Nick Bentley Likes Abstract Games More Than You

I focus exclusively on minimalist abstract games, usually perfect information. By "focus" I mean that I can't stop thinking about them, to the detriment of many other things in life. It's been this way for years.

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Revised Game: Glorieta 3.0

Nick Bentley
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Reposted from my blog.



This isn’t necessarily the last version of Glorieta (but it could be). I’ve made great progress on the game, using (for a second time) a mechanism I’ve not seen elsewhere, so I’m reporting on it. But the more I design games, the more I’m convinced they’re never actually done. Every ruleset is just a launchpad for another, better ruleset, always in pursuit of a platonic ideal.

Glorieta represents one attempt to design a game on a hex board where the goal is simply to form a connected loop of stones. I’m convinced that the goal has great potential, and it sounds simple enough, but realizing it has proven incredibly tricky, especially because I want it to satisfy a bunch of other constraints as well (example: draws should be impossible, and the game should be highly balanced, along with other constraints I won’t bother to record here).

I’ve been working on this project on and off for five years, and I have designed many, many (unpublished) games in an attempt to achieve it. Once in a while, I post an example: see here for the preceding version of Glorieta, see here for the one before that, and see here for a completely different attempt to solve the problem. Or don’t bother, because at the moment I like this new one more.

Equipment: Glorieta is played on a hexhex7 board with black and yellow stones that are pink on their undersides. The board is also surrounded with a ring of black and yellow spaces, as this picture of an empty board illustrates:



Definition - Loop: a connected group of like-colored stones, and (optionally) pink-side-up stones, which completely surrounds one or more spaces, regardless of what’s in those spaces. The picture below shows a board that contains two yellow loops and two black loops. Note that loops can also include like-colored spaces that surround the edge of the board (as illustrated by the small yellow loop on the right). The smallest possible loop is six stones/colored spaces surrounding a single space.



Rules

1. The board begins empty. One player owns the yellow stones and the other owns the black. To start, Yellow places a stone on any empty, uncolored space.

2. Then each player takes six of her stones and holds them in her hand.

3. From then on, starting with Black, the players take turns. On your turn, you must either take 1 or 2 stones from your hand and place them on any empty uncolored spaces on the board, or you must flip any one of your stones on the board so that it’s pink side up. If you run out of stones in your hand, your turn is over. If the board fills completely, you must keep playing by flipping a stone on each turn.

4. You must choose to flip a stone at least once for each handful of stones. You can do so after you’ve used all the stones from your hand, but before you pick up your next hand of stones, or on any earlier turn. After you’ve used up all the stones in your hand, and flipped at least one of your own stones, pick up another hand of six stones and continue.

5. The game ends when a loop is formed and the player who owns that loop wins.


Notes

-The game will always end with a loop and there will never be a draw.

-If I’ve designed the game right, the board will rarely fill completely before a loop forms. In any case, if you’d prefer to play a shorter, more tactical game, just reduce the number of stones in each handful.

-The picture at the top of this page shows a finished game, won by black, who has a loop near the bottom of the board.

-This mechanism can be applied to any pattern-completion game (as long as empty spaces aren’t part of the pattern), and it will make that pattern inevitable. I love this. Since pattern-completion games are a huge category, it’s cool to know that if nothing else, this game shows how to make a much wider range of patterns possible as game goals. A lot of those goals probably won’t make for good games, but maybe some will.
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Fri Nov 23, 2012 6:57 pm
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Best Combinatorial 2-Player Game of 2011/2012 Award (please submit nominations!)

Nick Bentley
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Somebody has decided to take on a task that many of us abstract games diehards have wanted for a long time. To help support that effort, I'm posting here to encourage all interested parties to post nominations for this contest, upvote, give geekgold, and make it's author feel loved. Here's the link:

BEST COMBINATORIAL 2-PLAYER GAME OF 2011/2012 AWARD
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Wed Nov 7, 2012 4:07 pm
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New Game: Shello – An Attempt to Solve the Problems of Reversi/Othello

Nick Bentley
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This is a repost from my blog



I promised in an earlier post that I would post other games built around a new mechanic (I think) I invented, which I shall call the Shifty mechanic, and here I am.

