Definitive List of 2-Player Abstract Strategy Games for iPhone, iPad

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.

9 Men's Morris - Create lines of 3 of your own pieces in a row to capture your opponent's pieces. Win by capturing all but 2 of your opponent's pieces. The app features 9, 11, and 12 Men's Morris, at 10 AI levels, or against another human, on an array of well-designed boards. The app has many other goodies as well.

Checkers - Capture opponent pieces by jumping over them. Win by capturing all your opponent's pieces or blocking him so he can't move. Play against AI at several levels or against another human. Excellent user interface that highlights legal moves on your turn. You can play with or without the compulsory capture rule.

Chess - This is almost certainly the premier app for the most famous western abstract game. Everything about it is amazing and I can't even begin to list the features. It has everything you'd expect plus crazy stuff like a database of more than 100,000 historic games for you to play and study. Check this out if you want a master class in app design.

Connect 4 - One of the simplest of the classic games. Drop chips into slots to be the first to a row of 4. Play against the computer, with friends via bluetooth or pass-and-play, or over the internet. Lots of achievements to play for, several different game modes, and even has cut-scenes and exploding chips. Ridiculous.

Dots and Boxes - Players take turns drawing lines between dots on the board. When a player draws a line that completes a box, the player "owns" that box. Whoever owns more boxes when the game board is full is the winner. Play against a friend via pass-and-play or against the computer opponent with several different difficulty settings.

Go - The Emperor of Boardgames. 2000 years old and deep as the ocean. It's notoriously hard to create good computer opponents for Go but this app has a pretty good one. As with Chess, there are many Go apps to choose from and this is one is very good. Has nice touches like the ability to replay a finished game from any given move.

Go Moku - A simple, ancient game from the far East. Players take turns placing stones to be first to create a row of 5. Play against one of four levels of computer opponent or against a friend. Multiple board sizes to choose from. Notable feature: you can start a game by bumping your phone with your opponents'.

Hex - Hex has among the simplest rules of any game, and yet it's deep. It's also the main inspiration for teeming hoards of abstract game designers (to the extent that they teem), me included. Play against computer opponent or over the internet against players all over the world (the computer opponent is weak).

Mancala - Another ancient game. Scoop up pebbles from a pit and sow them, one at a time, into other pits. A fantastic app with georgeous graphics. Play against the computer, over the internet, or with a friend via pass-and-play or bluetooth. Player ratings, leaderboards, and lots of other goodies.

Pente - This game is like Go Moku above (you try to complete a row of 5), except it has a capture rule and a few other enhancements. Play against a friend or 3 levels of computer opponent. This is the best Pente app I could find but it's not perfect. The computer behaves a little oddly and will be a little easy for some people.

Reversi (Othello) - Well known game where you flip rows of your opponents' pieces by bracketing them with your own pieces. Player with the most pieces on the board when it's full wins. Play against human or 6 levels of computer opponent, on multiple boards. Includes strategy hints and scoreboards.

Shogi (Japanese Chess) - This game, one of the most popular in Japan, has only lately become well known in the West. Many who play it, me included, end up liking it more than we like regular (Western) Chess. Captured pieces can "parachute" back into battle, which changes everything. Excellent app with all the features you could want.

Tafl - Game of unequal sides invented by Vikings (!!!) hundreds of years ago. One side tries to help his King escape, while the other side tries to capture him. Has lots of features and pretty graphics. You can play against humans in realtime or via email, or against the computer opponent, but the computer opponent is pretty weak.

XiangQi (Chinese Chess) - The national game of China and reportedly the most-played game in the world. It's like regular (Western) Chess, but the pace is faster and there's more action. There were tons of XiangQi apps to choose from, and this one is great.

 

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.

22 Apples - Move around the board and be the first to collect exactly 11 green apples or exactly 11 red apples, or force your opponent to collect more than that. 3 different variant games available, and 3 different levels of computer opponent. Or play against friends via-and-play, or over the internet. Includes leaderboard and achievements

Alchemy - Combine different pieces together in stacks and prevent your opponent from doing so. Stacks occasionally explode. Play against a friend via pass-and-play or against the computer opponent at different difficulty levels. Good graphics and competent computer opponent.

Arimaa - A popular modern abstract. Players race to move a piece from one end of the board to another. The app is high-quality, with lots of features: tutorials, various difficulty levels, handicaps, play against humans or computer opponents, rating system, email games, the ability to replay games, and more.

Blokus - Probably the most commercially successful modern abstract game, it's a little like Tetris: players try to fit differently shaped objects into a grid and prevent their opponents from doing so. Can be played with 4 players as well as 2. The app is great and colorful. Play against computer or against humans via pass-and-play or over the internet.

