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Programming Real Time Strategy (Games) Games

Developing StarCraft 2 Build Orders With Genetic Algorithms 200

Jamie recommends a blog post from software engineer Louis Brandy explaining how using genetic algorithms to evaluate build orders in StarCraft 2 has led to some surprisingly powerful results. Quoting: "One of the reasons build-order optimization is so important is that you can discover openings that 'hard-counter' other openings. If I can get an army of N size into your base when you do opening X, you will always lose. ... a genetic algorithm is a type of optimization algorithm that tries to find optimal solutions using a method analogous to biologic evolution (to be specific: descent with modification & natural selection). Put simply, you take a 'population' of initial build orders, evaluate them for fitness, and modify the population according to each element’s fitness. In other words, have the most successful reproduce. The program’s input is simply the desired game state. In practice, this means 'make N units' to determine some rush build order (but it also allows for other types of builds, like make N workers with some defensive structures and a small army)."
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Developing StarCraft 2 Build Orders With Genetic Algorithms

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  • Especially of the ones who frigging *know* what genetic algorithms are all about, as I expect a better half of /.?

    Paul B.

    P.S. Or was it auto-generated by a genetic algorithm? :)

    • by rsborg ( 111459 )

      Makes sense to me... do you know Starcraft or RTS's in general?

    • Re: (Score:3, Informative)

      by cgenman ( 325138 )

      The entire summary is devoted to explaining what a genetic algorithm is, though I'm not convinced this is a particularly "genetic" genetic algorithm.

      I've known this technique to be used frequently in game development. It sounds like someone is using it to find good opening gambits in Starcraft. I say "good", because generational algorithms can frequently find "local" optimal solutions, whereas there may be better solutions further away from your breeding start point. You're just never sure you've found t

      • by Ruke ( 857276 )

        What do you mean "genetic-genetic"? The only thing that I can see that might be missing is a reference to "sexual reproduction" or "mating" in TFA, but I don't think that's strictly necessary for a GA. I especially liked the potential for "junk DNA" to build up. In my own simulations, chromosomes did either something or nothing consistently; perhaps it's just the domain that he's working in, but it certainly lends itself to "situational" expression of a chromosome.

        It's certainly no Evolvable [damninteresting.com] Hardware [ucf.edu], but

    • by FrootLoops ( 1817694 ) on Tuesday November 02, 2010 @01:59AM (#34098550)
      Yes, I find the summary comprehensible and know what a genetic algorithm is. I don't know what an explanation of genetic algorithms is doing in the summary, though. Linking the Wikipedia page [wikipedia.org] would be much more effective, since so many readers get nothing out of this explanation (either they already know what a GA is and, like me, are annoyed at the minor waste of time, or they don't and a brief explanation isn't enough).
    • Yes, but it's painfully obvious. Even if I hadn't heard of it before, how can it not be obvious what a genetic algorithm is?

      Also, they did not mention the problem of local maxima.

  • I'd like to see a game that isn't a click-fest, but still would offer some action and nice visuals. Something with the gameplay involving giving orders to partially autonomous troops. After giving orders, you could watch and see how they fare and perhaps give some further orders, maybe with some possible penalty incurred for breaking radio silence. Or in the setting of a Total War type of game, there could be a limited number messengers who would take time to reach the troops and even have a chance to fail
    • by Iftekhar25 ( 802052 ) on Tuesday November 02, 2010 @02:00AM (#34098556) Homepage

      Well, to be fair there's a lot more to SC2 than just build-orders. :-) Build orders are mainly concerned with the "macro" aspect of SC2 gameplay, which is base management and economy, and they're also relevant only in the opening. Everything past the 7 or 8-minute mark is beyond build orders. Good micro (unit-level manipulation of movement and actions), harassment of workers, and timed expansions all kick in after that point, and those become the difference between winning a game and losing a game.

      Also, there is an element of "good practices" in SC2. Rushes, especially "all-in" rushes (referred to by TFA) are generally considered bad practice. Beating your opponent every time is cool, but this is usually indicative of a game imbalance that Blizzard will probably patch at some point down the line, at which point you'll rapidly fall in the leagues as you lose to high-level players clued in on countering that or who simply have the good practices to beat it (like early scouting, etc.).

