Sha'rah

There's only one "king", but it belongs to neither player. Winning condition is to move or direct the king to a square of your own color (red or green) or to clear the board of your opponent's "major pieces". 

I haven't ever played it, so I don't know if it works in reality. Maybe too many pieces (?), but the books that mention the idea had all of 33 pieces per player. 

Inspired by the description of a game in a work of fantasy, but not completely true to the description. Also inspired by Ultima, Maxima and Rococo.

Setup

The rim of the board is unoccupied at the start of the game. The inner 11x11 part is available to the players at the start.
Green's (instead of black) starting position:
Green's 2nd rank (files b to l) - AZIWIGIWIAA
Green's 3rd rank (files b to l) - UUUUUUUUUUU
Green's 4th rank (files b to l) - PPPPPPPPPPP

Red's (instead of white) starting position:
Red's 4th rank (files b to l) - PPPPPPPPPPP
Red's 3rd rank (files b to l) - UUUUUUUUUUU
Red's 2nd rank (files b to l) - AAIWIGIWIZA

The fisher king belongs to neither (or both) players. It occupies the center square (the g7 square). The fisher king is colored black and white.

(The entire board is 13x13.)

Pieces

F=The Fisher King    The fisher king moves like an orthodox chess queen, and captures by displacement. The fisher can never be taken off the board, so it’s immune to that.

P=Pawn    Pawns are berolina plus pawns, but always have a double step option, even after their first move. They can’t change direction during a move. They move 1 or 2 steps diagonally forwards in either direction when not capturing, and they take out enemy agents either 1 step to either side (orthogonally) or 1 step orthogonally straight forwards. 

U=Guardian    Guardians jump like a knight in the forward directions or they move 1 step diagonally forward, thus reaching at most 6 squares (4 jumping as a knight and 2 moving diagonally). They take out enemies by displacement the same way they move. 

G=The Gambler    The gambler moves as an orthodox chess queen (but doesn’t have the inherent capturing capacities that an orthodox chess queen has), and uses the type of capture or other power (displacement capture or immobilization, for instance) that any victim has upon the victim itself. The gambler immobilizes an immobilizer, given the right circumstances, captures a withdrawer like the withdrawer would have (had the situation been reversed), and so on … The gambler can never be immobilized itself. Multiple powers may be exerted by the gambler with the same move, affecting multiple targets. It may capture a withdrawer by moving directly away, and then take out a pawn or a guardian by displacement capture (and it can take out a pawn from a direction that the pawn couldn’t have moved along if it had been the opponent’s turn to make a move, and/or from a distance beyond the reach of a pawn’s move). The gambler still can’t take out the fisher. When taking out a guardian, for instance, it will move like the orthodox chess queen (not as the guardian), but it will use the guardian's displacement type capture when taking it out.

I=Immobilizer    Immobilizers move like orthodox chess queens, but can’t ever take out any piece. Instead they immobilize enemy agents, except for enemy immobilizers and the gambler, on adjacent squares (diagonally or orthogonally adjacent). They also immobilize the fisher. Regardless of who controls the fisher, if the fisher is adjacent to an immobilizer of either color, then the fisher is immobilized. 

W=Withdrawer    Withdrawers move as orthodox chess queens (but don’t have the inherent capturing capabilities that an orthodox chess queen has). They capture enemy agents that are adjacent (either orthogonally or diagonally) by moving in the opposite direction. The withdrawer may move unhindered (if no obstacles are in the way) all the way to the outer rim of the board when making a capturing move.

A=Advancer    Advancers move as orthodox chess queens (but don’t have the inherent capturing capabilities that an orthodox chess queen has). They capture enemy agents whenever they end up on a square adjacent to the victim, but the victim must be located adjacent to the capturing square in the same direction that the advancer traveled in. Thus only one enemy agent may be taken off the board each time an advancer moves.

Z=Zapper    The zapper moves as an orthodox chess queen (but doesn’t have the inherent capturing capabilities that an orthodox chess queen has). Zappers have two ways of capturing agents, either by custodian capture or by jumping the nearest agent along a diagonal or orthogonal line. They can move like an orthodox queen even when they’re not making any captures, and don’t need to jump any agent in order to move. Custodian capture means that the zapper actively moves into capturing position (either diagonal configuration or orthogonal configuration), and “sandwiches” an enemy agent in between itself and another friendly agent. The captured agent must be adjacent to both the zapper and the other agent for custodian capture to work. When jumping an enemy agent the square immediately beyond the jumped agent must be unoccupied. Then the jumped enemy agent is forever removed from the board. The zapper is even allowed to jump friendly agents, if the square immediately beyond it is unoccupied, but then the jumped friendly agent will remain in play.

Rules

Change of rules from orthodox chess:
¤ There is no castling, no checks, no mates, and no en passant. No royal piece exists, at least not in the orthodox sense.
¤ The player with the red agents moves first, and then the player with the green agents moves second, then they alternate – one move made each time it’s a player’s turn to move the pieces. The Fisher is a black and white piece, and belongs to neither player. 
¤ The game is played on a (mostly) black and white checkered 13x13 board instead of an 8x8 board, but only the inner 11x11 part of the board is available to both players at all times. Either player may step onto a square of their own color along the rim of the board (even when not taking out an agent or immobilizing it), or they move to ANY square along the rim if the moved agent takes out an enemy agent or immobilizes any agent during the same move. The fisher may not step onto the rim unless it captures an enemy agent located there. The player with the green pieces, for instance, may not just move the fisher onto a square that is green, unless it captures an enemy agent there.
Most squares on the board are black ones, and less than half are white ones. The four corner squares are black, for instance. The squares on the outer rim that would have been white along green’s half of the board are red instead, and the squares on the outer rim that would have been white along red’s half of the board are green instead. That means there are 12 red squares and 12 green squares.
¤ The player that first reaches his/her 10th rank (out of 13) with any of his/her agents will at the end of the move either take control of the fisher king himself/herself, or pass it to the opponent. If the control of the fisher is passed, then it can’t be passed back or taken back by free choice later. Whoever controls the fisher must take out enemy agents if the fisher can take out any enemy agent. If choices are to be had among the fisher and the player’s own pieces, then it’s up to the player to pick which one to take out and how. The player may capture enemies with an advancer, even if the fisher could capture some other enemy agent.If the fisher is immobilized by the opponent when the first player to reach his/her 10th rank does just that, then control of the fisher can still be seized (or passed, the player's own choice) by the player, but it still is immobilized.
¤ Once any agent is located on the outer rim, it may move along the rim without restraints for as long as it still travels along the rim. That goes for the fisher as well, but if the fisher can take out any enemy agent, then the player is forced to take out one of them (with the fisher or with another piece).
¤ Control of the fisher passes to the opponent with any of these occurrences: 1) The fisher gets immobilized by moving into immobilization or by the movement of an immobilizer(it can always be immobilized by either player’s immobilizers); 2) The opponent “sandwiches” the fisher by moving his/her zapper into custodian type configuration with the fisher; 3) The fisher steps onto a black square on the rim of the board; or 4) Either player’s gambler gets taken off the board. If two of the mentioned criteria are fulfilled at once, with the completion of the same move, then control of the fisher is NOT passed, since it would be the same as a "double pass".
¤ Pawns and guardians promote to advancers on the player’s 10th rank.
¤ The game is won if the fisher ends up on a square of one’s own color, or if the board is cleared of all the opponent’s major pieces – those are advancers + the zapper + the gambler.