This game flows on the annular ranks, annular diagonals and annular files, as well as on the two polar squares. The two polar squares are of an increased value as the 66 squares are fully used here. The pieces can pass symmetrically over squares X and Y, and can also be positioned over these squares.

In this third version of the game the polar squares (X, Y) behave as squares with a higher value. A piece positioned on one of these polar squares influences all files and diagonals on the sphere. Its influence can only be lessened or neutralized by other pieces on the board.

In this version, the pieces do not have to run into the edges and corners of the board, so the potential of the pieces is at their maximum in the horizontal, vertical and diagonal directions. The neutral polar squares known from the optimal version of the game become high-value squares since from the polar squares every square on the boards can be reached. So the opponent’s pieces can be harassed from any direction, starting from the X and Y polar squares.

In the opening, the pieces have fewer opportunities to switch files and diagonals through the polar squares since the pieces around the polar squares represent an impenetrable wall.

To open a corridor it is necessary to have a vacant polar square and also have vacant squares behind it. The pieces symmetrically pass over the corridors, for example Qd8 - Y - h8 - h4, Rh1 - X - d1 - d6. With the opening of a corridor the more demanding (and harder) version comes into play.

With the opening of files and ranks a piece positioned on a higher - valued polar square exerts total coverage and this way the maximum version of the game is achieved. In the endgame pieces will be usually positioned on these squares and exert all their positive and negative influence (total coverage). This requires strong combination capabilities and maximum concentration from the players.

The Rook
The rook can move both on the files and the ranks. The rook on a1 can reach 23 other squares (7+1+8+1+7=24-1=23) from both directions similar to the optimal version, though its capabilities are enhanced here with the use of the polar squares (the X and Y active squares). Over the polar squares the rook can travel to all of the 65 other squares, thereby covering the files.
The Bishop
The bishop moves on the diagonals and the polar squares. The bishop’s possibilities are further enhanced here with the use of the two additional X and Y squares. An innovation: In this version the player has an option to switch the color of the squares on which the bishop moves when it is on a polar square. Thereby the term “bad
bishop” known from classic chess theory loses its justification, because from now on the player chooses on which color the bishop will operate after it leaves the polar square. For example: the bishop is capable of holding the opponent’s pawns on squares of any color. On the other hand, it can follow the march of the player’s own pawns, or it can defend the square before the pawn from the polar square. This way it is always possible for a player to acquire a bishop of the needed color using the polar squares. At the same time the player can have two bishops moving on the same diagonal, that reinforce each other. The bishop’s value has considerably increased this way. By stepping on a polar square the bishop positions itself behind the other pieces in their starting position. This way the bishop not only strengthens the defense in critical moments, but it’s also ready to lash out on diagonally once its movement becomes free. Standing on a polar square the bishop can help in the attack of the other bishop that has been moving on a different color until now. For example the bishop on X reinforces the bishop on c1.
The Queen
The queen moves on the sphere like the bishop and the rook combined. On an empty sphere the queen can reach all of the remaining 65 squares if it moves like a rook from the X square, and the same 65 squares moving like a bishop. This way the queen is the piece with the greatest power in this version of the game. Going in the other direction (through the Y polar square) the number
of possible moves is doubled, 130 + 130 = 260. The white queen on a polar square delivers checkmate to a lonely black king.
The Knight
The knight can reach 16 squares from the polar squares. For example the knight on X can exert influence over ranks 1 and 2 (a1, a2, b1, b2, c1, c2, d1, d2, e1, e2, f1, f2, g1, g2, h1, h2). This means that it can reach X from the listed squares in a single L – shaped move, e. g. Nc2 – X, Ne1 – X or can leave X: NX – c2, NX – e1. The knight on b1 has the following squares within his reach: a3, c3, h2, d2, g1, e1, X.
The knights influence is greatly enhanced on the Ambit Chess Sphere as until now it couldn’t reach h2 (Nb1 – b2 – a2 – h2), g1 (Nb1 – X – f1 – g1), e1 (Nb1 – X – f1 – e1) and X (Nb1 – c1 – d1 – X). By moving to the polar square the knight gets behind its own pieces thereby strengthening the defense.
The King
The king can move to any adjacent square, if it’s not occupied by another piece of the player or the opponent. The king can move to the X polar square, from where it can easily reach the first and last rank of any file. By moving to the polar square the king gets behind his own pieces. In certain stages of defense the king strengthens the defense on the base rank around him. At the end of the game the king becomes an active piece and should not be separated from his pawn. The pawn too is important mainly because the king can hide behind it.
Castling
The pawn
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.
Summary:
1. Players should first get comfortable with the simple and easier version first. 2. The optimal version of the game is recommended for advanced players, where the neutral polar squares are utilized. 3. If you are familiar with the simpler versions of the game then you can advance to the ultimate version, where higher-valued polar squares are used (X, Y).