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Many Worlds Chess. Large variant, inspired by the many worlds interpretation of quantum mechanics.[All Comments] [Add Comment or Rating]
Anonymous wrote on 2016-10-17 UTC

I tried playing this game with a friend; here's a link to the game. 

It's organized by columns: leftmost column of boards is the starting position, next column is white's first turn, next one is black's first turn, etc. My friend was white (about 1100 elo); I was black (about 2000) elo. We didn't look at the comments beforehand so didn't see the winning strategy, but as you can see I won in four moves anyway.

Verdict: I think it's very difficult to avoid a quick end to this game. My proposed fix would be add two blank boards at the start of the game, and to allow kings to move between boards. Allows your king to escape danger more easily.

Another option to lengthen the game would be to require the capture of, say, three kings to win, rather than just one.

The main winning strategy using these rules would be to get the opponent to have several of their kings on the same board, and then fork those kings.

Jonathan Weissman wrote on 2010-01-17 UTC
'It seems to me that Weissman's perfect strategy could be foiled by
allowing non-splitting moves'

This just makes it take longer, as the main exploit, as Rich Hutnik pointed
out, is that White is able to create 2 boards which advance its position,
and then use the one Black doesn't respond on for its next move.

If black has the option of just making one response and not splitting the
board, then a winning strategy for white is:

As before, White starts with e3 and e4. Black responds on one board, on the
other White plays Bishup c4 and Queen h5, both threatening f7.

Now, if Black does not respond on the board where White moved the Bishup,
then on this board White moves Queen h5, otherwise Black did not respond on
the board where White moved the Queen, and on that board white moves Bishup
c4. Either way, White has created a board with its Queen on h5 and Bishup
on c4, threatening Queen takes f7 mate, and White's other move is Knight

So Black responds on the board where White just moved the Queen or Bishup,
otherwise White mates with Queen takes f7. So, on the board where White
moved the Knight, white again moves Queen h5 or Bishup c4 threatening mate,
and splits the board with Knight g5, threatening Bishup or Queen takes f7
mate. Black is now threatened with mate on two boards and can only respond
on one. White mates on the other. Black has not even been able to make a
move on the board where the mate occurs.

Anonymous wrote on 2009-05-12 UTCExcellent ★★★★★
It seems to me that Weissman's perfect strategy could be foiled by
allowing non-splitting moves, so that on your turn, you have three options:

1. Make two legal moves on some board, splitting that board.
2. Make a single move on some board.
3. Make a transfer move from one board to another.

Thus, you do not have to use the many worlds feature of this game unless
it is to your advantage.

Adrian King wrote on 2008-12-09 UTC
1. I think Jonathan Weissman's analysis shows that your concern is
well-founded; the flaw he found sounds like an example of what you're
thinking of. 

2. You'd surely have to put some constraints on the rule sets you could
create. Otherwise, if I were White, on my first move I'd just create a
rule that says 'White always wins'.

To be in the spirit of the original game, you'd want to have rule space
where each rule change was a small increment, more analogous to the move
of a single piece than to a wholesale shuffling of the pieces on a board.
I've never seen any such rulemaking system; do you know of one?

2a. Strictly speaking, in a game with a finite number n of possible
states, the number of possible rule sets is also finite. To see this:

. Define the rules of a game as a function f(s) => ss that maps each game
state s to a set ss of legal successor states.

. The number of possible state sets, nss, is finite. In fact, it is 2 to
the power n (because each state is either in or not in a given set).

. Therefore, the number of possible functions f(s) => ss is also finite,
and equal to nss to the power n (because f maps from each of n values of s
to one of the nss values of ss).

So, literally speaking, there is not an infinite number of rule sets that
can materialize, at least not if you disallow rules that make the game
state larger (e.g., by enlarging the board or dropping new pieces on it).
However, the maximum number of rule sets is really big -- (2 to the n) to
the n, where n is the already very big number of possible of states of an
FIDE chessboard.

Rich Hutnik wrote on 2008-11-19 UTC
It actually had been months since I looked at this, and don't remember my thoughts on this.  All I can do is speculate here regarding several things:
1. I think I was concerned that there may be a chance for allowing someone to end up moving multiple times on a single board, without the other side moving, resulting in one side mating due to neglect.  My thoughts may of been ways to prevent that from happening, without ruining what this variant is attempting to do.
2. I think I was also postulating whether or not you could then spawn off different rules with each new board that is launched and if there were an infinite number of rule sets that could materialize.

Adrian King wrote on 2008-11-19 UTCPoor ★
After not having looked at this page for years, I'm gratified that some
people have been generous enough to squander their time on it, and even to
rate it better than Poor.

As best I can tell from a two-minute back-of-the-envelope calculation,
Jonathan Weissman is right, and the game is fatally flawed. That relieves
us all of the tedium of actually trying to play it.

Mr. Hutnik, I'm not quite sure I understand your attempted repair. I
think you're just saying that each board remembers whose turn it is to
move, and that you can only make a move on a board where it's your turn.
May we assume that only splitting moves allowed, and not the transfer
moves in the original rules?

