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. Hex 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 I'd love to include Quoridor as well, but sadly the published version is from 1997, and there's an unpublished version which predates that by decades.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.

 

I've got a battalion of game designs in the pooper, which I'm usually too lazy to post here, 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

Here's a collection of iOS apps for 2-player abstract strategy games with no luck, with links to the iTunes App Store for each. It was a pain to collect them but collect them I did, both because I care about these games and because their visual simplicity works well with iPhones and iPads. Please link to games I've missed in the comments and I'll add them. Also comment with opinions about the apps I've listed, along with alternatives, to help readers find the best. I'll update this list regularly.

Classics

Multiple apps exist for each classic game and I've tested many. I've listed the best app I know of for each game.

Moderns

These games were invented recently and aren't as well-known as those above. In rare cases there were multiple apps for the same game and here again each link is to the one I consider best.

Quick, self-aggrandizing note: My game Ketchup is a finalist in Daniel Solis' 1000-Year Game Design Challenge, along with 6 other games, all of which look like they could be better than Ketchup.

So winning is probably still a long shot but who cares I'm awesome. 

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.  

 

This just popped into my head uninvited while I'm trying to go to sleep and it won't leave. I'm posting it here in the hope that I can make it go away by doing so. 

It's a way to solve a problem for a well-known win condition and an excuse to create another game on a colorful board I enjoy (the first was Swaparound). The game is called Spry, which is a contraction of the phrase "Spread Y". The problem is that if you play the game Y on a hexhex board, the center of the board is much more important than the periphery, especially on a small board. Spry is a way to fix that. 

It's for two players, played with Black and White stones, on this board:

Note that the green part of the board is divided into concentric hexagonal rings of different shades. The central cell is considered a "ring" here as well.  

Rules

1. The players take turns placing stones on the green area of the board.
2. On your turn, you may place a number of stones equal to the number of cells on one side of the innermost hexagonal ring on which you place a stone. You may also place fewer than that, but must place at least one. 
3. The first player to construct a group of stones which touches at least one yellow, blue, and red space wins. 

Note #1: if you place in the center, you can place only one stone.

Note #2: you don't have to place all your stones on the same ring. You can distribute them across rings however you want. It's just that the innermost ring on which you place a stone determines how many stones you can place.

This game will go quickly so you probably need a board larger than the one pictured here. 

There's nothing much original about this - it's really just a better, more rational way to use the concept of an earlier, not-great game of mine called Clots, to fix the center-vs-periphery problem for HexhexY.

Note that the limit on the number of stones you can place is proportional to the total number of spaces on the innermost ring on which you place a stone. From a space-filling point of view, this may be the most rational way to balance the different regions of the board by varying the number of stones you place by location. Maybe. I haven't thought about it much.

Whether it's a good game is another question. Goodnight.

This post is a bit of self-promotion to try to win a design contest. The contest is called the Thousand-Year Game Design Challenge and I'm mostly enamored with it because it's for the kinds of games I most care about: simple, elegant ones, requiring no special equipment.

The judges will consider evidence of each entry's popularity. This is my least favorite aspect of the contest, because there needn't be a correlation between a game's popularity and its quality - good PR skills can make a bad game popular in the short term. I'd prefer that the contest weren't a test of promotional skill. 

Despite the gripe, I love the contest and want to do my best to win, so I here I go promoting.

The following is a compendium of links from around the web showing how my entry, Ketchup, is being played and discussed by others. If for some reason you want to help me win, I invite you to post additonal links in the comments. I'll update these links regularly until the contest is over.

[last update: 12-28-11]

1. Ketchup has been implemented at two online sites, Mindsports and igGameCenter.
2. At igGameCenter, Ketchup has been played 146 times in the 121 days it's been there. I've participated in only 36 of these games, so it's not just me fishing for matches. 27 players have played at least one game.
3. There's a game group in Minnesota playing Ketchup a lot face-to-face. Here's the Ketchup tag page for that group's blog (with pics of people playing).  
4. Somebody from that same game group has posted a Ketchup opening analysis on BoardGameGeek.  
5. That same person posted a substantial, and super-positive review of the game, in which Ketchup is likened to a Bach Fugue. 
6. Two noteworthy Ketchup variants have been developed by other people: Spice (Ketchup translated onto a 3D, pyramidal stack of balls; this game has itself been entered into another design contest), and Ice Ketchup (a variant played with Looney Pyramids) 
7. Ketchup was played at the 2011 U-Con Abstract Games Tournament (in Michigan)
8. "Ketchup is a work of genius..."
9. "Nick's latest 'tweak' turned Ketchup into one of the very best games I've seen in a long time."
10. "Nick's game leaves little doubt about his intuitive notion: he definitely sensed a beautiful new game, a natural organism - only thing was how to capture it, and this has been a reluctant cookie to say the least. Now that's it's all cleaned up and polished, we have a new definition of territory and new mechanics to match, and a beautiful new game awaiting deep investigation."
11. Pic of face-to-face play posted to Boardgamegeek
12. ...and another
13. ...and another
14. Ketchup is a finalist in the Thousand-Year Game Design Challenge itself!

