Mar 102007
Today's design is a twist on the venerable game of chess, via quantum mechanics (See...I warned you).
If you're the kind of savvy reader that hangs out at the Chrome Cow, you doubtless are familiar with a certain theoretical feline belonging to one Erwin Schrödinger. This cat has the misfortune to be confined in a box with a deadly device that has a 50-50 chance of triggering with an hour. At the end of the hour, goes the thought experiment, the cat, sealed from observation inside the box, is neither dead or alive, but is in superposition, a combination of these possible states. The cat does not live or die until the box is opened by an observer, who through the act of observation collapses the possible dead/alive states of the cat into one or the other state.
So what's that got to do with Chess? What, indeed!
Enter Superpositional Chess (Super Chess? EigenChess? Quantum Chess? Schrödinger's Pawn?).
Like Schrödinger's experiment with the Cat, mine too is wholly theoretical, so to follow along you will need the following imaginary supplies:
- Two Chess Boards
- Two Sets of Chess Pieces
If each player moved the same piece on each board to the same spot, the game would be identical to standard chess. It's when the two moves diverge that things get interesting.
In this example, the white Knight has two potential legal moves.
If, on the two separate chess boards, he moves to each of these legal spots:
So before things get too confusing, here are the rules:
Basic Definitions
- Each board is set up like a traditional chess game
- Both boards have the same color pieces facing the same player
- If two of the same type of pieces of the same color occupy the same space on both boards, that piece Exists in that space.
- Only one piece can Exist in one space at any given time.
- At the beginning of the game, before anyone has moved,
- All pieces Exist
- If two of the same pieces of the same color occupy different spaces on both boards, those pieces are Superpositional.
- See example above
- Only two Superpositional pieces of any color and any type can occupy the same space:
- Existing pieces take precedence over Superpositional pieces
- No move can be made that creates a Superpositional piece on a space occupied by an Existing piece
Player's Turn
- Movement Round
- Player may move a piece of his color on each board, OR
- Collapse a Superpositional piece
- Player chooses two Superpositional pieces of the same type and color
- Player moves one of those pieces to match the position of the matching type of piece on the other board
- That piece now Exists (this example follows on from the Knight example above):
Resolution Phase
Two Superpositional pieces of different colors may occupy the same space, but what happens when one of those pieces is Collapsed, and now Exists in that space?
Above we see four Superpositional pieces.
Black chooses to Collapse their Pawn. At then end of Black's turn, we have a Black Pawn that Exists in the same space as a Superpositional White Knight. This is not allowed, so White now has a Resolution Phase to correct the problem:
In the above example, White chooses to Collapse the Knight to the space not occupied by the Black Pawn. If White had chosen to Collapse the Knight to the same space as the Black Pawn, the White Knight would have been forfeit.
- The first piece to Exist in a given square captures any piece that comes to occupy that space in the resulting Resolution Phase.
- White's move requires a Black Resolution Phase
- Black's Resolution Phase requires a White Resolution Phase
- And so on...
Threat and Check
For Existing pieces, the endgame rules of Check and Checkmate are the same as regular chess. It is when we bring Superpositional pieces into the mix that we need new rules.Threat
- When a Superpositional piece is placed such that it can execute a capture move on a King (Existing or Superpositional) the next turn, the player that moved it there must announce "Threat"
- Threat is one step less serious than Check
- The player would have to spend their next turn Collapsing the piece for it to escalate into a Check:
- When an Existing piece is placed such that it can execute a capture move on a Superpositional King the next turn, the player that moved it there must announce "Threat"
- Threat is one step less serious than Check
- The Threatened player can Collapse their King to safety:
What about the case where two Superpositional pieces are threatening two Superpositional kings?
This is still classified as a Threat.
- A Check or Checkmate is only possible when an Existing King is in peril from an Existing enemy piece.
Optional Rules
Entanglement
- For all pieces except the king and queen
- Number the pieces
- Pawns 1-8
- Knights 1-2
- etc.
- When placing the pieces in their initial position
- Lowest number go on the left
- So the leftmost pawn is #1, the rightmost #8
- Leftmost Knight is #1, rightmost is #2
- You may only collapse pieces
- Of the same Color
- Type, AND
- Number
Final Thoughts
This game (I kind of like the name EigenChess) might be a great way to introduce young Chess players to the world of quantum mechanics, and build up some intuition for some of the non-intuitive aspects of that branch of scientific inquiry.If someone really wanted to play this on an ongoing basis, the easiest approach is probably a software solution to manage the boards and states of the pieces.