If I've got it right, then starting at board 0-W (that is, board zero
with White to move), boards get created in a sequence looking something
like this (assuming that no identical ones are created and merged):

 W: 0-W => 1-B 2-B

 B: 1-B => 3-W 4-W, resulting in the set of boards {2-B 3-W 4-W}
  (White now has just two boards to choose from, 3-W and 4-W)

 W: 3-W => 5-B 6-B {2-B 4-W 5-B 6-B}

 B: 2-B => 7-W 8-W {4-W 5-B 6-B 7-W 8-W}

 W: 8-W => 9-W 10-W {4-W 5-B 6-B 7-W 9-W 10-W}

That is, on move n, White has n boards to choose from (if there have been
no merges), and Black n + 1 boards.

At least initially, it sounds better-behaved than my original. However, I
still have strong reservations about anyone actually attempting this (and
do please count me out). The most concrete worry I have is that the weaker
player will refuse to move on any board where he/she is starting to lose,
and instead concentrate on the boards where less progress has been made --
so that you wind up playing through all possible openings without ever
reaching a midgame.

But I'd still be interested in hearing the outcome if anyone ever does
come up with a version of this idea that actually works.

Rich Hutnik wrote on 2008-07-10 UTC
To prevent a 'mate in 4' thing where someone could make multiple consecutive moves on the same decision tree sets of boards, couldn't the game be restricted where you are not allowed to make two straight moves on a board, without your opponent making any?

An idea would be, as I see it (to prevent one side from making a ton of moves without their opponent moving):
1. Starting player makes two moves, creating two boards, with old board disappearing.
2 Their opponent picks position and moves two, destroying the old position, and sending two back their opponent's way.
3. The starting player then ends up looking at three possible positions, creates two new ones, and sends them back to his opponent.
4. Rinse and repeat until there is a winner in one game (capture enemy king).
5. Of course, no two identical board conditions are allowed to be in play at the same time.

We can go 'Heraclitian-Calvinball' by allowing different rule conditions per board.  I think this may address some early concerns, while maybe not being exactly what the original creator intended.

Rich Hutnik wrote on 2008-07-10 UTC
Calvinball in what way George? Heraclitian-Calvinball refers to rules set (no two games are every played with the exact same set of rules). This splitting of boards could lead to distinct set of rules per each board.

George Duke wrote on 2008-07-09 UTCExcellent ★★★★★
Many worlds and Chess. Calvinball would not be far afield. All possible universes, from one of which the Dragon carries over, in reading Clifford Simak's 'Way Station'(?). Dragon and all the Dragon's resonances East and West. We consider fashionable extremely strong anthropic principle. Mere strong anthropic points to the observable being as it is fully in order precisely for us to observe it. Weak anthropic addresses conscious life, numerical constants, the gravitational constant. If Earth is 10% closer, or Sol 10% cooler, or proton 10% heavier, no Life and all that that entails. Stronger, we get to all possible worlds, and where else intelligence can be. (Skeptics leave out ''else,'' questioning Earthly intelligence.) Strong anthropic posits different fundamental constants and laws of Physics in different universes. Extremely strong anthropic would hold that a universe came about in order to embody narrow agenda, like works of Shakespeare, or forms and moves of Chess, or some other preferred spiritual zealotry. Adrian King begins 'Scirocco' with H.J.R. Murray in 'A History of Chess': ''Of the making of these games there need be no end, and I have no doubt that many other varieties have been proposed and perhaps played, of which we have been spared the knowledge.'' -- 1912, anticipating Capablanca Chess, Cavalry Chess, and some others.

Anonymous wrote on 2008-07-09 UTC
To the previous poster - following is a copy of Mr. King's Strategy
section in his write-up:

No way I'd play this game! However, if anyone is actually crazy enough to
try to play it, let me know how it comes out.

There might be some benefit to trying to make splitting moves on boards
where you have a material advantage, or trying to create such boards by
transferring a lot of pieces there.

I'd recommend writing a computer program to manage all the different
boards, and also keeping a plentiful supply of aspirin on hand. 

In light of this, would you re-consider your rating?

Anonymous wrote on 2008-07-09 UTCBelowAverage ★★
Whoa. Ok, my IQ is over 140 and I still cannot wrap my mind around this game's lunatic complexity. Can you imagine a few moves into the game, when you have 10 different boards in the middlegame? And a King to protect on each? The number of boards increases every turn, and you only have to lose one king to lose the game? No offense, but this game is insane. Unplayable. Interesting concept, though.

Tim Stiles wrote on 2004-09-18 UTC
Assuming Jonathan Weissman is correct with White having a forced win, could anyone propose a rule so that White no longer has a glaring advantage? I'd really like to see this game become balanced.

Jonathan Weissman wrote on 2002-10-30 UTC
White starts with e3 and e4. Black responds on one board, on the other white plays Bishup c4 and Queen h5, both threatening f7. Black can stop this on one board, on the other, white captures f7 with Bishup or Queen and makes an inconsequential move. Black can take the Bishup or Queen with his king, but must make another board with another move. On that board, white captures the black king. Black has no way to capture the white king in less than 4 moves. Thus white has a perfect strategy.

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