 

 

 

[Author's Note: 5 years ago I wrote an essay about a game called Zendo and posted it to the site boardgamegeek.com. Because it's one of the more important things I've written about games, I've been periodically editing it for years (boardgamegeek tells me that 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.
3. 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.
4. 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.
5. 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.

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.

 

 

Another post about my game Ketchup. I'll wait here while my game-designer friends who endure my frequent discussions of this game go and retch in a corner. Done? Ok here goes. 

This time I'm indulging my enthusiasm with strategy notes. If you don't know the rules, read this first.

There's still much I don't understand, so while these notes help you against players who have what now passes for experience, and to trounce noobs, they won't make you an expert so much as slightly prevent idiocy.   

Key Strategy Concepts

First is the central rule of thumb: if you take the lead, you'll be giving an extra stone to your opponent. Therefore don't take the lead unless, by doing so, you ensure that at least one of your opponents' stones on board will be separated from his largest group. i.e. don't give away a stone without taking at least one (and preferably more) back at the same time.

The winning player's stones usually end up in one of 4 possible kinds of patterns, or as a hybrid of 2 of them. Being aware of the 4 patterns makes you instantly better. On every turn, try to see which of the patterns are most achievable for you, and which are most achievable for your opponent. This will guide both your offensive and defensive choices. Here are the 4 patterns:  

The Fork:

This pattern is one of the most common in hex-board connection games: a chain of stones dividing the board into three segments, profoundly limiting your opponent's ability to create a large group.This is how experienced players shellack newbies. It only happens when the losing player is terrible or makes a dumb mistake, as it's easy to prevent.

The Knife:

This is the Fork's more achievable but less-powerful sister. It's a chain of stones dividing the board approximately in half. As with the Fork, it limits your opponent's ability to build a big group, but not as much, and as with the Fork, you usually have to give up bonus stones to your opponent in the attempt. This creates two problems:

1. If you fail to get all the way across, you can end up losing to a Wrap pattern (see below)
2. Even if you get all the way across, you can end up losing to the Sandwich pattern (see below)

The Wrap:

This pattern often comes into play when one player tries too hard to secure the center of the board (as connection-game players often do, because the center of the board is more important in most connection games than it is in Ketchup). The idea is to let your opponent dominate the center, but as she does, you create a containment perimeter around it, the ends of which are anchored to the edges such that her center clump is cut off from much of the board. To pull this one off, you have to force your opponent to take the lead to secure the center, which gives you bonus stones with which to build your perimeter. The difficulty with this one is that it takes a lot of stones.  

The Sandwich:

If you see that your opponent is trying for a Knife, you can try to build this to neutralize it. The idea is to build parallel flanking walls to your opponent's knife. It usually works best when you subtly push your opponent into making a knife which doesn't run directly across the middle, but rather is shifted or bent so that the board isn't evenly divided. Your opponent will usually be forced to take the lead to create a Knife, which will give you extra stones with which to make a Sandwich. As with the Wrap, the Sandwich takes a lot of stones to make. 

As I've mentioned, the winning pattern often ends up being a combination of 2 of the above patterns. Example: sometimes you may be going for a Knife, and thanks to an oversight of your opponent, you may be gifted a sudden opportunity for a Wrap, so you bend the ends of your Knife toward one side of the board and wrap around your opponent's largest group there. 

A caveat: it's hard to plan any of these patterns from the beginning if you're opponent is aware of them. Instead, the best I have been able to do is create an opening that keeps me open to at least two of these patterns and then make a run for one of them when I get an opportunity. I'm beginning to develop opening concepts however, so I may have more advice to offer on this point soon.  

Key Tactical Concepts

A key goal is to avoid giving extra stones to your opponent. The only way to do so is to keep your groups small. But then the only way you can win is by retaining the capacity to connect your small groups into an unbeatable big group later. How to do that? Answer: by creating strong virtual connections. This is a more subtle task than in normal connection games and is one of the main reasons I love this game. Here are two important virtual connections:

The Conditional Stretch:

The picture above shows a conditional stretch between White groups. Consider what would happen if Black tried to prevent White from connecting his 2 groups together: if Black placed 2 stones in the gap between White's groups, White could then place three stones around the end and connect his groups anyway. Note that the conditional stretch is breakable if your opponent can place 2 stones in the gap without giving you a bonus stone (which Black can't do in the picture). This means you can only establish a conditional stretch in certain places in on the board, relative to your opponent's stones. An important part of the game is to manipulate your opponent's placements so that you can secure conditional stretches in key spots.  

The 3-way Stretch:

The picture above shows a 3-way stretch between White groups. This is like a conditional stretch except it takes 3 stones to fill the gap instead of two, which makes it much harder to break. On the other hand, it's expensive to create this connection since it requires 4 stones minimum. Sometimes your opponent will forget to keep an eye out for it, because it's not something that comes up all the time, and if she fails to defend against it, it can give you a powerful edge. 