      The other (more important) factor is that a gamer specializing in an all-in rush deteriorates his/her gameplay, because he won't have the variety to compensate for a failure of that rush. A rush usually means a sacrifice of something or the other (the tight game-mechanics of an SC2 opening means there's always an opportunity cost; to get that extra army, your economy suffers, or to get those extra resource-collectors, your army will be smaller). All-in rushes, and rushes in general sacrifice some thing or the other which a good opponent can exploit if he/she manages to push back the rush. Someone over-playing one tactic will lack the skills to compensate for its failure, so varying one's game by mastering different build-orders and plays is the better way to do this (if slower).

      • Re: (Score:3, Interesting)

        by Coryoth ( 254751 )

        If you read through some of the forum posts linked in the article you'll see that after not too long he encountered protoss players who easily countered his rush based on scouting and knowing what sorts of things to do. In this case the right thing to do is see that there are no zerglings out, so whack down a forge and at the last minute warp in some cannons behind a building wall. That pretty much stops the rush dead, at little cost to the protoss economy, while the rushing zerg has little left, with the c

    • by thygrrr ( 765730 ) on Tuesday November 02, 2010 @02:50AM (#34098700)

      You have three choices (assuming the Total War series cannot be counted as viable Multi Player choices)

      More Strategic: R.U.S.E (awesome visuals, very autonomous units, very indirect control)
      More Direct: Supreme Commander - Forged Alliance (decent visuals, unprecedented scope of war and great control over your units)
      More StarCrafty: Supreme Commander 2 (think ugly Starcraft with the ability to fully zoom out)

      • More StarCrafty: Supreme Commander 2 (think ugly Starcraft with the ability to fully zoom out)

        Supreme Commaner 2 is a bastardization of the franchise (which started with Total Annihilation). I would recommended the original Supreme Commander if you want a great alternative to the Starcraft style RTS. Be forewarned, the learning curve is very steep. In exchange you have an RTS where every bullet, every laser, every unit/building exploding is physically modeled in real time in game. Where Starcraft has upper high and low ground, things like a gently sloping hill will effect battles in Supreme Command

    • Re: (Score:3, Informative)

      A recent game like that is called Globulation 2 (Linux, not sure about other platforms). Instead of telling unit X to do task Y, you say "I want task Y done, with as close to N units working on it as possible." and the AI for your team does its best to fulfill your requests. If you ask for impossible things (say, building 20 buildings, each with 10 units, while you only have 100 units), it instead prioritizes as well as it can based on available resources and location of units. You can also script your own

    • Supreme Commander 2 is this for me.
    • Comment removed based on user account deletion
    • The indie game AI War [arcengames.com] might be similar to what you're looking for. At least it focus a lot more on strategy than clicking.

      Try the demo, see if it's something you like :)

      • AI War is a great game, and it's definitely a lot more toward the "large-scale strategy" side of things than the "clicky micromanagement" end. I don't know if the demo or tutorials are any better than they used to be, but when I started they barely even gave a sense of how the game worked and mostly just managed to explain what some of the most important buttons/keys did. The learning curve can be kind of brutal, and I find it a lot more fun with other people than in single-player, but I'm very happy I pu

    • Try Combat Mission, though the troops can require a lot of manual pathfinding. Simultaneous turns (RT optional in the latest).
    • by gmueckl ( 950314 )

      Then you might be interested in Majesty and Majesty 2, strategy games in which your units are totally autonomous. You control them by giving them monetary incentives and sometimes helping them out with magic (which also costs money). Each type of unit also has its own character in addition to strengths and weaknesses, so they react differently to your incentives. It's quite fun to play actually and not that high on actions per minute.

      • by tibman ( 623933 )

        I'll second this. I recently played Majesty 2 and had a great time. Though it can be frustrating with upper level heroes.. they don't respond to small bounties.

    • by azaris ( 699901 )

      I'd like to see a game that isn't a click-fest, but still would offer some action and nice visuals. Something with the gameplay involving giving orders to partially autonomous troops. After giving orders, you could watch and see how they fare and perhaps give some further orders, maybe with some possible penalty incurred for breaking radio silence. Or in the setting of a Total War type of game, there could be a limited number messengers who would take time to reach the troops and even have a chance to fail in delivering your orders.