Today’s game is an attempt to capture the spirit of Othello (AKA Reversi) in a form better than the original.

Some people like Reversi but I think it’s meh. It’s hard to have interesting strategy ideas about it, I think because it has waaaaaaay too much negative feedback. By negative feedback, I mean that the closer you get to winning, the harder it gets to win. The goal is to have more of your pieces on the board than your opponent does when the board’s full, but during much of the game the player with more pieces is at a disadvantage, because her opponent can flip them in big bunches. As a result it’s hard to understand what the state of the board means, which makes it hard to strategize. Too hard.

Some negative feedback is a good thing, but too much or too little is bad. It’s tricky to get it just right, and Reversi goes too far. The best games seem often to have just a little. Go comes to mind (don’t get too greedy trying to capture or you’ll find yourself out of position).

Digression: want to play a great Go variant? Try Redstone. I usually see no reason for Go variants to exist but Redstone is an exception. You’ll have to try it to find out why because this isn’t a Redstone essay. End digression.

Anyway I’m trying to invent a game with the same satisfying flipping mechanic as Reversi, but with a better level of negative feedback. I’ve been thinking occasionally about this problem for a couple of years and this is the first promising idea I’ve had about how to solve it.

Shello is a game for 2 players, played with chips that are white on one side and black on the other, on a 9×9 square grid (or larger, as long as there are an odd number of cells in the grid. But 9×9 is all you’ll need for a long time.)

The game starts with an opening board layout shown in the picture above.

The pieces in the corners are called Neutral Pieces. These count as both black and white. They never move and they’re never flipped, but they can be used to flip pieces of either color during the game.

Rules

1. One player plays pieces black side up, and the other plays them white side up. Starting with Black, the players take turns. On your turn you must either place a piece on an empty space orthogonally-adjacent to any friendly piece, or or you must move any friendly piece, by a chess queen’s move, to any empty space orthogonally adjacent to fewer friendly piece than the space it started on.

2. If you have no legal moves, you must pass.

3. After placing or moving a piece, flip all enemy pieces lying in an uninterrupted straight orthogonal or diagonal row between the piece you placed or moved and any friendly pieces.

4. The game ends when the board is full. The player with more pieces on the board wins.


Notes

1. Rather than start with the fixed opening setup above, players can take turns placing a piece non-adjacent to friendly pieces until there’s two of each color on the board and then proceed according to the rules above. I haven’t experimented with this method much, but there’s a chance it’ll be better than the fixed setup. Might require a pie rule.

2. Why the neutral pieces in the corners? In Reversi, it’s an advantage to have your pieces in corners because they can never be flipped there. On the other hand, it’s hard to get your pieces to the corners because all the pieces grow out slowly in one big clump from the center the board. In Shello, players have more control over where their pieces go, and consequently the opening of each game might devolve into a race to the corners. With neutral pieces in the corners, the corners are dangerous. Problem solved.

3. I’ll wager that most who play this will find it more stimulating than Reversi/Othello. There’s less negative feedback. The reason is that in Shello, the more pieces you have on the board, the more pieces you can move, which gives you better access to strategically important spots. Also, because you can move your pieces, you can move them out of threatened spots, and break up your threatened rows. This transforms the game. Pushes the awesomometer to the right. I believe.