However, you could also set up two physical boards, place a top-down video camera over each board and then superimpose the two video streams, which would give you a result like the Superpositional Board used in the above illustrations.
Either way, drop me a line and let me know how it works...};^)
-game over-
Thanks for reading another action-packed installment of Design a Day. For background on the Design A Day challenge, take a peek here and here.
By far the coolest chess variation I’ve ever seen. Thanks for the great ideas!
The final graphic show the Board B incorrectly — the pawn is one space to the right, checking the king on that board, not in front of the king as shown.
how about a reference?
Ahh…you are correct L. Scott. Good catch!
Graphic is fixed. Thanks for the feedback.
I assume the next step below (less serious than) check is “situation normal” — that is, no impact at all (other than the announcement that Threat exists).
That is, a player is free to leave his king in Threat, move his king into Threat, and castle through a space under Threat.
Yes. The threat announcement is a courtesy, much like announcing three-in-a-row in a game like Pente. It is, after all, a gentlemen’s game, what, what!
It seems like natural extension of the Check announcement, which gives you fair warning before the irrevocable Mate.
I was thinking, in attempting to play this in real life, what if you made a board where each piece was split into two halves. Then instead of needing two boards, you could have a bunch of half pieces, which when in the existing state would literally form a whole piece.
You would need to show on each half whether it’s part of the Right space or the Left but still, it might work. Thoughts?
Wow! very clever aardvark :O, i’ll have to make a board myself!
Unfortunately my Shrodingers pawn board would likely look hideous.
Nice one, EA!
Doable, but you’d probably want to have a bit of extra weight at the base, or magnets to increase stability, as the players will need to make a lot of moves with the half pieces, and it would be easy for someone with thick fingers like me to make a mess of the board.
I’ve got a couple of webcams and some live mixing software, and as soon as I track down a couple of small identical boards, I’ll try that method and post the results.
Hmmm… question. What happens when you cannot legally move a piece to collapse it during a reaction phase? For instance, if a pawn would have to move backwards to collapse. Is it then considered captured? Then you would have a different number on each board…
> What happens when you cannot legally move a piece to
> collapse it during a reaction phase?
That doesn’t happen. The piece doesn’t have to make a “legal move” to collapse. Collapsing *is* legal.
> For instance, if a pawn would have to move
> backwards to collapse.
That’s fine. He collapses backwards. See also the graphic of the knight’s “move” under the “Player’s Turn” heading.
Some other points that should be resolved before play:
(Correct me if my assumptions are incorrect)
If a pawn collapses back to the second rank (collapsing onto a pawn that hasn’t moved), then that pawn is considered not to have moved (and can move forward two squares as usual).
Likewise, if a rook or a king collapses to an unmoved rook or king, then that piece is considered to be unmoved (and may castle later).
So you could move a rook on Board A, collapse it with an unmoved rook, then move that rook on Board B, then collapse it again to its (now-unmoved) partner on A, and then castle with it.
A superpositional pawn cannot be captured en passant (so the would-be capturing pawn, whether real or superpositional, cannot make a diagonal move to the en passant square).
Collapsing a pawn to a space through which a superpositional pawn made a two-square initial move and became real as a result will not result in en passant capture.
Aardvark,
This is where the non-intuitiveness of the quantum physics metaphor comes into play. When two pieces, say the pawn you are concerned with, are on two different spaces (superimposed), they have the possibility of being in either square, but their fate is not decided until they collapse. The collapse is not a move at all, it is a clarification of where the piece does/does not exist.
So the short answer is, don’t think of the collapse phase as a move, but as a choice.
What is possible and this is *very* important, is that one collapse may trigger another collapse, and another. Each time a piece triggers a collapse, that collapse is dealt with, no matter who’s turn it is. That’s what the resolution phases are for.
There’s some great feedback coming in, and I’ll do a pass after a bit to integrate some of this stuff back into the main ruleset.
Good questions, L. Scott.
I guess in my mind I was always thinking about using the entanglement rules (in which you always move the matched piece on both boards), which would eliminate most of those concerns (because you would never collapse back to an unmoved piece).
Maybe I’ll remove the optional tag from Entanglement. There’s a bookkeeping task involved either way (keeping track of matched pieces vs. keeping track of unmoved pieces), but Entanglement makes more sense with the games underlying metaphor.
Your last two points about the en passant capture are correct, and more broadly clarified:
- No pawn, real or superpositional can make a capture move against a superpositional piece AND
- No superpositional pawn may make a capture move against a real or superpositional piece
Where the capture move is either diagonal or en passant.
Yeah it was late at night so I should have figured that one out. Thanks guys :c)
I wish I had the skills/time to try making this board, I think it’d be fun to (try) to play!