Clara - This is like Hex in the classics section above, with the key difference that there are no spaces on the board. You place objects in an open field and try to connect them to create a chain across the board one way before your opponent can create a chain to cut you off. I don't know much about the app - it's one of the few that I haven't played.

Coffee - This game is like Gomoku above, but your opponent can limit where you place a stone on your turn. The game is quick and light. Play against computer opponent or other humans over the web. Features chat, ranking system, and nice graphics. Note: this game has nothing to do with actual coffee.

Connect6 - This is like Gomoku in the classics section except players place 2 stones per turn instead of one, in an effort to form a row of 6. The game is more balanced and has more interesting tactics than Gomoku, in my opinion. The app features computer opponents, pass-and-play against a friend, internet play, and puzzle-solving challenges.

Diaballik - This game is a little like rugby or soccer: you pass a ball between your pieces to try to move it to your opponent's side while your opponent tries to get his own ball to your side. Play against a friend via pass-and-play or against a computer opponent. Two different variants of the game are available.

Hey, That's my Fish! - An ice-floe with a bunch of penguins on it is breaking up and you try to get your penguins on the biggest chunks and strand your opponent's penguins on the little chunks. Play against the computer or human opponents on any of several different board layouts. Game includes an optional move-timer with several settings.

Hippos and Crocodiles - Place pieces to crowd out your opponent and make it impossible for him to place his own pieces. One player's pieces are shaped like hippos and the others' like crocodiles. Play against computer or online against other humans. Features chat, high scores, rankings, and great graphics.

Hive - Take turns placing and moving pieces on a table, making sure to keep all the pieces connected in one big group, and try to surround your opponent's "queen" piece. This app is not an "official" version of Hive - it's a ripoff. I'll list it here until the rightful owners of Hive create an official app. As it is, this app is pretty good.

Jin Li - Fish swim around obstacles and get points for swimming close to other fish. Play against a computer opponent or against a friend via pass-and-play. You can play without time-constraints or use the adjustable game timer. You can adjust the length of the game by changing the number of points needed to win.

Mana - This one is for iPad only. Winner of an international game design competition called the Concours International de Créateurs de Jeux de Société. A fast, Chess-like game with unusual mechanisms. Play against a computer component or against friends via pass-and-play. Features a game timer for high-pressure games.

Martian Chess - Chess-like game where the pieces change sides depending on where they land. Score points to win. Play against another human via pass-and-play or over the web, or against the computer opponent. Beautiful, soothing graphics. This app is free but it has ads (you can disable the ads by paying a small fee).

The Octagon Theory  - You place pieces on the board, rotate them, and push enemy pieces off the board. Push more pieces off than your opponent to win. Play against a friend via pass-and-play or against the computer opponent at 4 difficulty levels. Play a basic or pro variant, and timed or non-timed games, on any of 3 board-sizes.

Pentago - One of the most commercially successful modern games. This is like Gomoku in that you try to complete a row of stones. But here one quadrant of the board is rotated 90 degrees on every turn, which leads to surprises. Play agaist a friend via pass-and-play or against the computer opponent. It doesn't have a ton of features but it's well done.

Quoridor - One of my favorite games, though this app is pretty poor. Players construct a maze on the board, and each tries to set the maze up so that his piece can get through it faster than his opponent's. Play against a friend via pass-and-play or against a computer opponent on one of 3 difficulty levels.

Taiji - Build groups of pieces in your color, and try to prevent your opponent from doing so. The player whose groups have the largest combined group size wins. Play against a friend via pass-and-play or against the computer opponent. The free version has a small board and you can pay to expand the game to it's full size.

Tix  - You place cubes on a board, move them, activate them and inactivate them. The goal is to inactivate all your opponent's pieces. Play against a friend with pass-and-play or against 3 levels of computer opponent. Includes achievements. Great graphics and smooth play.

Trax - Simple, deep game, which could just as well have gone in the "classics" section, given that it's widely admired and was invented in 1980. Place pieces on a board and try to be the first either to form a loop or a line in your own color. Play against a friend with pass-and-play or against the computer opponent.

Versus - Score points by moving pieces to various locations on the board, but your pieces can be moved by opponent pieces which act like magnets, or even converted to the other side. There are 2 game-modes (fast and slow), and you can play against a friend via pass-and-play, but note: there is no computer opponent.

Wizard Hex - Transmute your pieces and use special piece powers to gain territory. Maybe the best graphics I've seen - like playing with enchanted amulets from Middle Earth. Play against the computer, with a friend via pass-and-play, or over the internet. Features voice chat and internet leaderboards. For 2-4 players.