4. However, while I like the feel of play, there’s a potential fly in the ointment: I can’t prove that it’s theoretically finite. There remains some chance that an infinite cycle will be found, even though I haven’t been able to find any. If you find one, please tell me ASAP. If it turns out there aren’t any, this feels like it’ll turn out to be one of my better creations.
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Sat Jun 23, 2012 6:40 pm
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New Game: Snype - an attempt to improve the game of Y

Nick Bentley
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This is a repost from my blog



This game represents progress on a problem I've been working on for a long time: to improve the gameplay of The Game of Y, especially when it's played on a hexhex board, my favorite of all regular tilings. Y has what is regarded by many as one of the most beautiful win conditions, but gameplay falls flat for me, on account of the supreme importance of the center of the board, which limits the effective branch factor and opportunities for creative moves. This is true for me even on the "modified topology" boards which are supposed to address the issue.

I've taken a bunch of stabs at solving this problem, and I've posted a couple (see here and here). Snype, I'm betting, will be better than my earlier attempts. I say this even though I haven't played it - I'm willing to go out on a limb because Snype resides in a region of game-space I understand well.

As always, I'll start with the rules and then explain why they are the way they are.

Snype is a game for 2 players, played with black and white stones, on this initially empty board (actually, you should play on a board larger than this. This is just for illustration. 7 cells on a side is good):



Rules

To begin, one player places a white stone on any empty space, and the other player decides whether to play as White or Black.

From then on, starting with Black, the players take turns. A turn consists of two actions, which may be performed in any order: 1) place a stone of your color on any numbered empty space; and 2) optionally, move a stone in a straight line, any number of spaces up to the number on the space from which it starts, so that it lands on an empty numbered space. No jumping allowed.

The game ends when one player creates a connected group of stones which is adjacent to at least one blue, one yellow and one red space. He wins.

What's the deal?

The inspiration for Snype starts with the game Slither. Slither has a similar "place a stone, move a stone" turn protocol, except in Slither you can only move a stone one space. This protocol has turned out to be magnificent for connection games because it improves their weakest feature, tactics, while leaving intact the strategic contours which make connection games great in the first place. It also dramatically increases the meaningful branch factor.

So I wondered: is there a way to solve the center-problem of Y by employing a modified version of the "place and move" turn protocol? The answer was obvious: make center stones weaker by giving them less freedom to move. And so Snype was born.

One open question is whether the pie rule is sufficient for balancing the game. There's a good chance it won't be. I don't think I'll be able to deal with this issue, if it is an issue, until I've playtested the game a bunch, so for now it remains an open question.
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Sat May 19, 2012 11:56 pm
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New Game: Shifty

Nick Bentley
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This is a repost from my blog

My favorite game is Slither. One complaint I've read about Slither is that for some players, it feels too "crazy". The situation can change a lot in a single turn, more than some people like. I don't know what they're smoking, but it occured to me that I might be able to design a game with Slitherish dynamics but with a more stately, ruminative pace, using a move protocol that's been ricocheting around in my head for months with no place to land.

The result is a game which (I'll put down my false modesty and be frank for a moment) I really like.

(Also: I'm working on several game designs with the new move protocol, and I'll try to publish them soon, but for now I'll present this square board connection game, since fellow designer Luis Bolaños Mures has become a factory for square board connection games and I figure I better publish one before he INVENTS THEM ALL)

Shifty is played on an initially-empty square grid, where one player owns a pair of opposing sides of the board and the other player owns the other pair. I recommend a 10x10 grid for beginners, like so:



One player owns the white stones and the other owns the black.

Rules

1. Black places a single stone on any empty intersection, and then White decides whether to switch sides with Black.

2. White places a single stone on any empty intersection.

3. From then on, starting with Black, the players take turns. On your turn you must either place a stone orthogonally adjacent to at least one friendly stone or you must move any friendly stone, by a chess queen's move, to any empty intersection orthogonally adjacent to fewer friendly stones than the intersection it started on.

4. You may not place a stone so as to create this pattern (or any rotation of it):



5. You must take an action if possible on your turn, but if you have no legal options you must pass.

6. The game ends when one player makes an orthogonally and/or diagonally connected chain of stones connecting her two opposite sides of the board. She wins.

Here's an example game that will be available through 5.6.12. Note the breathtaking comeback executed by yours truly just when all hope seemed lost. Note also that this was a 10x10 board and the game lasted 56 turns, but each player only had 18 stones on board at the end. So each of us chose to move instead of place stones about 1/3 of the time.

Notes

Why might this lead to interesting play? This is a square board connection game, which means position is deadly critical. Because you're limited in how you place your stones, you often have to shoot your stones into strategically critical spots. This "sharpshooting" activity is the reason for my affection.

For most connection games, the only viable strategy in the opening is to spread your stones out. In Shifty, there's a cost to doing this: if you want to spread out on your turn, you have to forego placing a stone. Even so, you *still* have to spread out frequently both because it gives you a positional strength and it increases your branch factor. But the way you proceed in spreading out seems more fraught than it is in say, Hex.

The board fills up more slowly than for most connection games because you don't have to place a stone on every turn. The slow change aids clarity and maybe provides more initial accessibility than Slither (if that's your thing). It reduces the branch factor (from thousands to hundreds in the midgame).

Another useful comparison is with Crossway. The knock on Crossway is that blocking is hard due due to the "doublecross restriction" (rule 4 above), so you need a gigantic board. This isn't the case for shifty because most of the time it take two turns to make a diagonal connection, rather than one. There's an extra cost to making a diagonal connection which makes it less powerful as an offensive move.

Speaking of Luis, he doesn't like the feel of the opening, because when you only have one stone on the board, you only have four options for placements. After some test games with myself I've decided that I disagree: I like this aspect because it makes individual matches feel different based on the initial placements (the branch factor grows rapidly as the game progresses out of the opening), but if you agree with Luis, I suggest the following: Allow players to place more than one singleton each before the "place or move" turn rule kicks in.

On the temperature scale, this game is hotter than Slither but colder than Crossway, for reference. It's temperature so far seems similar to that of Hex.

Although I believe deadlocks are impossible in this game, I can't write down the proof. If any of you can, please do!

General note about this move protocol (rule 3 above): the reason I like it, and the reason I'm going to publish several other games that use it, is because many stone placement games have "spread out" opening strategy, and this protocol can spice up that strategy in many contexts. For example: it might make an Othello-like game more interesting.
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Tue May 1, 2012 7:58 am
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Employing the Concept of "Economy" in Cephalopod Strategy

Nick Bentley
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Xifeng wrote a sweet strategy article about a concept in Cephalopod of which I wasn't aware. A must read for Cephalopod fans.

Check it out here.
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Sat Apr 7, 2012 7:00 pm
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My Dream Book: 10 top games from the last 12 years, with 30-40 pages of strategy for each

Nick Bentley
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This is a repost from my blog

Abstract games are at their best when players take the time to learn and share strategy, and though we're in the middle of an abstract-game-design renaissance, even some of the best modern abstracts remain strategic mysteries.

So I have this dream: a book featuring 10 of the best abstract games designed this millenium, with say, 30-40 pages worth of strategy discussion for each.

How to choose the 10? If it were up to me, I'd limit the candidates to games without chance, and I'd focus on games with good "architecture", meaning games which are finite (or likely soft-finite), balanced, decisive, conceptually "unified", and with the simplest of rules and equipment.

The only game that would be a lock for inclusion for me is Slither. Oust should probably also be in there, along with Arimaa, and TZAAR, IMO the one profound game from the Gipf Project. I'd love to include Quoridor as well, but sadly the published version is from 1997, and there's an unpublished version which predates that by decades.

Beyond that I don't know. No doubt there'd be a lot of arguing about which games should be included. I can already hear my fellow designer Mark Steere groaning about Tzaar.

It would take a loooooong time to put together such a book, because there would have to be an effort to develop strategy for each game before writing anything, and most of the games don't have much recorded strategy (except for Arimaa, which already has its own whole book, and Hex Oust, which has a little online strategy guide to start from). Perhaps the effort could be made in collaboration, with the designers and best players of each game contributing the ideas, and the author/editor focusing on presentation and language.

