular files (64 squares are used fully and 2 squares partially). The pieces can pass symmetrically over squares X and Y, but can’t be positioned on these squares.

In this version of the game the polar squares (squares X, Y) behave as neutral squares. Even though they exist, they are not used in practice (pieces cannot step on them).
Compared to the first version of the game now even the lower and upper edge of the chessboard disappear (next to squares X and Y), consequently the movement of pieces is unobstructed even in vertical direction. A new opportunity is to move from the first square to the first square of the opposite file, or from the last square to the last square of the opposite file. Thereby the edges and corners of the traditional board are removed from every side and as a result of this the power of the pieces is enhanced in vertical, horizontal and diagonal direction. From now on, the movement of pieces can only be hindered by each other.

In the optimal version of Globe – chess all unfavourrable effects of the traditional chessboard are eliminated, but a new positive effect is created with the 2 neutral squares! (an opportunity to pass over the polar squares). The function of the neutral squares enables further development of the agility of pieces. The opponent’s pieces can be attacked from any direction – meaning around the sphere, from left and right, up and down – within the observance of rules. Every square has its neighbouring squares. All the 64 squares could be regarded as central squares of equal value and therefore the pieces can move in optimal conditions exerting their maximum influence. The difference in the value of the respective squares (which depends on the current position on the board) can be modified only by the strength and potential of the pieces. This is a great development compared to the classic board, where these differences in value originate in the effect caused by the edges and corners of the board! (The closer we get to the edge or corner of the board the worse our position gets).
On the traditional board the target square can be reached from a given square from only one direction, e. g. the rook, the bishop and the queen can attack or defend a square using only one route.
On the other hand, these goals can be achieved using several routes on the chess – sphere. The easiest way is to use 2 routes, but it is also possible to create 4 routes on the four sides of the sphere. The queen’s combined movement (rook – bishop) further enhances the number of possible routes.


  
The rook (figure nr. 8)
The rook moves on vertical files (across neutral squares) upwards (Ra1 – a2, a3, a4, a5, a6, a7, a8, Y, e8, e7, e6, e5, e4, e3, e2, e1, X) and downwards (Ra1 – X – e1, e2, e3, e4, e5, e6, e7, e8, Y, a8, a7, a6, a5, a4, a3, a2).
On horizontal ranks the rook moves around the sphere to the right (Ra1 – b1, c1, d1, e1, f1, g1, h1) or to the left (Ra1 – h1, g1, f1, e1, d1, c1, b1).
A given square can be reached from two directions on every rank and file. The rook on a1 can reach the opposite square e1 using four different routes. In case of annular movement empty ranks and files are required. A rook can check the enemy king from four different directions, from left and right (horizontally), upwards and downwards (vertically).

  
The bishop (figure nr. 9)
The bishop moves on diagonals of a given color. Compared to the classic game its value has enhanced, because it can symmetrically pass over the neutral polar squares and cross the invisible border between the a) and h) files. The bishop moves in an „S“ pattern over the polar squares.
The path of the bishop from c1 to the right is as follows: Bc1-d2, e3, f4, g5, h6, a7, b8, Y, f8, e7, d6, c5, b4, a3, h2, g1, X, c1. The bishop always steps diagonally to the next square to the right. This way it reaches b8, symmetrically passes over square Y to the f8 square and turning to the right it continues to g1. Its path seen from above resembles a big S letter.
The second option is going to the left from c1 to g1: Bc1 – b2, a3, h4, g5, f6, e7, d8, Y, h8, a7, b6, c5, d4, e3, f2, g1, X. Over square d8 symmetrically passes over the neutral square to the h8 square and continues to the left. Its path seen from above resembles a big inverted S letter.

The two routes cross each other on 6 squares and meet on one square: e3, g5, a7, e7, c5, a3, g1. Starting from the first rank they diverge left and right, on the 3., 5. and 7. rank they cross each other in a right angle and meet again on g1.
These intersections appear where the two big S letters cross each other. Attacking, reinforcement and checking (double check) is possible only on a free diagonal.
In the opposite direction the route passes over the neutral square X to the g1 square, here the route splits left and right and reaches the named squares from the opposite direction. This way it is possible to deliver quadruple check (or checkmate) at the same time on the highlighted squares of the 3., 5. and 7. rank.
Attention: A piece of the opponent can be captured only once. If three of four diagonals are closed by other pieces, it is still possible to attack or defend on the remaining diagonal. The only option in classic chess turns into four on the chess – sphere!
The ability of the bishop to attack a square using four different diagonals is a revolutionary concept in the history of chess, the grasping and utilization of which is the alpha and omega of the new game.