> No superpositional pawn may make a capture
> move against a real [...] piece
Not even if a superpositional pawn on the other board also moves to capture the same real piece?
(e.g., superpositional pawns on A-e4 and B-g4 both moving to capture a real piece on f5 — even more fun if they’re an entangled pair!)
(And thanks for being so quick with the answers, Sean.)
Aadrvark, no worries. I wish I had the skills to play it. I’m rubbish at Chess…};^)
L. Scott, yes, you’re right. The resolution phase needs to be updated to reflect two superpositional pieces capturing a real piece. But I think this clinches it for Entanglement, it needs to be part of the base rules, otherwise I foresee a cloud of undifferentiated pawns devouring everything in their path.
Thanks for the good questions!
> But I think this clinches it for Entanglement,
> it needs to be part of the base rules, otherwise
> I foresee a cloud of undifferentiated pawns
> devouring everything in their path.
Hmm. I don’t think it would turn the pawns into locusts, since the pawns are still useless against superpositional pieces, and have only their normal power against real pieces when they themselves are real or when paired with another pawn in exactly the right square (both of which would be obvious to the player controlling the real piece).
I’d be inclined to leave entanglement as an option (or as an “advanced rule” to be added to experience the “full game”), to leave the “basic game” as accessible as possible (which is already a big hurdle for most multi-board chess variants, due both to the material requirements and to the complexity that comes with having to track multiple boards (dimensions) at once, overlaying them in your mind).
You could use entanglement as part of the “real” rules, but still start players off with the version that requires less bookkeeping.
I think this one will need a quick playtest to sort out. I’ll try to make a little time for that this weekend, if I can.
You know I grew up with a “3D Chess” board and that would have almost worked here. I had alternating black and transparent squares and had 3 boards held vertically stacked.
You could kind of look down through the boards, though sadly only through the “white” squares I think.
Of course as luck would have it, the board broke after too much use a few years ago…
A laser cutter and some plexiglass would be a good approach to be building such a board. My wife and I are looking into TechShop up in Menlo Park which would be a great place to put together a project like this. The Fab Lab in South Boston also has the tools for this, and they are free and open to the public.
For the purity of the metaphor entanglement should always be a rule.
Also, considering metaphorical exactness, the movement rules should be slightly modified. I say this because there is only one REAL piece, but movement can result in a superpositional piece. In theory, we don’t know which spot the piece ACTUALLY occupies until it is acted upon. So during the next turn, the super positional piece could have legal moves from EITHER of the new starting locations. So when the player moves, the piece should collapse to ONE of the two possible starting locations and then make a new legal move. In this way pieces always have to move like in the original. In quantum, we don’t see two halves of a wave function going in two separate directions where they can not instantly and legally recombine.
Finally, there is still a problem of turn resolution. It is possible (but rare) that a super positional piece 1 shares its two locations with two pieces 2 and 3, and that pieces 2 and 3 share a square. If a fourth piece moved its exact location to annihilate the 2-3 square and 2 and 3 collapsed backwards, piece one would have no location. This would be a fun and new type of capture!
I am really a fan of this idea. Would you be offended if I wrote software for this game just for fun?
Hi Dan,
Interesting idea with the movement. Have to think about that one. Being a game designer first and a quantum engineer…farther down the list, I try to never let reality (or metaphor) trump gameplay. My gut feeling is that you would end up with fewer active supers, and less of what makes the game interesting. But now were getting to the part of the cycle where playtesting would be quite valuable.
When I have a moment (my day design-job is pretty demanding right now), I’ll write these up in the optional rules, and move entanglement out of options and into the main set.
I’m having trouble seeing the alternate capture you are proposing. With three sets of super positional pieces, every combination I set up with shared squares ends up with three sets of real pieces at the end of the resolution round. Am I missing something? Probably need to start calling these things out in chess notation:
Algebraic Notation
The rabbit hole just keeps getting deeper on this little project…};^)
I think a few extra notations would be needed:
< = Piece becomes Superpositional
> = Piece becomes Real
~ = Threat
[...] Brackets denote moves that happen during collapse phase
As for writing software, let’s talk offline. My address is on the Contact Sean page.
I’ve kept this post bookmarked so I can check in every once in awhile. Please be sure to update if you guys get a program running, I’d love to playtest!
Hmm, checked back here after a bit before your initial post of this article, and it seems much more feasible. Though its exams week for me, I may try to program up something for this in java, though I would like it much better physically with a few chess boards
This idea is brilliant. Recently, I’ve been surfing around this site, and most of the ideas are incredible. Let me know when you can get a program up and running.