If I were writing the book, I'd also include one of my own games even if it doesn't deserve to be there; if I'm going to the trouble I'm gonna reward myself for it. (Self-Indulgent Bonus Chapter, I'd call it)

Anyway this is all a daydream because I don't know how to frame the idea to attract a wide audience. It's not worth pursuing without a plan to solve that problem. I'd love to get suggestions in the comments about how to do it.

One thing of which I'm certain: I'd make sure the language was uber-understandable and non-technical. I'd make sure that an uninformed 14-year-old could read it without breaking a sweat. I wouldn't go deep into strategy esoterica, but rather focus on the big, defining concepts for each game.

I'd also make it funny because there's never a reason not to be funny.

Perhaps the book could be launched in conjunction with a year-long tournament with prizes for the winners at the end, administered through the igGameCenter. The designers of the featured games could be asked to contribute to the prize-hopper to defray costs.

On the off chance that this post generates a lot of interest, I might get serious about exploring the possibility, so if you're interested, let me and world know in the comments.
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Tue Feb 28, 2012 5:59 pm
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New Game: Magnapoco

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This is a repost from my blog

I've got a battalion of game designs in the pooper, which I'm usually too lazy to post, but my friend and fellow game designer Corey Clark is goading me to make some public, so here I go.

Because Corey is the one encouraging me, the first game I'm posting is one I designed for him. Corey likes games with cold elements (which means situations arise in which you'd rather pass than take your turn) and he likes square grids. This game has both.

Magnapoco is a game for 2 players, played with black and white stones on this board:


You can play on larger grids (they must have an odd number of spaces), but I recommend starting with the one above (7x7). Good players will swiftly graduate to 9x9.

Before the game begins, one player takes ownership of the white stones and the other takes ownership of the black. Also, place 2 white and 2 black stones on the board, like so:



Definition

A group is a collection of orthogonally connected like-colored stones on the board. A single stone is considered a group as well.

Rules

1. To begin, white places a single stone on any empty intersection.

2. From then on, starting with black, players take turns. On your turn, you must place 1 or 2 stones onto any empty intersections. Passing isn't allowed.

3. The game ends either when one player has fewer than 2 groups on the board (in which case she loses), or when the board is full. In the latter case, the player whose smallest group is largest wins. If the players' smallest groups are the same size, compare their second smallest groups, and so on, until you come to a pair which aren't the same size. Whoever owns the larger of the two wins.

Notes

1. If you have multiple groups of the same size, they're considered separately. What I mean is: let's say you have two groups of size = 1. In that case, your smallest group is considered to be of size = 1, and your second-smallest group is also considered to be of size = 1.

2. I doubt the first rule is necessary, because of the coldness (there are times when you don't want to add two stones to the board), but it satisfies my sense of symmetry to include it.

3. I don't know if the starting setup I've chosen is best. I won't have sufficient understanding to know for sure until I've played many more games.

What is Magnapoco about?

I'll give you the overall gist and you can discover the rest. You want to create, ideally, two large groups without being forced to connect them together, while trying to force your opponent to make small groups in small territories. Sounds easy right?

[EDIT] - Magnapoco can be played on a hex board as well, and it may even turn out to be better there if edge-play gets to be too important on the square board. But for now my suspicion is that the square board is better.
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Mon Feb 27, 2012 12:45 am
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New Game: Breach (plus a discussion of the problems of n-in-a-row games)

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Reposted from Blog



I'm in a pitched battle with my own incompetence to design an n-in-a-row game I enjoy, even though I don't enjoy most n-in-a-row games. I'm doing it because trying to make lemonade from lemons is a way to improve at game design. The battlefield is littered with rinds, yet I fight on.

The challenge has forced me to understand the problems of n-in-a-row games and to think creatively about avoiding them. My best success so far is Morro, but I'm not sure about it. Now I have a new attempt to explore. First I'll present the rules and then the why's and wherefore's.