      Scourge of War: Gettysburg [scourgeofwar.com] and its predecessors Take Command: 2nd Manassas and Take Command: Bull Run pretty much work that way. The graphics are dated (think Medieval: TW quality) but functional enough, the gameplay fairly slow and meticulous. Most battles start with 5-20 minutes of maneuvering into attack positions, after which you order your divisions/brigades their set targets and watch them march into the fray. If and when things start looking bad you start to micromanage individual batteries and regi

    • I once played a 3rd person shooter called Gunlok. It had an active pause mode, where you could pause your game, give your guy a set of orders and then he does it.

      Since then I've wished every RTS I've played has had that feature. When you see the enemy approaching you just slip into active pause, give all your guys their defensive orders, and then you just need to react to the outcomes of each battle rather than trying to keep everything straight right from the start.

  • Who knows, with the help of this kind of technology, maybe I can play against Koreans without BEING HORRIBLY MURDERED! (Until they start doing it, at which point we're all proper-fucked.)

    • by bonch ( 38532 )

      If you want to beat Koreans, you need to sit in front of your computer 10 hours a day doing nothing else but playing Starcraft, like in the professional Korean burnout camps. After you beat them, you'll finally get to play!

    • by antdude ( 79039 )

      This old 46.75 minutes National Geographic documentary talked about cybergaming competition on http://educatedearth.net/video.php?id=4164 [educatedearth.net] ... It was interesting. They play a lot. :(

  • by Anonymous Coward

    Traditional RTSes are all about memorizing the optimal build order (which apparently can now be calculated via an algorithm, removing the player almost entirely) and then being able to click really fast, and this is why I think it's a terrible genre. Hand-eye coordination should not even come into play in a game that calls itself a "strategy" game.

    There are exceptions--those that aren't traditional RTSes, but are more real-time tactical games that focus on maneuver, flanking, suppression, and other actual

    • Re: (Score:3, Interesting)

      by Homburg ( 213427 )

      I remember reading a review of one of the early RTS games that pointed out that they weren't so much strategy games as logistics games; the reviewer predicted the failure of the genre on the basis that everyone wants to play the general, they don't want to play the quartermaster. Obviously, he was wrong, and a lot of people do want to be the quartermaster; but he captured what I've always found so boring about RTSes.

      • by Lloyd_Bryant ( 73136 ) on Tuesday November 02, 2010 @03:04AM (#34098742)

        I remember reading a review of one of the early RTS games that pointed out that they weren't so much strategy games as logistics games; the reviewer predicted the failure of the genre on the basis that everyone wants to play the general, they don't want to play the quartermaster. Obviously, he was wrong, and a lot of people do want to be the quartermaster; but he captured what I've always found so boring about RTSes.

        What we call "strategy" in in fact mostly a matter of logistics - having a perfect tactical plan is worthless if you can't keep your troops supplied during the course of it. RTS games are generally just a simplified/idealized version of how things work in the real world.

        Amateurs study tactics, professionals study logistics

        (attributed to Gen. Omar Bradley)

        It sounds like what *you* want is a large-scale RTT (Real-time tactical) game, where all you have to worry about is deciding on which units to move and where to move them. Personally, I would consider *that* boring, as it removes a lot of the complexity that makes a good RTS challenging.

        • What General Bradley did in WWII could hardly be described as "fun". The very word "amateur" means one who does it for the love of the task, while conversely "professional" means someone who does it for money. Logistics is a lot of hard work, and nobody does it without a full staff to assist. Indeed, logistics is well-known for its dryness and it is not something that anyone would do as recreation. It's essentially the same thing as keeping the shelves stocked in a grocery store.

          I played Starcraft, an

        • It sounds like what *you* want is a large-scale RTT (Real-time tactical) game, where all you have to worry about is deciding on which units to move and where to move them. Personally, I would consider *that* boring, as it removes a lot of the complexity that makes a good RTS challenging.

          Actually, I quite enjoy the battles in the Total War series.

    • by moenoel ( 1897920 ) on Tuesday November 02, 2010 @03:47AM (#34098854)
      The fast and coordinated clicking stuff is only the first part of learning SC (II). Strategy comes after that.