  
The queen (figure nr. 10)
The queen moves on the sphere like the bishop and the rook combined. From the first rank it exerts its influence over 21 squares if it moves like a rook, but the queen can reach 23 additional squares moving like a bishop. This way the queen is the piece with the greatest power. In case of Qd1 the powers of rook and bishop are combined in one piece and the route meets on 3 middle squares (besides the neutral squares): d5, Y, h5, h1, X. For the queen on d1 these squares are of a strategical importance. Naturally, depending on the movement of the queen, these meeting points vary.		  
The knight (figure nr. 11)
The knight on b1 can reach the following six squares: a3, c3, h2, d2, g1, e1. The power of the knight has also increased on the chess – sphere, because on the classic board it couldn’t reach h2 and over the neutral squares g1 and e1. For example Nb1 – X – e1, Nb1-X-g1.
The knight on b1 symmetrically passes over the polar square (in the direction of the opposite file) as follows: 1: X, 2: f1, 3: e1 or g1. These two possibilities provide the knight great defensive capabilities. Even though its a short – range unit, its strength (near the polar square) lies in the fact, that it can be captured only by a piece of a higher value. The knight can close down gaps in the defence before the enemy queen, bishop or rook.

  

The king (figure nr. 12)
The king can move to any adjacent square, if it’s not occupied by another piece of the player or is not attacked by an enemy piece. The king can move one square in any direction. It can pass over the neutral X and Y polar squares , if they’re not attacked
by enemy units.
The king cannot move to the polar square, so from the starting square it moves to the first rank of the opposite file, for instance Ke1 – X – a1. It goes to a1 without castling, so he can also escape in a vertical direction. He can reach the opposite vacant square with a move equal to castling. This variation of Globe – chess gives optimal capabilities to the king.

  
Castling (figure nr. 13)
A new option is, that if the knights, bishops (and the queen) leave the first or the eighth rank, the position after castling occurs aically (on the free annular rank). The position is then Ra1 – Ke1 – Rh1. This natural annular position gives the king protection from both sides.
On the annular first rank the king can castle either side, with either of the rooks. (On the left or right side with a rook that hasn’t moved yet).
  
The pawn (figure nr. 14)
If the pawn reaches the last rank (for white it is the eighth, for black the first rank), it is promoted to a chosen piece of the same color, except for the king. This new piece is immediately ready for action. The pawn cannot step on the X and Y polar squares, nor can it pass over them.		  
 
Summary:
Beginner players should learn the simple version of the game first. Then I recommend the optimal version of the game with the use of the neutral polar squares. In this version the pieces can pass over squares X and Y, but cannot be positioned on them. The left, right, upper and lower edges of the board disappear. The ranks horizontally, the files vertically and the diagonals diagonally become endless. The traditional disadvantages are eliminated (corners, edges and short diagonals). Very important is for the pieces to be positioned favourably as soon as possible. It is recommendable to put a piece to a protected square, which is especially important for an attacking piece. Pushed pawns should be protected. A needless loss of a pawn is hard to recover in the endgame.
The new attacking strategy of the bishops enabled by the structure of the chess – sphere is to be put into practice. When using bishops, their ability of using the two adjacent diagonals in order to effect the opposite diagonals has to be taken into account. The same goes for the rooks, which can enter the opposite file through the polar square, and for the queen, which combines the advantages of the mentioned pieces.

In order to acquire material or positional advantage it is necessary to pay more attention to development along the a) and h) files, contrary to the classic game. The main direction of the attack can be quickly shifted to these files (for instance a double – direction opening: 1) e2-e4, 2) a2-a4...). The plan has to be chosen according to our ability to create a harmonic cooperation between the pieces starting from their base rank, also having regard for support from the opposite files and ranks.

In defence it is useful to ensure multiple protection of the pieces (depending on the current position). This requires stronger concentration and stamina from the players. The players must count with the new three – dimensional possibilities given by the neutral polar squares X and Y during the whole game, and this is rewarded with un unseen increase of the pieces’s effectivity.
The 64 equally central squares give opportunity - for the first time in the history of the game – to use the traditional pieces in optimal circumstances (in a perfect environment for the pieces, because they have adjacent squares in every direction at disposal) so that they exert their maximum potential on the chess – sphere with its innovations and beauty.


 
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