Breach is for 2 players and is played with Go stones on an initially-empty square grid that looks like this:



The column on the right is called the scoring track. One black stone and one white stone are set aside to be scoring markers for the scoring track.

I don't know what the best size is for the board, but 10x10 seems a good place to start.

Definitions

A Row is an orthogonal or diagonal straight line of same-colored stones. The Score of a row is the number of stones it contains.

Rules

1. White begins by placing 1 stone on any empty space.

2. Then, starting with Black, the players take turns. On your turn you must place 2 stones on any 2 empty spaces.

3. If you complete a row with a score of at least 2, and that score is higher than any previous score by either player, you must move your scoring marker to that score on the scoring track.

4. After you move your scoring marker, your opponent gets an additional option on her next turn (and only on that turn): instead of placing 2 stones, she may choose to place 1 stone and then replace any one of your stones on the board with one of her own.

5. If the longest row is broken up due to a stone replacement, the scoring marker is not moved back - scoring markers never move backwards.

6. The game ends when the board is full and the player with the highest score on the scoring track at that time wins (in practice the winner will be obvious well before the board is full, and the trailing player should resign at that point).
Where did it come from?

All n-in-a-row games (that I know of) suffer from some mixture of 4 problems:

1. not enough strategy (tactics dominate)
2. draws
3. imbalance
4. the pylon problem

I only recently added the pylon problem to this list (the term is from fellow game designer Corey Clarke). It refers to the tendency of stones on the board to clump together and stop mattering before the game is over. They become dead pylons. I'd like to design an n-in-a-row game where more stones "live".

For the record, my favorite n-in-a-row game at the moment is Pente, because its capture rule partially addresses all 4 problems. I think that rule's brilliant now that I understand all of its effects. However,

1. Though Pente is more strategic than most n-in-a-row games, it's still too tactical.

2. Though it's more balanced than some other n-in-a-row games, there's still a first-mover advantage.

3. Though draws are rare, they're still possible.

4. It isn't a "pure" n-in-a-row game because you can also win by making 5 captures (a condition which, one suspects, was added to reduce draws).

5. The rules are more complex than I like.

Maybe there's still room for improvement?

The lack of strategy is the most difficult issue to fix so I start with that. Morro creates strategy through negative feedback. Negative feedback here refers to a penalty for taking the lead or getting closer to the win condition. In Morro, when you take the lead, your opponent gets a stone advantage.

It's the opposite of "the rich get richer" dynamic. With negative feedback "the rich get poorer": sometimes taking the "lead" is a bad idea. As a result the players have to take the long view and play toward the endgame, rather than focus just on taking the lead. Voila. Strategy.

The great difficulty is providing just the right amount of negative feedback. If it's too strong it can wipe out tactics and if it's too weak it can fail to create strategy.

Morro's drawless and pretty balanced, but maybe:

1. it's too strategic
2. it's too opaque
3. it suffers some from the pylon problem.

The first two problems arise because players place an increasing number of stones per turn as the game progresses. The result is a tsunami of stones in which both tactics and clarity are lost. The pylon problem exists because it always exists in n-in-a-row games unless you design it away and I didn't - I wasn't paying much attention to it back then.

So back to the drawing board. The tsunami of stones can't be calmed without also dumping the feedback mechanism, so I decided to try other negative feedback mechanisms. I lit upon one which also addresses the pylon problem: when you take the lead (i.e. when you build a row longer than any built up to that point in the game), your opponent can (optionally) replace one of your stones with her own, in lieu of placing one of her stones on her next turn.

Example: lets say you're playing on an 8x8 board and your opponent has a row of three and a row of four on the same column, and they're separated by one of your stones. In a normal n-in-a-row game the whole column would be dead. But here you can't take the lead without allowing your opponent to remove that one stone of yours and to create a row of 8, which is an automatic win for him. By this kind of effect, the stones on one part of the board are important to what goes on in other parts.