New Game: Breach (plus a discussion of the problems of n-in-a-row games)

Small-lemons
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:

Breach_board

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

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.  

 

New Game: Spry

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:

Spry_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.

Ketchup Popularity Tracker

Popularitycontest
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!

 

 

 

Zendo as a Tool for Teaching the Scientific Method

Galileo2
[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.
    Acrylic_pyramids
  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.

 

 

Ketchup Strategy Basics, Plus an Example Game

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:

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:

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:

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:

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:

Cstretch

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:

3stretch

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). 

(download)

(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. 

 

The Beauty and Wonder of igGameCenter

G3005

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 would have jobbed were he into abstract games. 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 4.0 - 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:

 

 

Games of Interest from the 1000-Year Game Design Challenge

I just submitted my game Ketchup to an interesting game design contest, called the 1000-Year Game Design Challenge, and I couldn't help but riffle through the other entries to see what the competition looks like. Below I've listed the entries that caught my eye. These strike me as the most simple, elegant, and original of the bunch, at least from a reading of the rules, which come to think of it doesn't mean much because you don't really know how a game will come alive until you actually play it, but anyway...

Tricala - Multidirectional Mancala on a Triangular Board. Could make brain melt out through nose.

Charing Cross - A minimalist crossing game. Could be great if good play doesn't lead to infinite cycles. Hard to tell.

Fuckin' Do It Then - Here I was taking pride in being the worst namer-of-games, and then I see this. Despite the heroically stupid name, this strikes me as a fantastic idea. A word is picked from the dictionary.  The player who bids the lowest number wins that word. That number represents the number of words he can use to get another player to guess the word from the dictionary. Imaging the kind of clues I'd come up with, and how I'd evaluate bids fills me with sheer delight. If I had to pick a winner from the rules only, this might be it. [EDIT - Someone indicated to me that this appears to be either a ripoff or an independant reinvention the concept implemented in 25 Words or Less. Takes some of the shine off it for me.]

Cartography - This could be bland or it could be great, but it certainly is elegant in conception. Players take turns placing triangular tiles in order to form loops. I've been trying to design an elegant loop-forming game for a loooooooong time (here's my best attempt so far) and this one might steal my thunder if it turns out to be good. This one gives me that I-can't-believe-I-didn't-think-of-that feeling.

Librarium - A parlor game for bibliophiles (I'm one).  Players sit around in room full of books, somebody reads a passage from a randomly selected book, and then there's a mechanism by which the players try to guess which book the passage came from. It's simple and original, and the clincher is that you might learn a lot while playing.

Pandora's Box -This is a completely psychological game, looks to be bluffing-heavy. If there's enough open information to make the bluffing interesting, this could be great.

Sygo - This is a Go variant using an unusual and original turn protocol that greatly effects the game's dynamics. The core idea is that you can either place one stone not adjacent to any of your others, or you can add one stone to each of your preexisting groups. There's much tension in deciding when to do which.

Yodd - Players build groups of stones on a board. There must be an odd number of groups at the end of each player's turn. The player with the fewest groups on board when the board is full wins. Simple and brilliant in concept. Could be my abstract game of the year.

Note that the submission period isn't over yet.  I may add more to this list as they come in.

 

Revised Game: Glorieta 2.0

Circular_reasoning

Here's an improved version of my game Glorieta. First I'll present the rules and then explain how they got this way.

Glorieta is a game played for two players with black and orange stones on a board that looks like this:

Glorietav2

The filled spaces on the board are called Neutral Spaces.

Definitions:

  • Loop - a connected group, composed of like-colored stones and possibly neutral spaces, which completely surrounds one or more spaces, regardless of what's in those spaces.  The picture below shows an example of a black loop and an orange loop. Note that loops can overlap, because they can share neutral spaces.

Glorietav2_loops

Rules:

  1. Player 1 places one black stone on any non-neutral space and Player 2 two decides whether to take ownership of the black or the orange stones.
  2. Starting with Orange, the players take turns, each dropping 1 stone on her turn. Stones may not be placed on neutral spaces.
  3. The first player to form a loop wins. If no loop forms, the game is a tie.

That's it for the rules. How did they get this way?

Last week I played a bunch of matches of an earlier version of the game that I call "chicken" Glorieta. The extra experience revealed that the game isn't what I thought. I expected it to become more strategic with increasing experience, but instead it's grown more tactical. And now I see that optimal play is probably entirely tactical, for reasons I couldn't see before.

