Since then, I've pondered some simplified versions of the game (if you're going to do the probabilistic moves, the rest of the game had better be dead-simple), but they all still wind up requiring a computer to mediate. Last night, I found myself contemplating (much of the night) how to build a board game somewhat in this spirit, which was playable by real people without a computer. The result was what I'm calling "Ice Checkers".
Equipment: The game is played on a conventional checkerboard. Each player has three colors of Icehouse pyramids, to serve as his playing pieces; specifically, he uses 12 of the 15 pyramids in each color. (For those who don't play it, Icehouse is a family of games invented by Andy Looney and expanded endlessly since then. Each player has one or more sets of colored pyramids, usually 5 each of small, medium and large. The pyramids are constructed such that they can be either nested or stacked. For purposes of this game, we'll do stacking, with smaller pyramids on top of larger ones.)
Setup: Each player takes one color of his pyramids and places them on his back row of the board (only on one color, as in Checkers), one small-medium-large stack on each space. He takes a second color and places it on the second row. He reserves the third color to be used as Kings. (Given the chaos to ensue, I don't think we need to fill the initial board as full as in normal Checkers.)
Basic Rules: Movement is as in Checkers. Ordinary pieces move diagonally forward one space, or jump (and capture) an opposing piece. Kings can move backwards as well.
Simple Ice Checkers: The strangeness of this game is that, each turn, you must move one small, one medium and one large pyramid, but they can be any of these, not necessarily from the same square; even when they are from the same square, they don't have to move the same way. Pieces only interact with other pieces of the same size: so for example, smalls can only capture other smalls. You can wind up sharing a space with enemy pieces of different sizes. When a pyramid reaches the far rank, only that pyramid promotes to a King; you don't get a whole new stack. In this simple version of the game, you effectively have three checkers games running in parallel on the same board. The winner is the player who wins at least two of those games. (That is, when all is said and done, he has men of at least two sizes left.) The distinction between the colors doesn't matter in this variant.
Variation -- Cross-Captures: This is where things begin to get interesting. This variant works like the simple game, but with one additional twist: larger pieces capture smaller ones. They can still occupy the same space, but a large can jump over a medium capturing it. Thus, the three otherwise separate checkers games begin to interact with each other. (A possible further variant is to make the cross-captures run in rock-paper-scissors style: large captures medium, medium captures small, small captures large.)
Variation -- Quantum Ice Checkers: This is actually where I started; the above are simplifications. Quantum Ice Checkers adds another twist. A player may skip both his current move and his next one, and instead call "Collapse". At this point, both players must meld their pieces back together again, to make complete small-medium-large stacks. Stacks must be of a single color (so the multi-color opening matters, as does the fact that Kings are a different color). A space that held a complete stack remains unchanged; partial spaces must be combined, with some vacated and others filled. Any pyramids that are left over wink out of existence. If both players attempt to fill the stack in a space they shared, both stacks are annihilated.
I have no idea of whether the game will prove to be interesting: it's distinctly possible that the degenerate case of basic Checkers is actually the best strategy, in which case the game isn't very interesting. (In which case I might try yet a further variant, actually changing the movements of the different sizes, so that you cannot play the degenerate game, but that violates the "quantum" concept a bit.) But it would be interesting to try it out, and see if it's worth playing -- I may have to bring my pyramids over to mindways's sometime, to try this...