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The Game Courier preset isn't linked to game's page.

In a different note, what if the game was played with Marseillais Chess
style? That is: at each turn, except white's first, the player makes a
move, move a square, than makes another move.

If you implement the moving board by simply covering the squares that are supposed to be holes with an obstacle, as I suggested below, you would not have that problem. You could use draughts chips for marking the holes, but it would perhaps be nicer to have some square tiles of a third color that completely cover the squares.

This is much more likely to work than actually trying to construct a board where all squares can move.

What's the command to slide the squares for this?

At present, the Game Courier preset for Amoeba will not let you make any move at all. The only line of code in it is the conserve command, which will now give an error message that it has been removed. Until someone can make one that does enforce rules, I have made one that doesn't at

/play/pbm/play.php?game%3DAmoeba%26settings%3Dbare

In this one, you can move a space with two moves. First, delete a space by preceding it with a hyphen, then add an empty space to it. You can do this by adding an @ to the space, or by moving the "piece" on the space nowhere. So, assuming you want to move the space at d3 to d4, your move could look like "-d3; @-d4" or like "-d3; d4-". Using commands, which are not banned in this bare preset, but which could be in a programmed one, your move could look like "delete d3; add @ d4" or "delete d3; empty d4". The delete command deletes a space from the board, while the empty command empties a space of any pieces, a side effect being that it will undelete any deleted space. Alternately, you could move the "piece" on one space to another, then delete the origin space. For example, "d3-d4; -d3". In a game that allowed it, this notation would have the advantage of letting you move a space with a piece on it. But that is not allowed in Amoeba.