Ordinarily in chess the outcome of a confrontation between two pieces is predetermined: whichever piece gets the jump on another wins, even if somehow it can be contrived to have a pawn take a queen. The “strength” of the pieces is in the freedom of moves they can make. But suppose you make the outcome non-determined? Let’s say that each class of piece has offensive and defensive stats, so an “attack” by an opposing piece has a greater or lesser chance of succeeding? So for example a queen would have a significant chance of fighting off a pawn, with the pawn being taken as a result; while a pawn would have a tiny but non-zero chance of defeating an attack by a queen.
Slightly related: there’s a version of chess where players write down their next move on a scrap of paper. They reveal simultaneously. Like regular chess, the moving piece always removes the piece it lands on from the board. (If both moving pieces move to the same square, they both get removed.)
Different wrinkle: On your turn, you can simply remove one of your own pieces from the board instead of moving a piece. It’s gone, out of the game. This might sound like you’re weakening your board but getting a pawn out of the queen’s way can be a huge win.
