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Subject: Feedback solicited; help me improve a "history of the game" for Mind Ninja rss

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Nick Bentley
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Hi all,

I'm trying to spruce up the website for Mind Ninja a little, and I've been tinkering with the section on the game's history. I've pasted the text below. Any feedback/ suggestions for improvement will be greatly appreciated.

The History of Mind Ninja

In the 1940s, two mathematicians (Piet Hein and John Nash, the Nobel-prize winner made famous in “A Beautiful Mind”) independently designed a game now known as Hex. It's played with stones of two colors on a board pictured at right.

Each player owns all the stones of one color, and the players take turns placing stones, one by one, on the board. The object is to construct a chain of stones in your color that runs between two opposite sides of the board. Your opponent tries to construct a chain of his stones running between the other two sides of the board. The second picture at right is an example of a finished game, won by red.

Hex is a landmark in game design: it has simple rules, deeply strategic play (at least one book has been written on Hex strategy), and some attractive mathematical properties.

In Hex, each player tries to form a particular kind of pattern. Its beauty lies in the fact that the patterns are mutually exclusive, but one is inevitable: when the board is full of stones, one and only one of the patterns must be formed. Thus, neither draws nor infinite positional repetitions can occur.

Beyond these beautiful and convenient properties, Hex has a special relationship to the human visual system. The brain is evolved to detect patterns, but it's better at detecting some kind of patterns than others. It's especially good at grouping similar elements together in order to see "higher level" objects. For example in the pictures to the right, you can see the board not only as individual cells of color, but as "islands" of color, where each island is made up of several like-colored cells. This capacity for grouping is critical for our ability to perceive and think, and it allows the human brain to play Hex intuitively and at an extremely high level (with practice, of course). As a neurobiologist and mathematician, I find this fascinating.

More important, Hex is a stellar training ground for the brain, perhaps because it demands exactly those skills for which our brains are most evolved. You can feel your own mind change as you improve, moreso I believe than one would playing better-known games like Chess. The one drawback is that what you learn when you play Hex is limited; you learn how to think about the one kind of visual pattern that is important in Hex and no more. For a long time, I wished for a game that was like Hex, with the same mathematical properties and relationship to the human visual system, but where all possible kinds of patterns matter, not just one. Such a game would likely improve visual thinking skills in general, not just for a single kind of pattern. The added variety would also make it more fun to play. In 2006, I realized how to design such a game. In order to understand how, one must first see that there is another way to describe the goals of Hex.

The traditional way to teach Hex is to describe to each player the pattern that he must try to form, but it’s not the only way. Instead, you can tell one player to try to form his pattern, and then tell the other player to try to block it. You only need to describe one of the patterns, and the other will emerge naturally when one player tries to block the described pattern.

With that in mind, I realized that the pattern you describe doesn’t have to be a chain between opposite sides of the board. It could be anything. If you specify almost any pattern, there will be another one that can block it, but you needn't be able to describe it in order to play.

That was the key insight, but I didn't have a game yet. In order to make a fair game, one must ensure that the goals of the two players are about equally difficult. Let's call the two players the builder and the blocker. In order to make the game interesting, the builder and blocker must have equal chances, if their skill levels are equal. There are lots of patterns that are easier to build than to block or vice versa, so whoever decides the pattern can easily win if he knows whether he’s the builder or blocker beforehand.

I found a simple solution: first, one player should invent the pattern first, and only after that should the other player decide who is builder and who blocker. That way, the player who invents the pattern must choose a balanced one, or else his opponent will get an advantage by taking the easier role. This rule ensures that the players own choices will lead to a balanced game.

This led me to another problem. There are many, many more unbalanced patterns than there are balanced ones, and I wanted a game where all (or nearly all) patterns were balanced. I needed to add some other balancing mechanism that would automatically turn unbalanced patterns into balanced ones.

I found a simple solution here as well: the player who chooses the pattern may also fill in as many spaces as he wants with any color, *before* the other player chooses whether to be builder or blocker. By making moves that favor the builder or blocker, he can compensate for differences between the two roles, and bring the game into balance for just about any pattern.

With these rules in place, I had the basic game, which is described as "Rules for Casual Play" in the rules section of this site.

The “Rules for Tournament Play” solve another problem that I discovered later, when I tried to imagine what would happen if players studied the game intensively, like some study chess. I realized that a player could study intensively one particular pattern, so that he knew more about it than others did. Then, in any game in which he had the opportunity to propose a pattern, he could propose that one. Even if the pattern was balanced, his expertise in that pattern would grant him an advantage. To fix this, I added a bidding phase at the start of the game, where players bid for the right to propose a pattern.

So, Mind Ninja is a generalization of the rules of Hex to any arbitrary pattern goal. But it’s not only a generalization of Hex. Many other games, Like Y, Star, 5-In-a-Row, and One-Capture-Go, as well as many others, are all contained as specific patterns in Mind Ninja.
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David Molnar
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I like this. It seems like Unlur should be mentioned (I've always assumed that it was the jumping-off point for your design) and I'm also wondering if you've played Atoll yet. Not that I think it specifically needs to be mentioned (it would be too much to list all games that are special cases of Mind Ninja), but I've been playing it a lot online, enjoying it for some of the same reasons you mention, only possibly more so. It's on yucata, if you haven't.
 
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Russ Williams
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I think the history of Mind Ninja is interesting (and the game itself has interested me for a while, though I have yet to convince a friend to try it with me, alas). But your actual text has too much info about Hex and its rules and history - cut to the chase sooner. You're supposedly giving a history of Mind Ninja, not of Hex.

E.g. compress the initial 60% of the history into a single paragraph like:

my simplification proposal wrote:
Hex is a modern classic, discovered independently in the 1940s by John Nash and Piet Hein. In Hex, each player tries to create a pattern on a hex grid, namely a connection between their pair of opposite sides of the board. But the mathematics of Hex are such that exactly one pair of sides will inevitably be connected. Thus you could equivalently view the game as one player trying to create a pattern and the other player trying to thwart the pattern. You only need to describe one of the patterns, and the other will emerge naturally when one player tries to block the described pattern.


And then continue from there, actually talking about Mind Ninja.
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Nick Bentley
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molnar wrote:
I like this. It seems like Unlur should be mentioned (I've always assumed that it was the jumping-off point for your design) and I'm also wondering if you've played Atoll yet. Not that I think it specifically needs to be mentioned (it would be too much to list all games that are special cases of Mind Ninja), but I've been playing it a lot online, enjoying it for some of the same reasons you mention, only possibly more so. It's on yucata, if you haven't.


Good guess! Unlur *was* the jumping off point, or it was the game that gave me the idea that a "multiple pattern" game might be possible. I'm not sure how to fit it in without dragging out the intro even longer. Hmm. I'll reduce the stuff about Hex, as per Russ' suggestion (thx Russ), and then see if I can find a graceful way of fitting Unlur in.

I have played Atoll. Very cool discovery. I've heard that alot of people are playing it on Yucata. Maybe I'll put it in the list of special cases.
 
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