      To (not literally) quote Sean 'day[9]' Plott [day9tv.blip.tv]: If you are interested in american football and want to play various tactics on the playfield, you first need to train your body. I.E. if you are a scrawny guy, with no muscles and stamina whatsoever, you can think about football tactics all you want, but you simply won't be able to execute them for lack of the basic requirements.

      Same goes for SC (II) and every (balanced) RTS in general. The *real* strategy part only comes into play, after the player mastered the basic mechanics of gameplay.
      • I'd argue that you're backwards, although I may be arguing the same point that you are but wording it differently. I'm not sure yet. Anyway, in order of importance, macro (economy management) comes first, then strategy, then tactics and micro (fast and coordinated clicking stuff) come together last. It really only takes about 45 APM (basically the level of most people who are are new to Starcraft, but not gaming in general) to get a strong macro going, and then you can start to focus on what units you want

      • Publius (or Gaius) Cornelius Tacitus brought us "tactics", and Strategos, plural strategoi Attic-Ionic (Greek: , pl. ; Doric Greek: , stratagos; literally meaning "army leader") brought us "strategy".

        Strategic planning is _all_ about logistics. Your comment seems to infer a distinction that doesn't exist there.

        Strategy is getting you units to the right places with the correct intelligence and provisioned and equipped for their task.

        Tactics is executing your task in the best possible manner, with contingenci

        • Colonization was far more strategic than most RTSes are. Not all your colonies are going to be able to sustain themselves. Some of them should be placed in specific places to control the land around them even if there is a dearth of certain resources. Your supply lines exist and can be attacked, so you must defend those as well as the colonies themselves. Supplies take wagon trains or ships to move, and those take time to arrive.

  • by Kenja ( 541830 ) on Tuesday November 02, 2010 @01:56AM (#34098534)
    No one just plays the dang game anymore. Its all about winning via pre-built key sequences.
    • by khchung ( 462899 ) on Tuesday November 02, 2010 @03:12AM (#34098768) Journal

      No one just plays the dang game anymore. Its all about winning via pre-built key sequences.

      Yes, and nowadays football games are all about winning using pre-planned passes, and chess is all about memorizing opening moves. /sacarsm

      At your level when ppl are just learning how the game works, then, yes, a pre-planned built sequence can often win you the game. Much like a football team with well practiced passes can win low level games with little more than executing their practiced passes. Or beginning chess players can win games by playing from memorized opening moves.

      However, once you reached a higher level, then if you cannot adapt your strategies to the situation at hand, you WILL lose against opponents who can.

      This is the same with ANY competitive sports.

      Yes, that involves a lot of practice and hard work. Seems like you just never reached that level. (Neither did I, BTW). But you can see it in the pro-level SC games in Korea. How the players respond to the unexpected is what differentiates good and not so good players.

      • by spottedkangaroo ( 451692 ) * on Tuesday November 02, 2010 @04:29AM (#34098960) Homepage

        I think the point of your post is clear and correct. I'm not arguing that at all, but...

        Or beginning chess players can win games by playing from memorized opening moves.

        I don't actually play chess, but I know a few people who do. I think you actually have this backwards. You can get by playing the game at the low levels, but if you want to get advanced you need a really big library (of actual books) so you can memorize things. You have to get to the very very top to get back to playing.

        I'm not saying there isn't a lot of thinking and analysis going on, but it appears to me (from the outside and from comments from "expert" level players) that memorization is key to winning chess at the higher levels.

        Then again, I'm told (by an expert level player who hates this) that it can be hilarious to memorize archaic openings that nobody bothers with and using those as your opening, so you can hopefully get to a middle game that isn't memorized.

        • by khchung ( 462899 )

          I think you another the other poster misunderstood my point. The OP's point (as I understand) was memorizing build orders is the only way and sure way to win. My point is that while it helps at low level, it is not enough at high level play.