When the Two Largest Groups End Up Being The Same Size

This happens often (~10-30% of my games with similarly-skilled players), and I believe that as players improve it will happen even more often. If you want to be good, you have to learn to make sure your second-largest group is bigger than your opponent's second largest group. This opens a realm of strategy/tactics of which new players aren't aware. It's a realm that I'm only now exploring, so my ideas about it are tentative. In fact the only thing I can say confidently is that it increases the value of the sandwich, because the sandwich is the best choice for creating a large second group. Now, most of the time I only end up creating a sandwich in response to something my opponent does. I have yet to try planning a sandwich from the outset. If it's possible to do so with any success, the sandwich may be powerful.  Flip through the following pictures to see an example game in which both players end up trying to Sandwich each other at the same time. Both players succeed to about an equal degree, the two largest groups end up being the same size as a result, and white ends up winning because he made smarter (and earlier) efforts at building his second-largest group (see turns 14 through 19 for his key moves in this regard). 

(This game was a test game played without a scoring track, which makes it harder to follow. Apologies for that.)

I'm convinced that high level play will almost always require players to attend to their second-largest groups, and maybe even their third-largest. It may be a good idea to track your two or three largest groups by using multiple stones on the scoring track. Good players will probably graduate to larger boards, and that will only strengthen the need to strategize around multiple groups. I'm excited for this to happen because I think the game will flourish under those conditions. 

 

As someone whose enthusiasm for abstract strategy games often shades into hallucinatory mania, I wish there were yearly awards with tuxes and gowns where prizes were given to those who contribute the most to the world of these games. If that happens the first nominee should be Arty Sandler, because he's the brain behind the single best place to play abstract games online, ever, the igGameCenter.

He's committed enormous time and effort in polishing the place into a shimmering ruby, with more polish to come, and I think that with a few pushes the site will find the gigantic audience that it richly deserves. No doubt it'll happen without my help, but I've so enjoyed the site that I want to compensate it for all the pleasure it's given me. This plug is my payment.

The best way to grok the igGameCenter's unholy greatness is to play there, but if you're hesitant I'm going to convince you with the following scintillating bullet-pointed list:

1. It has 132 games, many of which you can't play anywhere else. They aren't a random gallery of dreck. Most are good, a lot are great, and many are sublime. 
2. The interface is the job Steve-Jobs-Level good. Clean lines, nothing extraneous, everything is where you expect it. An interface to make grown men weep and wish they were more beautiful.
3. The players are uniformly thoughtful and almost never refer to their dicks. I played more than 100 games there posing as a 19 year-old woman (don't ask), and I was subject to one gross dick moment the whole time. Unprecedented for an online site. Digression: I noticed that nearly everyone was "warm" to me while I was a woman, much warmer than men normally are when I'm a man. Everyone seemed excessively kind and polite. Proposal: To make the world a better place, we men should pretend that all other men are women and treat them that way. No more war, no more arguments. Just awkward attempts at flirting. A better world.
4. In contrast to most sites for abstract games, these games are in real time. They're better that way. 
5. The site tracks your ratings for every game, as well as other stats. You can watch your rating rise and say to yourself "Yes sir ma'am, I really am getting smarter", or you can watch your rating fall and it will remind you to take your Alzheimer's meds.
6. You can play with or without time controls, ranked or unranked games, and your games can be private or public. I play all my games public because then other players stop by to say hi and chat in the chat window while I'm playing. Especially when I'm a woman.
7. You can find lots of well-known classics there: Chess, Go, Checkers, Mancala, Othello, Connect 4, Shogi, Dots and Boxes, a Scrabble clone, and even Battleship for when you want to feel like a bored 8-year old. You'll also find variants of these games as well, like Grand Chess, or Russian Checkers, or Anti-Othello
8. The Sandbox: this is a utility that lets you play abstract games which haven't been coded into the site yet. Abstract games designers use it for playtesting their new games. I would marry it if I could
9. Bots. This is a new development. Some of the games have AI players you can play against.
10. The greatest strength of the site, though, is that nearly *all* the best modern abstracts are there. It's amazing. Abstract game design is in the middle of a renaissance, and nowhere is the fruit of this period on better display than at the igGameCenter. Example:
11. The single greatest abstract strategy game ever invented (objectively speaking), called Slither, can be played at the igGameCenter, and nowhere else. I swear to you. I've been obsessively designing and playing abstract games for many years and Slither stopped me in my tracks. It's a watershed game.

Top 10 Modern Abstracts You Should Try at the igGameCenter, in My Unassailable Opinion.

1. Amazons
2. Arimaa
3. Dameo
4. Emergo
5. Gonnect
6. Havannah
7. Hex
8. Hex Oust
9. Lines of Action
10. Slither

The One Other Game That You Absolutely Must Try at igGameCenter

1. Ketchup - I just happened to have designed this one, but that fact is totally incidental to my recommendation.

Go play there or else I'll sneak into your house in the night and break all the eggs in your fridge. I'll make it easy for you. Another nice feature is that I can embed the igGameCenter anywhere, like so: