KenKen or KEN-KEN is a style of arithmetic and logical puzzle sharing several characteristics with sudoku. The name comes from Japanese and is translated as “square wisdom” or “cleverness squared”.

Related: list of logic puzzels

Rithmomachy, sometimes known as The Philosophers’ Game) is a highly complex, early European mathematical board game. The earliest known description of it dates from the eleventh century. A literal translation of the name is The Battle of the Numbers.

I have a description of the game, but I can’t find a decent rule book. Anyone ?

Henry Ernest Dudeney (10 April 1857–24 April 1930) was an English author and mathematician who specialised in logic puzzles and mathematical games. In 1917 he published Amusements in Mathematics, 430 puzzles with solutions. Amusing indeed!

An example:

Two trains start at the same time, one from London to Liverpool, the other from Liverpool to London. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?

Solution: One train was running just twice as fast as the other (hint: when the trains pass eachother they are running for the same time).

Modern video games mean big business, and big controversy. Yet most of the charges levelled against games—that they stunt minds and spark addiction—are based on an outdated understanding of what gamers do when they sit down to play.

Opinion by Tom Chatfield in the June issue of Prospect.

A selection at Mensa.

Way back, my first video games were : Pong, Donkey Kong and Pac-Man. If I see my sun playing now, than video games have come a long way.

My sun came home with a rubik’s cube ! I hadn’t seen any since… 20 years at least. The whole weekend he has been studying and trying to solved it.

And now some more work to beat Edouard Chambon, the world record holder for fastest single time on a 3×3x3 Rubik’s Cube with a time of 9.18 seconds and fastest average time of 11.48 seconds. These records were set at the Murcia Open February 23, 2008:

The famous chess player Bobby Fisher died yesterday in Iceland aged 64. Great at playing chess, but controversial as a person.

Solution to yesterday’s puzzle. The top row must be one of the four following numbers: 192, 219, 273, 327. The first was the example given.

It will be seen in the diagram that we have so arranged the nine digits in a square that the number in the second row is twice that in the first row, and the number in the bottom row three times that in the top row. There are three other ways of arranging the digits so as to produce the same result. Can you find them? (Answer)

– Henry Ernest Dudeney, Amusements in Mathematics, 1917

1. Open Excel.
2. In a blank worksheet, select “Save as” and choose “Save as web page”.
3. Click on Publish and Add interactivity.
4. Save as any name you like.
5. Load in the page with MS Internet Explorer, Excel will appear in the webpage.
6. Go to row 2000 Column WC
7. Highlight all of row 2000 and press Tab.
8. Hold the keys Ctrl, Alt, Shift and click on the Office Icon.
9. And…

Use the arrow keys to drive your car. The “0″ key to drop paint slicks. The spacebar to shoot. The “H” key for headlights. NOTE: you need DirectX for this to work.

The game of chess has its roots in rationalism. And, like the Enlightenment itself, argues Sally Feldman, it’s a force for both liberation and tyranny.

Whatever became of Geff, the Talking Mongoose of Doarlish Cashen? What this baffling creature was doing on the Isle of Man to begin with is mystery enough. And what of Pasquale Erto, the Human Rainbow from Naples, who would appear nude and in a self-induced trance, with rays of light six yards long emanating from his body? It is a pity no camera ever captured the full effect. Adrian Searle attends a very strange exhibition – and wonders how these pictures ever fooled anyone.

“Ma’am, books are like Kryptonite to gangs.” Steve Wasserman worries about the decline of coverage of books in newspapers.

Want to outsource your personal life ? Indian call centers is the answer (it’s an American thing… – not something I see myself doing)

And here is a story about an egg that costs 8.9 GBP, eh 8.9 million GBP, a Fabergé egg that is.

Related to my previous posts Virtual worlds (A-L) and Virtual worlds (M-Z), Howstuufworks has a post on how MMORPGs work. More info at the unavoidable wikipedia, the Daedalus project, a series of articles posted at Gamespy, and the Evolution of MMORPGs – a paper written by Jiyan Wei, London School of Economics.

Link to Virtual worlds (A-L)

The Manor is my personal statement to the world that the lone coder is alive and well, and still writing programs that count. You can build your own world here, customize the experience to your hearts content, or yes, just chat with new and old friends. It’s a 2D visual chat experience that runs on almost any personal computer. And it offers everyone a choice of virtual online worlds, where you can be anyone — or anything — at all (according to the web site). Basic functions free. Membership $20 per year.

Many One is building the Public Internet Media System — a service that empowers non-profits, companies, agencies and individuals to build and operate financially self-sustaining community and web portals. ManyOne Networks is a for-profit company backed by individual and institutional investors. The company will become wholly owned by the non-profit ManyOne Foundation in the future. Thus, the company is structured to ensure that its activities and assets remain dedicated to public benefit, while providing financial partners with a responsible, capped return on their capital. Through this groundbreaking socially responsible business architecture, ManyOne will become the Internet’s first truly public information service, designed to serve the needs of citizens worldwide, in partership with the world’s most trusted institutions. Seems to be an effort to create a digital universe. Wikipedia entry. Perhaps this does not really qualify as a virtual world. Still in progress.

Microsoft Flight Simulator is a flight simulator program for Microsoft Windows, marketed and often seen as a video game. But it’s more than that with virtual flight networks such as VATSIM and IVAO. Wikipedia entry. Players must purchase Microsoft Flight Simulator X Deluxe Edition, which retails for about $45.00.

Millsberry is an advergame developed for General Mills. Free.

Moipal is a friend you create on the internet and that lives in your phone. With MoiPal you can play fun games or just hang out and have a talk with some other pals. Free.

Mokitown is the exciting city of the mobile kids on the internet. The mobile kids or simply the Mokis, invite you to explore the city, meet other kids, chat with them, experience thrilling adventures and learn more about your safety in road traffic. You turn into a Moki too, as soon as you take part in the adventures of Mokitown.
Explore the nine different areas of Mokitown and discover the great games or meet Benedikt, the flying robot. Click on Benedikt and he will ask challenging questions about road safety, geography or general knowledge. Sometimes you can also play little games with Benedikt. If you succeed you will earn Mobility Points which you can use to get new things throughout Mokitown. You can also earn points playing the big games at the Airport, MokiCabaña, Port Kikomo, Mokington Heights or Kikiyama Square. Meet the challenges of Mokitown successfully and you will receive more points. Mokitown is one big chat area. Meet other Mokis from around the world and explore the city with them. Buy a cell phone and you can chat with other Mokis that own a cell phone throughout the city. A virtual world where kids can learn about traffic safety provided by DaimlerChrysler. Free.

Moove Online is a 3-D chat world in which users can customize their own avatars, including clothing, postures, and movement. They can also create their own chat rooms. The publisher also recommends Moove chat rooms as ideal venues for online professional meetings or sales sessions. Webcam and voice support offered. Wikipedia entry. Free.

My Noggin is an educational online subscription service brought to you by the creators of Nick Jr. and Noggin in which you interact with Nickelodeon characters. 7 days free trial.

Neopets is a virtual pet website based around the eponymous virtual pets that inhabit the virtual world of Neopia.Wikipedia entry. Free.

Nexus: The Kingdom of the Winds is an MMORPG loosely based on Korean mythology and on a series of graphic novels by an artist named Kim Jin. A few features that distinguish Nexus from other MMORPGs are its 2D tile graphics, intense player involvement, a central storyline, and its anime-like style. The highly popular game Lineage was based on a fork of the Nexus server software. Wikipedia entry. Free play to level 49.

Nicktropolis (also known as NT, Nicktrop or Ntrop) is a massively multiplayer online game that is part of Nick.com. The game is aimed at 9- to 14-year-old children, however, the game can be appealing to anyone. There have been almost 100 rooms in Nicktropolis, some of which have been removed or temporarily closed.Wikipedia entry. Free.

Piko Island is a 3-D environment featuring high-quality graphics, customizable avatars, chat, and the ability to own online space, but since 03 Nov I read : “Our hosting company has experienced a problem (ok, a meltdown LOL) with the server hardware hosting the main database and objects. The good news is we have recovered a majority of our objects but the bad news is others are still M.I.A. and some of our textures are muddled up.”

PlanetSide is a massively multiplayer online first-person shooter computer game published by Sony Online Entertainment and released on May 19, 2003. In PlanetSide three empires fight for control of 10 vast planets. Each soldier in each Empire is a human player.Wikipedia entry.

Red Light Center is an online adventure in a virtual Red Light District modeled after Amsterdam’s Red Light District, where you have the freedom to enjoy a wide variety of world-class interactive adult entertainment. You can anonymously meet, chat and interact with other visitors in RLC. You can go to movie theatres, strip clubs or go shopping, together with other avatars or alone, just like in the real world! VIP’s can get a free hotel room, or head to the passion club and have private encounters with other users in RLC. Wikipedia entry. Limited free access and VIP access from $20 a month.

Runescape is a massively multiplayer on-line role-playing game (MMORPG), it is also the name of a virtual world with monsters to kill, quests to complete and treasure to win. RuneScape is more than just a game: it is an evolving world of remarkable depth and flexibility. Players control a character and train them to improve and become more powerful, or simply to become more skilled. A player may even decide not to improve at all, and simply trade goods in one of RuneScape’s many markets.Wikipedia entry. Very popular. Free basic access. Upgraded access start at $5 a month.

Second Life is a 3-D virtual world entirely created by its Residents. Since opening to the public in 2003, it has grown explosively and today is inhabited by millions of Residents from around the globe. Competitors are There, Active Worlds and Red Light Center. Wikipedia entry. Basic features free and several membership plans for additional features like land ownership and weekly stipend

Shanda operates a series of MMORPGs like The Legend of Mir II, The World of Legend, The Sign, The Age, Magical Land, RO, D.O., and Dungeons & Dragons Online (links to all these via the Shanda portal).

Sims 2 Online (or here) is a massively multiplayer online game variation on Maxis’ highly popular computer game The Sims. Links to wikipedia: The Sims, The Sims 2 and The Sims Online. Free trial possible and than $9.95 a month.

Spore is a multiplatform god game under development by Maxis and designed by Will Wright (The SIms…) that allows a player to control the evolution of a species from its existence as a multicellular organism to a spacefaring sapient creature. The game has drawn wide attention for its massive scope, and its promise to simulate this development of a species through open-ended gameplay using procedural generation. Spore is expected to be released sometime in 2008. Wikipedia entry. Price ?

Star Wars Galaxies Players enter an online universe modeled after the successful Star Wars film series. They can choose to take rolesin one of nine professions, including Jedi, Bounty Hunter, Smuggler, Office and Commando, among others. Missions take place both in space and on the ground, and between missions, players can socialize with other players. Wikipedia entry. Free trial.

Stardoll is (according to their site) a paper doll dress-up community site for everyone who enjoys fun, fashion and making friends. At Stardoll you can create your own doll or choose from our always growing collection of celebrity dolls and dress them up in our virtual fashions. Every celebrity doll has a wardrobe full of unique clothes and outfits, each month there are new and there are new dolls released every week. The membership is completely free and most of our members are girls and boys between the ages of 7 and 17. Stardoll is one of few places on the Internet developed with an emphasis on girls’ self-expression and fantasy fashion play.

There is an online hangout where users can meet friends, play games and explore a 3-D virtual world that they can also help design and build. Players can customize avatars. Wikipedia entry.

Ultima Online is a fantasy role-playing game set in the Ultima universe. It is online-only and played by thousands of simultaneous users on various game servers, also known as shards. It is known for its extensive timing-based player versus player combat system. Wikipedia entry. 14 day free trial period.

uWorld is a Matrix-kind World with NHCI(Natural Human Computer Interaction), it provides the internet users with an environment to experience virtual living. In this matrix-kind world, internet users can have an life experience that is completely different with their real life, communication, entertainment, production, exchange, study etc. uWorld gives them an opportunity to reincarnate themselves in this fascinating virtual world, and accomplish the life goals that they’ve been dreaming of all the time. uWorld is the next-generation natural interactive platform. The users not only can live in this fascinating matrix-kind world, but also can receive and process all types of information on the internet through the use of certain tools or methods; uWorld is a platform for creation – both the users and the other matrix creators can create their own items, rules or magic zones on the platform; uWorld is a platform for shared resources – users can share their resources with each other through this platform; uWorld is a platform for highly interactive society and economy – facilitates the formation of social circles and value chains among users and organizations.

Virtual Ibiza is built in an immersive 3D environment which has the look and feel of all the coolest places on the island of Ibiza. Invite people back to your own apartment, chat, meet and make friends with people via the instant messenger and web-cams. Free.

Virtual Magic Kingdom is a free massively multiplayer online game run by Walt Disney Parks and Resorts Online. It is a virtual representation of the Disneyland and Magic Kingdom theme parks, and it contains areas and games which are based on real park attractions. Wikipedia entry. Free.

VZones, originally called WorldsAway, is the latest incarnation of a virtual world whose roots go all the way back to the very first visual virtual world, LucasFilm’s Habitat (launched in 1985 for Commodore 64 machines). VZones maintains the original Dreamscape world developed by Fujitsu, plus two other worlds called newHorizone and Second Kingdom that must be accessed and paid for separately. Fee varies depending on features.

Webkinz is a virtual world targeted at owners of Webkinz plush toys. Wikipedia entry. Free but you must first buy a Webkinz pet, which gives you one year of access.

Weblo is a parallel universe based on the real world. Members own and manage websites that are virtual replicas of real cities, states, properties, domains and celebrities. Members earn real money via hits, Internet ads and by selling or auctioning assets for a profit. Members enhance their online portfolios by claiming popular social networking profiles, blogs, emails and videos in Weblo’s Calculate Your InterNET Worth section. Free citizenship.

Why Robbie Rocks is an avatar-centric 2D fashion world offers its target audience of 12-20 year olds the ability to play with avatars that function as virtual paper dolls. WRR taps into celebrity culture by offering pre-made avatars that resemble popular celebs, including Justin Timberlake, Beyonce, J-Lo, Orlando Bloom, and Paris Hilton. Members are also encouraged to create their own unique looks which can be individualized with a wide variety of trendy clothing and accessories. Dressed-to-the-nines avatars can interact in glamorous social settings like pool, beach, and lounge areas or the cityscape or country-themed rooms, which are a mix of graphic illustrations and photographic backgrounds. Free.

Whyville is an educational virtual world for children and teens, ages 10-16. Originally established to support an LA Times weekly science education article, this world’s motto is “learning by doing.” True to its word, Whyville actively engages its visitors and encourages them to participate in fun, educational events that give kids “hands-on” experience with science projects (in a virtual way, of course). Wikipedia entry. Free

World of Warcraft is probably the most popular MMORPG around and is set in the fantasy Warcraft universe. Wikipedia entry. Free 10 day trial.

Ending this list with World of Warcraft seems fitting. Did I miss any ? Of course. There are numerous other virtual worlds and it’s also not always clear if something qualifies as a virtual world or not. Still the purpose was to list some examples and that’s what we did. Suggestions are of course welcome.

A virtual world is a computer-based simulated environment intended for its users to inhabit and interact via avatars. This habitation usually is represented in the form of two or three-dimensional graphical representations of humanoids (or other graphical or text-based avatars). Some, but not all, virtual worlds allow for multiple users. Some examples (yep, a complete list is next to impossible) to give you an idea of what is available:

A3 Awakening: Alien Adoptation Agency. While there are countless space games, or games with medieval themes, the AAA is based on aliens! And while there is a somewhat sci-fi feel to the game, in places, you’ll soon find that these aren’t your typical aliens. Ever seen an alien, wearing a sun dress, go fishing? No? Then you’ve clearly not played the AAA. $ 4.50 per month.

Activeworlds. In Activeworlds, players can create their own virtual homes, and visit the homes of other users. Hundreds of thousands of users inhabit over 1,000 unique worlds. See also Wikipedia entry. Simple user account is free, “citizenship” costs $6.95 a month.

Adellion. This MMORPG (Massive Multiplayer Online Role-Playing Game) will be set on the island Aryiure in the Adellonic year 3200 TS. This is a time when technology is medieval and several different cultures dominate the island.The game has not yet been released so cannot be currently played. It is currently undergoing a closed alpha test. Price ?

Asheron’s Call. AC is a fantasy MMORPG for Microsoft Windows-based PCs, released on November 2, 1999. The land of Dereth and its surrounding islands are a vast, seamless 3D world that is occupied by thousands of players. Wikipedia entry. Free trial (14 days) and then $ 12.95 a month.

Barbie Girls. Designed to be a safe, fun, and exciting place for girls to play online, you can create and decorate a virtual room, adopt a pet, have a B Chat™ with your friends, go to the mall, earn and spend B Bucks™ on cool fashions, accessories, and more. Free as far as I can tell.

City of Heroes (CoH) is a massively multiplayer online role-playing computer game based on the superhero comic book genre. In the game, players create superhero player characters that can team up with others to complete missions and fight villains belonging to various gangs and organizations in Paragon City and its surrounding areas. Wikipedia entry. $14.99 a month.

Club Penguin is an online game developed by New Horizon Interactive and later bought by Disney. The game is designed for children ages six to fourteen, though available to anyone. Using cartoon penguin avatars, players can waddle around, converse, play minigames, and participate in other activities with one another in a snow-covered virtual world. Wikipedia entry. $5.95 a month

Coke Studios is a massive multiplayer online community (MMOC), much like Habbo Hotel (see below) and Virtual Magic Kingdom (see below), created in 2002 by Studiocom for The Coca-Cola Company as part of CokeMusic. Wikipedia entry. Free.

Cybertown is a private 3D VR (virtual reality) home with your own personal chat, inbox, message board and free e-mail. You can invite your friends over to hang out, chat and party – all in full 3D. Free trial available. Membership $5.00 per month.

Cyworld is a South Korean virtual world focusing on chat and communities. Seems to be very popular. Wikipedia entry. Free.

Dark Age of Camelot is a 3D medieval fantasy MMORPG that revolves around the war between three realms at the end of King Arthur’s rule: Arthurian-inspired Albion, Norse mythology inspired Midgard, and Celtic Hibernia. Wikipedia entry. $14.95 per month.

Disney’s Toontown, created by The Walt Disney Company and billed as the first such game intended for kids and families. Toontown’s 3D virtual world takes its theme from the colorful style and humor of classic animated cartoons. Wikipedia entry. Free to enter, but full access costs $9.95 per month.

Entropia Universe is a massively multiplayer online virtual universe set ¡iIn a distant Sci-Fi future. Participants assume the roles of colonists who must develop the untamed planet of Calypso and can explore its two continents, Eudoria and Amethera. Populated with fierce and dangerous creatures, the perilous wilderness on Calypso is also rich in minerals and ore, both of which can potentially be a source of income for would-be colonists. Wikipedia entry. Free.

Eve Online is a player-driven persistent-world massively multiplayer online game set in a science fiction space setting. Players pilot a wide array of customizable ships through a universe comprised of over five thousand solar systems. Wikipedia entry. EUR 14.95 or 19.95 for 30 days of game time (not clear). Free trial period.

Everquest – Everquest II is a MMORPG where players use their character to explore the fantasy world of Norrath, fight monsters and enemies for treasure and experience points, and master trade skills. Everquest II takes place in the same game world as the original Everquest (Norrath), but the setting is 500 years later than the original. Wikipedia entry Everquest. Wikipedia entry Everquest II. Free trial (10 level trial on the Escape to Norrath server), then $14.99 per month.

Final Fantasy XI is a MMORPG in which players join as citizens of one of three nations (San d’Oria, Bastok, and Windurst), all preparing to defend themselves against an invasion of the dreaded “beastmen.” In addition to the usual quests and slicing and dicing of monsters, players can also engage in more peaceful enterprises, such as fishing, mining, and creating jewlery. Wikipedia entry. $12.95 a month.

Frenzoo is an online social network with detailed 3D character models. Popular in Hong Kong. A bit like Shanghai’s Shanda and the Chinese HiPiHi World. Free.

Gaia Online. Founded in 2003 by a few comic book fans in a garage, Gaia Online has become the fastest-growing hangout on the web. Millions of teens come to Gaia every month to play games, make friends, and participate in the world’s most active online community. Gaia provides a fun, social environment that inspires individuality and creativity. With everything from art contests and poetry forums to fully customizable profiles and digital characters, Gaia is a place where teens can create their own space and express their individual style (so they claim on their site). Wikipedia entry. Free.

Google Earth combines the power of Google Search with satellite imagery, maps, terrain and 3D buildings. Googe Sketchup, and Google Sketchup pro, companion products, are 3D modeling tools that can be used to design or create 3D buildings, in virtual worlds and elsewhere. Wikipedia entry. Free basic access. Extra functionalities range from $20 to $400.

Guild Wars is an episodic series of multiplayer online role-playing games created by ArenaNet. A very popular game.
Wikipedia entry. Free.

Habbo Hotel is aimed at teenagers, and it combines the two concepts of a chat room and an online game. Wikipedia entry.

HiPiHi World is a 3D digital world as rich and complex as the real world, and is created, inhabited and owned by its residents.The residents are the Gods of this virtual world; it is a world of limitless possibilities for creativity and self-expression, within a complex social structure and a full functioning economy. Well, if you put it like that… Often compared with Second Life.

Playstation Home. Sony announced some time ago PlayStation Home, a new free-to-download community based service for the PlayStation Network, which allows users to create an avatar character for their PlayStation 3 system. This avatar will get its own apartment, which can be adorned by items players can receive in several achievements. In the future the service will also expand, allowing players to have more sorts of clothing, as well as hold pets. Home will be a Second Life-like experience and will allow gamers everywhere to interact in a virtual world. Home will also act as a meeting place of sorts for players who want to play multiplayer games on the PlayStation 3. It seems that it will be available in 2008. Wikipedia entry. Free ?

IMVU is 3-D instant message software targeting young teen users. Users can create their own avatars, clothe them, build their own home pages, and similar sorts of things. Wikipedia entry. Free.

Infinity: The Quest for Earth is a massively multiplayer online game set in a futuristic persistent universe. Players can discover a huge galaxy with billions of planets and can explore, combat, trade, socialize.Wikipedia entry. Free.

Kaneva is the first virtual entertainment world that unifies the 2D web with a 3D experience by integrating social networking, shared media, and collaborative online communities into a modern-day, immersive 3D Virtual World. Wikipedia entry. Free.

Lineage 2 is a fantasy massive multiplayer online role-playing game (MMORPG) for the PC, and a prequel set 150 years before Lineage. Players create a character as their avatar in the game’s medieval-style virtual world. Wikipedia entry. Free trial. Than depending on the server a monthly fee.

Of course this is only a small list. I’ll be posting I posted a list M to Z as well. In the meantime any suggestions are welcome.

Matchbox is a die cast toy brand currently owned by Mattel, Inc. Matchbox toys were so named because the original models were packed in boxes similar in size and style to boxes of matches. The series became so popular that the Matchbox name was once widely used by the public as a genericized trademark for all die cast toy cars measuring approximately 2.5 inches (6.5 cm) in length, regardless of brand. In the 1970s, Matchbox switched to the more conventional, plastic and cardboard “blister packs” used for other die cast cars such as Hot Wheels, although the box style packaging was re-introduced for the collector market in recent years, particularly successfully with the release of the “35th Anniversary of Superfast” series in 2004.

Matchbox labels Flickr photoset from around the world but the majority are Eastern European from the 1950s and 60s by Mariad. Several collector sites: here, here and here. A community and some books, like Matchbox Toys 1947 to 2003: Identification & Value Guide, or the Encyclopedia of Matchbox Toys.

Today it’s my sun’s birthday. He is in charge !

His (our) to-do-list :

• Install Playstation III
• Have breakfast at ‘Le pain quotidien’ in Leuven
• See Harry Potter and The Order of The Phoenix
• Buy some books at Plato

Update: all done except buying books at Plato. perhaps tomorrow.

n., a place where one is free from intrusion. Sanctum is (was ?) also a two-player computer collectible card game, played exclusively online against human opponents.

Flit! A paper plane went shooting across the classroom. Flit! Another dived from the other side of the room. Then conflicting squadrons of these folded darts met in messy combat. Flit! And then one flew with precision into the back of humourless teacher’s head.

12 paper planes with folding instructions

My recent post about the GIPF project got me thinking about starting a series of posts about this category of games. So, here we go.

Game theory

Game theory is a branch of mathematics that deals with the analysis of games (i.e., situations involving parties with conflicting interests). In addition to the mathematical elegance and complete “solution” which is possible for simple games, the principles of game theory also find applications to complicated games such as cards, checkers, and chess, as well as real-world problems as diverse as economics, property division, politics, and warfare.

Game theory has two distinct branches: combinatorial game theory and classical game theory. In classical game theory, players move, bet, or strategize simultaneously. Both hidden information and chance elements are frequent features in this branch of game theory. Combinatorial games have no chance element, and players take turns.

Abstract strategy games

The analysis of a abstract strategy game tends to fall under combinatorial game theory (CGT). To qualify as an abstract strategy game several conditions need to be met:

• There are two players (usually named Left and Right in theoretical analysis)
• Players alternate taking turns
• There is no hidden information (such as cards or tiles that a player hides)
• The game is deterministic (no dice or shuffled cards)
• Every game must end in a finite number of moves
• As soon as there are no legal moves left for a player, the game ends, and that player loses

Let’s have a closer look at these conditions.

Using only 2 players does not limit the analysis of games. If we extend the analysis to n players than the compexity just increases exponentially.

Taking turns. Games are either simultaneous or sequential. Simultaneous games are games where both players move simultaneously, or if they do not move simultaneously, the later players are unaware of the earlier players’ actions (making them effectively simultaneous). Sequential games (or dynamic games) are games where later players have some knowledge about earlier actions. This need not be perfect knowledge about every action of earlier players; it might be very little information. For instance, a player may know that an earlier player did not perform one particular action, while he does not know which of the other available actions the first player actually performed. CGT analysis sequential games. Strategy games with hidden information, bluffing or simultaneous-move elements are better served by Von Neumann-Morgenstern (classical) game theory, while those with a component of luck may require probability theory.

An important subset of sequential games consists of games of perfect information. A game is one of perfect information if all players know the moves previously made by all other players. Thus, only sequential games can be games of perfect information, since in simultaneous games not every player knows the actions of the others.
Perfect information is often confused with complete information, which is a similar concept. Complete information requires that every player knows the strategies and payoffs (rewards) of the other players but not necessarily the actions. Or, you might know the rules of the game but not what action the other player is taking. In this case we have complete but imperfect information. Examples of incomplete but perfect information are more difficult. Suppose you are playing a game of chess against an opponent who will be paid some substantial amount of money if a particular event happens (an arrangement of pieces, for instance), but you do not know what the event is. In this case you have perfect information, since you know what each move of the opponent is. However, since you do not know the payoff function of the other player it is a game of incomplete information.
Go and chess are examples of perfect information games. The card game bridge is an example of a game with imperfect information because some cards are hidden from the players.

Deterministic means there is no luck involved in the game.

Finally abstract strategy games are so-called zero-sum games. It is so named because when the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Chess and Go are examples of a zero-sum game: it is impossible for both players to win. Or, a game ends with one player winning and one player losing. Zero-sum can be thought of more generally as constant sum where the benefits and losses to all players sum to the same value. Cutting a cake is zero- or constant-sum because taking a larger piece reduces the amount of cake available for others.

Know also that while many of us use the term ‘game’ to refer to things like “chess”, “Go” or “bridge”, CGT also uses the term game to refer to positions, a specific situation of the game (a bit confusing…, I know).

What next ?

So, now that we have defined abstract strategy games, we can start analysing them. Follow-up posts will be a combination of theory and practice. I will try to provide more insight in the theoretical concepts and results of CGT, but I will also post about real life abstract strategy games like Xiangqi (Chinese Chess), “n-in-a-row” games, go, hex and many others. And why not, the occasional ‘paper and pencil game’.