This illustrates a key point: your opponent's longest row is actually the sum of his longest two rows which are separated by one of your stones, unless you're in the lead and can remain that way for the rest of the game. That's the key insight around which to start evaluating possible moves and build your strategy.

Time will tell how good this game is. It shows promise but I'll reserve my opinion until I've played it more, per general policy.

There are two other feedback rules that I tried and (tentatively) discarded. The first, which I felt was too weak, entailed choosing optionally to flip an enemy stone instead of taking your normal turn, after your opponent takes the lead. The second, which I felt was too strong, was to flip an enemy stone in addition to taking your normal turn. If further experience shows that I chose wrong, I'll revisit these. It's easy to get designs like this wrong, as I've discovered time and again.
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Fri Dec 16, 2011 11:55 pm
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Zendo as a Tool for Teaching the Scientific Method

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Reposted from my off-site blog

[Author's Note: 5 years ago I wrote an essay about a game called Zendo and posted it to the BGG Zendo page. Because it's one of the more important things I've written about games, I've been periodically editing it for years (BGG tells me I've edited it 48 times). It's now different and better than it was when I first posted it, but it's also buried deep in the bowels of the site where few see it. So I've decided to republish it here with additional modifications.]

Despite my obsession with games, I'm ever aware that they're mostly trivial. They're idle pastimes. I wish it weren't true, because it makes me uneasy to care as much as I do for such a frivolous thing.

Once in a while however, a game appears with a connection to the wider world which endows it with value and meaning. This essay is about one such game, called Zendo.

I'm a scientist, and Zendo's about the scientific method, but not only - playing it makes you skilled at the scientific method. It's also fun and addictive, rare qualities in a game with real (nay profound) educational value. I want more people to understand what an important learning tool this game is.

When a kid first learns about science in school, she usually doesn't actually learn science. Instead her teacher makes her memorize a collection of trivia and calls it science. Then the kid gets bored and stops caring. That's how it was for me anyway - I didn't appreciate science until I was older and began educating myself outside school. Only then did I realize that science isn't lifeless trivia, but rather it's a method and an art, like playing the violin, and by mastering it you can do near-miraculous things, like change the way we view reality or fix intractable problems.

When I finally understood this, I was intoxicated and I never looked back. I wonder how many others would catch the same fever without the misconceptions of grade-school.

I also wonder how many more scientists-in-training would have a better clue about how to do science. Imagine if early violin training consisted mostly of discussions about the violin. How many great violinists would there be? Not many.

Yet that's how we train young scientists, even undergrads. Sure, we hold labs for students, but a) they're infrequent, like playing the violin once a week; and b) they don't really nurture inductive reasoning or experimental design skills - they're often just recipes to turn some solution red or whatever, which have little to do with real scientific thought.

Lucky for us, there's a way to practice the scientific method, rigorously, at any level, from kindergarten to post-grad and beyond, on a table top without pricey equipment:

Zendo - the scientific method in a box.

First, an overview of the game, in which I've taken the liberty of re-theming it as an exercise in the scientific method (the original theme is some Buddhist-sounding mumbo jumbo having nothing to do with real Buddhism):

Let's say we have three players (the minimum number).

1. To begin, one player (let's call him The Universe) secretly invents a law of nature. The law describes the conditions under which an arrangement of objects on a table are to be marked with a white stone, or a black stone. Here's a simple example law: "If the arrangement contains at least 3 objects, then it's marked with a white stone. Otherwise it's marked with a black stone." The objects are usually acrylic pyramids of different colors and sizes (see picture below), but they can be anything: Legos, wooden blocks, coins, even words on paper.



2. Then, the other two players (let's call them Scientists) take turns doing experiments. Each Scientist sets up an experiment. The experiment takes the form of an arrangement of objects on a table. The outcome of the experiment is either a black or white stone which the universe places next to it, according to the secret law of nature.

3. As the game proceeds, experimental results build up on the table. The more there are, the more information the Scientists have about the law of nature.

