I like your (1) and (2), although (3) and (4) seem like the sort of bookkeeping that could only be fun if you had a computer to keep track of them.
> 1) Start with all pieces off the board. To make a move, you can either put a piece onto your half of the board, or move an existing pieces. Captured pieces cannot be reused (or maybe they can, if you want some sort of bughouse variant).
Can a piece be moved into any unoccupied position on your half of the board, or only its usual starting position? Can this be done when your king is in check (in hopes of blocking the check)?
> This of course means you have a 1/4 chance of the opposing king being in check, in which case you can capture it and end the game right there.
I think I don't understand this. The Wikipedia page doesn't seem to describe the starting set-up, but I guess it's the usual one for chess. Are you referring only to the first move? (Otherwise it seems to me that the chance of check depends in an extremely complicated way on the game so far.) In that case, I agree that there's a 1/4 chance of one of the pawns that could check the king being the assassin, but you still have only a 1/2 chance of picking that pawn correctly (even if it's there), so it seems more like a 1/8 chance to me.
You can move to any unoccupied position in your half in (1). We didn't analyse it deeply tbh, mostly we'd just build an ultra-castle of some sort. And yes, you can put in a new piece to block check. We didn't initially realise this, but the king should be the first piece played, or obviously some smart alec will just leave it off the board.
With the assassins, yes it's just a normal setup. But if your first move as white is to turn over the black d7 or f7 pawn, and one of those is the assassin, then you get to take the king. If they're normal pawns, you've spent the move, setting you back in development. Probability-wise I just mean there's a 2/8 chance that it's one of these pawns.
That's not the setup. You don't have two assassins, you just have one assassin, so it's not 8 pick 2. But there are two squares the assassin can be on that give a move 1 mate. That gives the 2/8.
> Probability-wise I just mean there's a 2/8 chance that it's one of these pawns.
Right—there's a 2 in 8 chance that the assassin is one of those pawns, and a 1 in 2 conditional probability, given that one of them is the assassin, that the one you pick is the assassin; so, by 'deconditioning', a 1 in 8 chance overall.
(I think it might make this more plausible—just in terms of probability, not a better rule—to imagine that the rule is changed so that the assassin has to be one of the pawns who can check the king. Then the probability of one of those pawns being the assassin is 100%, by fiat; but you've still only got a 50% chance of picking that one.)
> 1) Start with all pieces off the board. To make a move, you can either put a piece onto your half of the board, or move an existing pieces. Captured pieces cannot be reused (or maybe they can, if you want some sort of bughouse variant).
Can a piece be moved into any unoccupied position on your half of the board, or only its usual starting position? Can this be done when your king is in check (in hopes of blocking the check)?
> This of course means you have a 1/4 chance of the opposing king being in check, in which case you can capture it and end the game right there.
I think I don't understand this. The Wikipedia page doesn't seem to describe the starting set-up, but I guess it's the usual one for chess. Are you referring only to the first move? (Otherwise it seems to me that the chance of check depends in an extremely complicated way on the game so far.) In that case, I agree that there's a 1/4 chance of one of the pawns that could check the king being the assassin, but you still have only a 1/2 chance of picking that pawn correctly (even if it's there), so it seems more like a 1/8 chance to me.