As I mentioned when I first presented Glorieta, the key to designing the game is to make it sufficiently easy to form a loop (they don't form naturally on Hex boards). What I failed to see is that if I made all possible loops easier by the same degree, I'd end up with an overly tactical game. 

The reason is that, since the smallest loop is only 6 stones, if it gets too much easier to make that loop, the game will become entirely about doing so, and that will involve mostly tactics. Maybe this wouldn't be bad, except that my reason for designing this game is to unlock the strategic potential of loops. 

Glorietta makes loops possible by the introduction of neutral stones which both players can use to form loops.  But here's the thing: if two or more neutral stones can be close enough to all be part of a six-stone loop, then it opens up the possibility of very easy-to-build six stone loops. 

With "chicken" Glorieta, the players have control over where the neutrals go. If optimal play required players to place neutrals far apart, there would be no problem, and optimal play would also lead to the most interesting play, but that appears not to be the case.

As far as I can tell, good play in "chicken" Glorieta requires a player to place neutrals close together in such away that his stones are better connected to them than his opponent's are.  As both players do so, neutrals pile up close to one another and the game swiftly ends. Neither player ever bothers trying to create large loops. 

So the key insight here is that in order to ensure a strategic, as opposed to tactical game, something must keep neutral stones from being too close together. 

There are two general ways to ensure that:

  1. Impose a rule limiting how players use neutrals.
  2. Create an initial layout of neutrals to ensure a good game.

After much fiddling, it became clear that the second possibility is much better:

  1. By designing the initial neutral layout, I can adjust the balance between tactics and strategy. The more stones the initial layout has, and the closer together they are on average, the more tactical and the less strategic the game gets. This was the biggest selling point. Rarely do games admit of such control over the balance between strategy and tactics. It gives me confidence that I can make this a good game.   
  2. I also learned that a good initial layout can ensure that the edges of the board aren't wastelands, and that play spreads out.
  3. This choice yields a simple ruleset (not only is it my simplest loop game, it one of my simplest of any kind).
  4. I can't figure out how to impose a rule limiting how players use neutrals which isn't awkward.

Note: the layout of neutrals at the top of this post isn't the final word. The best layout can only be determined over time by many players. 

I don't love that ties are possible, but it's an asthetic objection rather than a practical one because you can make the draw ratio as low or as high as you want with the initial layout. I can live with that. In fact, I kind of like it, because it means I can make the draw ratio about the same as it is for Havannah, which is ok because my original design goal was to create "Havannah but for loops only".

(Note: there's a way to eliminate even the possibility of ties by imposing an additional rule that if you make it impossible for your opponent to form any loop at all, you lose instantly.  But I don't like it enough to include it. I'd rather just increase the number of neutral spaces.)

For those interested in allowing players to control the neutrals, here's the best ruleset I've come up with which gives control of the neutrals to the players:

  1. The board begins empty. To start, black drops a friendly stone.
  2. From then on, starting with orange, the players take turns. On your turn you must drop 1 friendly and 1 neutral stone such that they're not part of the same group, if possible.
  3. The first player to form a loop containing at least 6 friendly stones wins.

You'll notice that there's no longer an option to decline placing neutrals.  I've become convinced that neither player would ever be motivated to decline, because each player can always find a spot for a neutral that helps her more than it does her opponent.  If there's never a reason to decline, it may as well not be an option.

These rules don't address the problem completely, since you can still place neutrals in close proximity.  But it's less useful to do so because they can't be used to make the smallest loop threats.  This game is still pretty tactical even if it's an improvement over the earlier version.  For example, it remains possible to build a loop containing eight stones in total, two of which are neutrals. I also feel that maybe the game is a bit more opaque. For these reasons, my jury's out. I'm sure it's an improvement over the "chicken" version of the game I presented in my last post, but I doubt that it approaches the quality of the fixed-layout version.

There are other rules that I could have chosen that would have solved the problem more completely, but I couldn't find one which wasn't too awkard. For example, I could have imposed a rule that on each turn, a player drops 1 friendly and one neutral stone. the distance between any two neutrals on the board must be at least 3 steps, if possible.  Failing that, the distance must be at least 2. Failing that, 1. Failing that, none.  Awwwwwwkward. 

So, I leave this as a challenge: find a way to give the players control of the neutrals such that the neutrals end up spaced throughout the board with optimal play. 

Finally, below is a pdf of boards for paper and pen play (red and black pens will do).  Note that I've provided three different initial neutral layouts to play with. The "official" one is the one on the far right.

Click here to download:
PnP_boards.pdf (218 KB)
(download)