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Subject: order and chaos solved? rss

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Stephen Sniderman
United States
Ohio
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Order and Chaos: A Strategy Game for Two, one of my game designs, originally appeared in the September/October, 1981, issue of Games Magazine and is currently described by Wikipedia and BoardGameGeek, but I'm afraid I'm responsible for a crucial discrepancy between the original version and Wikipedia's description of the game.

Here are the rules as they appeared in Games:

Materials. Two pencils and a piece of paper on which a 6 x 6 grid has been drawn.

Playing Time. About five minutes.

Object. One player (representing “Order”) tries to get five Xs or Os in a row—horizontally, vertically, or diagonally. The other player (representing “Chaos”) tries to prevent order from achieving that goal.

How to Play. Order plays first. Alternating turns, each player puts either an X or an O in any empty square on the grid.

Winning. Order wins by getting five consecutive Xs or Os in a row in any direction. Chaos wins when both players agree that getting five in a row is no longer possible.

The description on BoardGameGeek says essentially the same thing in fewer words:

Order and Chaos is played on a 6 x 6 square grid. On a turn a player writes either an X or an O in any empty space. The object of the first player (Order) is to complete a line of five Xs or five Os in any direction. The object of the other player (Chaos) is to prevent this.

However, the description of the game on Wikipedia, which otherwise paraphrases the previous two, adds this caveat: “If Order creates a line of six pieces, this is not counted as [a] win.”

Benjamin G. Turner, who claims to have “solved” Order and Chaos, seems to be aware of this discrepancy. He says, “Variants allow or disallow winning with 6 in a row.”

So the question has to be asked: Does it matter? Does allowing or disallowing 6 in a row as a win make a difference in strategy or affect the fairness of the game? I think it does. Consider Wikipedia's strategy suggestion:

“As in gomoku, an open-four (4-of-a-kind with two open ends) is an unstoppable threat, which Chaos must watch for.” Turner agrees: “Order effectively wins if it creates an open four (4 in a row with nothing on the ends).”
However, if 6 in a row does not constitute a win, then an “open-four” is not “an unstoppable threat.” Chaos can prevent Order from winning by not playing either an X or an O in either of the two open ends and forcing Order to do so. (Remember, Order takes the odd moves, so there will always be an even number of squares for Order to choose from.) If Order fills in one of these end squares and makes five in a row, Chaos plays the same letter in the square at the other end of the line, making 6 in a row, and that “unstoppable” threat is thwarted. If Order plays the opposite letter, Chaos plays that letter at the other end and there are only four in a row.

I'm assuming that Wikipedia got its strategy advice from the description of the game in Games Magazine, which says, “Order can win by getting four Xs or four Os in the middle of any six-square row, because Chaos cannot block both ends in one move.”

Since the original version of Order and Chaos says nothing about 6 in a row, the open-four threat would indeed be unstoppable in that variation.

So why does Wikipedia include a statement about 6 in a row that does not appear in the original version of Order and Chaos? It's possible that I am responsible for this “mistake.” When I first ran across O&C on Wikipedia, I had not paid the game any attention for many years. In the meantime, I had come to the conclusion that Order had too much of an advantage, and I hoped that not counting 6 in a row as a win would bolster Chaos's chance of thwarting Order.

By the time I happened upon Wikipedia's description of the game, I forgot that 6 in a row had not been mentioned in the original version, and I proposed a “correction” to Wikipedia's version. I noticed that my revision got added right away but in a few days was removed. More recently, I noticed that it's back. If my ill-advised addition was the cause of this confusion, I apologize to all concerned.

In any case, I believe that adding “6 in a row is not a win” makes a significant difference in the strategy of the game and any attempt to plumb the depths of O&C. In fact, I don't believe that Turner has solved Order and Chaos if 6 in a row is not a win. I agree with him that if both players play perfectly, Chaos cannot prevent Order from creating 4 in a row in the middle 4 x 4 section of the grid and that will lead inevitably to 5 or 6 in a row, a win for Order in the Games Magazine version.

However, if 6 in a row does not constitute a win, as in the Wikipedia version, I believe that Chaos can prevent Order from winning if only one 4 in a row is created in the middle section. If Chaos avoids filling in either of the end squares in that row, Order will eventually have to do so (since Order plays the odd moves). Whatever letter Order plays on either end, Chaos plays the same letter at the other end, making 4 or 6 in a row, a win for Chaos.

Can Order force a win if there are two 4 in a rows? Not necessarily. It depends on where they are on the grid and whether there are other threats from Order.

If the goal is to make Order and Chaos the best game it can be, then I recommend including the rule that 6 in a row is not a win. An added bonus of this rule change would be that the game would be harder to solve.

If it turns out that the 6-in-a-row rule does not compensate for Order's advantage, we can look for other ways to make the game fairer. The simplest of these is to give the win to Chaos if there are 6 in a row of either letter at any time in the game. I'm aware of the irony of this rule (6 in a row is the opposite of chaotic), but we could always change the name of the game. One possible title would be Order and Chaos?

Another suggestion would be to have one player black out one square on the board and have the other player choose whether to be Order or Chaos. Such a rule would undermine Order's mechanical strategy of playing symmetrical moves. A similar rule would have one player put two letters (same or different) anywhere on the board and the other player would choose to play Order or Chaos. A related variation would allow the weaker player to call for a switch of roles within the first n turns. The bigger the difference in skill level, the higher n would be.

In any case, Order and Chaos can be tweaked in dozens of ways to make it more interesting, more challenging, more surprising, less predictable, less robotic, and less solvable.

 
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Benjamin Turner
United States
New York
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Hi, Stephen! I just saw this post, also linked from the Wikipedia article. I've gotta say, I agree with another Wikipedia entry - the one on "solved game" - where it says, "Whether a game is solved is not necessarily the same as whether it remains interesting for humans to play." We had loads of fun for many months with this game! But we're also a bunch of software engineers, so trying to come up with a heuristic, and eventually a solution, is in our DNA. That finding one required a combination of human understanding (how to play the board edge) and brute force (solving the 4x4 interior) I think shows the relative complexity and interest of the game. Even in the interior, the best moves for order are often counterintuitive.

That said, I'd love to try more variants. Even without the solution, once we all got good at it, whoever was playing as order seemed to have an advantage. We also tried some variants to make chaos stronger, such as letting chaos flip a single piece's color exactly once during the game, but weren't able to come up with something that made it feel balanced. (That one made it too easy for chaos, if they played well enough to use the ability late-game when order's winning move was clear.) It's a great game, and having variants available only adds to the intrigue. Thanks for creating it! thumbsup

(Sorry, I tend to refer to "color" instead of "letter" because we used Go stones, to avoid using up a ton of paper. )
 
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