I’m not saying this is a good version of this idea, or even that this is a good idea.
But it SHOULD be playable…

*There are three colors of pieces, white, black, and red.

*Black and white are both lines up on one side of the board, with the white pieces being the left half of each line, and the black pieces being the right half. There is no queen, instead both black and white have kings.

*Red pieces are set up normally on the opposing side.

*One player runs the white pieces, and one runs the black pieces. They work together, and are considered to be on the same side (for example, their pieces cannot capture one another).

*The red pieces represent the opposition, and their movements are determined randomly.

*White moves first. Then red. Then black. Then red. Repeat this sequence until a king is in checkmate, or normal rules of chess would indicate a draw.
*Number all of the Red pieces, 1-16, starting with the pawn on A7, running right to H7, then moving up to the rook on A8, and running along the back row to H8.

*On Red’s move, move it’s pieces by following these priorities:

1. If its Red’s King is in check, it takes a legal move to capture the piece placing its King in check (if this removes the King from being in check from any piece), block check, or remove the King from check. If multiple such moves are possible, Red prefers capturing a checking piece, then moving the King out of check, then using another piece or block the King. If multiple such moves exist determines which move it makes randomly.

2. If Priority 1 move does not occur, and a Red pieces is in a square where a black or white piece can capture it on the black/white’s next turn, and the piece can legally move to where that will not be true, it does so. If it can capture an opposing piece with this move, it does so (see Priority 3 if there are multiple pieces it can capture).

Otherwise it moves the fewest squares it legally can to move to a square where it cannot be captured on black/white’s next move. If multiple such squares exist, select which one it moves to randomly.

If multiple Red pieces can fulfill priority 2, move the one that is of the highest value. If multiple pieces of the highest value exist, move the one that can capture an opposing piece. If none can capture, determine which one moves randomly.

3. If a Priority 1-2 move does not occur, and Red has a piece that can legally capture a black or white piece, without exposing its king to check or ending in a square where a black or white piece can take it on their next move, it does. If there are multiple such legal captures, it takes the highest-value piece it can. If there are multiple such captures of pieces of the same value, determine which one it takes randomly.

4. If a Priority 1-3 move does not occur, and Red has a piece that can legally capture a black or white piece, without exposing its king to check, but doing so leaves it in a square that can be immediately taken by a black or white piece on its next move, roll 1 six-sided die. On a 1-3, the Red pieces makes the capture. On a 4-6, it does not. If there are multiple such captures possible, roll once to see if Red makes any such capture, and if it does use the rules from Priority 3.

5. If a Priority 1-4 move does not occur, and Red has only a single legal move, it takes it. This is true even if it is a move that was ignored during Priority 3.

6. If a Priority 1-5 move does not occur, roll three dice, total them, and subtract 2 from the sum. If the result is 1-16, and that Red piece is still on the board, move the piece matching that number. If that Red piece is no longer on the board, go to Priority 7.
6a. If the piece is a Red pawn, and it can move to the Black/White home row without ending in a square where it can be captured by a black/white piece on its next turn, the pawn takes the move and is promoted to a Queen. It retains its original numbering.
6b. If the piece can move to a square where it could take a black or white piece on its next move, it does so. If there are multiple such squares, it selects the one with the fewest black or white pieces able to take it on their next move. If multiple such squares exist, determine which one it selects randomly.
6c. If no move is indicated by Priority 5a, make a legal move that goes as far as that piece can go, in a randomly determined direction, that does not end with it in a square where it could be captured on black or white’s next move.

7. If the Red piece indicated by the die roll is no longer on the table, instead move the remaining Red piece with the closest number. If two remaining Red pieces are equidistant in numbering, go with the lower number if the result was odd, and with the higher number if the result is even.
7a. If the newly-selected Red piece can legally capture a black or white piece, it does. If this would expose its King to check, the King is moved in a randomly determined direction however many squares are needed to keep it out of check, in ADDITION to the Red piece making a capture. If there are multiple black/white pieces the Red piece could capture, use the preferences from Priority 3.
7b. If the newly-selected Red piece cannot capture a black./white piece  with a legal move, it is moved in the following manner. Roll 1d6 and add one. This is the numbered row the piece moves to. Roll 1d6, with 1 being B, 2 C, 3 D, 4 E, 5 F, and 6 G. This is the column in that row the piece moves to.
If there is a black or white piece in that space that is not a King, it is captured, if there is a black or white King in that space, the Red pieces is captured. If there is a Red piece in that square, the higher value of the two Red pieces takes the square, and the other is capture. If the two red pieces are of the same value, determine randomly which one gets the square.

*If either the Black or White king is placed in Checkmate, or if both are ever in Check, Red wins. If the Red King is ever in Checkmate, black and white win.

PATREON
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