4. Finally, Scientists can earn the right to make guesses (hypotheses) about what the law of nature is. When a Scientist states a hypothesis, the universe must create an experimental counterexample which disproves it, or else that Scientist wins.

5. I've left out a few details, but that's all you need to know to follow my points below. In summary, Scientists do experiments, observe the results, and based on those results, make up hypotheses about the law of nature, which are disproved if they're wrong.

The sequence of events mimics the real scientific method well (with one exception to which I'll return at the end). Here's the great thing: issues that pop up in real science also emerge in the game. Here are four:

1. Ambiguous Hypotheses - Sometimes, a Scientist will state an unclear hypothesis. In this case, the universe must ask for clarification to construct a counterexample. This is one of the central problems of real science too: how to construct testable hypotheses? Zendo's a forum in which to practice the kind of precise language needed to do so. Awesome.

2. Superstitions based on spurious correlations - Sometimes, thanks to the Scientists' experimental choices, a pattern of white and black stones builds up on the table which all conform to an incorrect hypothesis about the law of nature. This is how real Scientists get stuck too. And just like in real science, you get unstuck by finding an experimental counterexample to the incorrect hypothesis, at which point the Scientists undergo a "Paradigm Shift". Paradigm Shifts also happen when new investigators without the usual biases (who can interpret experimental results in a new way) enter the field. For this reason it's said that science proceeds by retirements (the older biased Scientists retire and make way for new and differently-biased ones). In Zendo, the same thing happens when someone who's not even playing walks by the table, glances at the experiments, and points out a hypothesis that the players missed due to group-think. It makes clear the value of fresh perspective and independent thinking.

3. The value of simple, systematic experimentation - In Zendo, it helps if Scientists do experiments in series, where each experiment differs only slightly from the last. This allows Scientists to quickly pinpoint the variables that matter to the experimental outcome. Scientists also learn to minimize the number of variables in each experiment, to minimize the chance for spurious correlations as described in point 2 above. These are essential practices for real Scientists.

4. The value of Occam's Razor - Scientists quickly learn how to make their hypotheses as simple as possible, because then it's easy to interpret the counterexamples that disprove them. The more parts a hypothesis has, the harder it is to infer from a counterexample what part is wrong.

These are the fundamentals of the scientific method, and Zendo presents them as no real-life lab exercise ever could, because it presents them free of the distracting technical details of real-life experiments. There's no faster or clearer way to learn them.

You can make the law of nature as easy or as hard as you want. Playing as the Universe, I've made laws which are easy for nine-year olds and I've stumped Ph.D.s. The game matches your skill level, like the exercises through which one progresses in violin training.

Further: it's not very competitive. There's usually much table-talk, and the players feel they're collaborating rather than competing, which is good for learning.

I alluded earlier to a way in which Zendo fails to mimic real science. Here it is: in real science, the universe doesn't magically construct counterexamples to your hypotheses, nor does it tell when you when your hypotheses are correct. So a real Scientist can never be sure that a hypothesis is right. There might always be a counterexample just around the corner, but he might be too stupid to find it. If there's one thing that frustrates me about science, that's it.

It's a good thing that Zendo doesn't work that way - it's a simulation of the good stuff without the bad, which makes it easier to see what's great about science. The caveats can come later.

I can't emphasize enough that Zendo isn't just a way to train Scientists. It's a way to improve thinking generally, which can make life better. Example: A few years ago I developed a debilitating health problem which doctors weren't able to diagnose or treat. Left to fend for myself, I was able to relieve the condition by the application of the scientific method over about 2 years. Had I not been so steeped in the scientific method, I might not even be here now. That's how valuable it is.

Because of all this, if I had a child I'd play a lot of Zendo with her. If you have a child, you should too. If you need to throw out the science texts to make time, do it. The facts are fish. Don't give your kid a fish. Teach her how to fish.
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Wed Nov 2, 2011 8:14 pm
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