          Of course, it doesn't mean you don't memorize build orders at high level, it means that, like football passes and chess openings, the memorized build orders became part of your toolbox that you can use as the situation calls for it, and more importantly, recognize it w

          • Wrong. I got your point. I was talking about chess. The key to winning at moderate and high levels is memorizing. Little else matters once you memorize enough. That is the problem that AdamThor is talking about below you.
        • I don't actually play chess, but I know a few people who do. I think you actually have this backwards. You can get by playing the game at the low levels, but if you want to get advanced you need a really big library (of actual books) so you can memorize things. You have to get to the very very top to get back to playing.

          People play Fischer Random Chess for this reason. SEE http://en.wikipedia.org/wiki/Chess960 [wikipedia.org] It randomizes the order of the not-pawns (with some other rules) so that memorized routines can'

      • Re: (Score:2, Interesting)

        by StDoodle ( 1041630 )

        There is a go proverb that states "Learning joseki loses two stones strength" which would apply. (Joseki are "are generally agreed-upon sequences of play resulting in what is considered a fair outcome for both players.") The basic idea is that you'll handicap yourself out of learning why and how to respond to your opponent if you focus too much on standard patterns. It's generally accepted that you shouldn't spend too much time on joseki until your understanding of the game is at a level where you can actua

      • by brunes69 ( 86786 )

        The OP doesn't want to play SC as a "competitive sport". He wants to play it for fun. The difference is a backyard neighborhood weekly pick-up game vs. the NFL - it is night and day.

        The OP's PROBLEM is it is impossible to find that kind of game online anymore.

        This is why I stopped playing FPS's online. Games to me are a way to unwind for an hour or two a week. I don't consider myself any kind of champion and have no desire to be, I just want to have some fun.

        When everyone takes things too seriously it suck

        • Oblig penny-arcade [penny-arcade.com]
    • Even games old games were subject to this kind of scrutiny. I remember my grandmother telling me how she came up with a path in pac-man which if followed would maximize her points (she would get every ghost and every fruit for every level), since the behavior of the ghosts is deterministic. Honestly I feel going through that process takes what little fun there is to be had in pac-man.
  • by Nursie ( 632944 ) on Tuesday November 02, 2010 @02:29AM (#34098628)

    If I get SC2 I'll play the single player campaign only.

    I'm really not interested in being pwned by someone who has a bunch of rush tactics memorised, let alone someone who's used genetic algorithms to optimise their deployment/build strategy.

    • by Warma ( 1220342 ) on Tuesday November 02, 2010 @03:02AM (#34098732)

      A lot of people seem to complain about this and especially about the realtime requirement in strategy, but the truth is that in addition to the kind of economically suboptimal rush build orders you seem to hate, there are strategies designed to securely carry you into the midgame, where the opponent no longer benefits from memorized build orders.

      Moreover, the whole gripe seems misplaced, as I doubt that the same players are against people memorizing openings in chess, board states in go or probabilities in poker. It's simply being intimidated by people better in the game than you - being afraid of losing. You must realize that a video gaming company the size of Blizzard is very aware of this, and the whole mentality is precisely why Starcraft has a very friendly ladder system, which tries to match you against people of your own skill level.

      • by Nursie ( 632944 )

        It's not quite the same as chess, go or poker, in that timing does not have the same factor.

        Either way, it takes something away from the game, IMHO.

        Also never really cared for chess or Go.

        • by khallow ( 566160 )

          It's not quite the same as chess, go or poker, in that timing does not have the same factor.

          Either way, it takes something away from the game, IMHO.

          It's a problem with any game where you might be able to win shortly into the game through an aggressive gamble. Your opening needs to be good enough to keep you from losing to an opponent's aggressive opening. In old Starcraft a common approach is the "no-rush" rule where players don't attack for the first X minutes of the game.

        • > Also never really cared for chess or Go.

          I found Chess to be pretty boring for the most part once you get to a certain [skill] level.

          Go is a completely differetn world.

          Go is infinitely more interesting then Chess. There are no hundreds of standard openings to memorize like in Chess -- every game is pretty much guaranteed to be unique. The golden era of Chess was the early 1900s with famous players like Alexander Alekhine, Jose Capablanca, etc, as everyone was still exploring opening moves -- the commen

      • by Pulzar ( 81031 ) on Tuesday November 02, 2010 @05:44AM (#34099174)

        A lot of people seem to complain about this and especially about the realtime requirement in strategy

        Actually, only a handful of people complain about this, and mostly those that haven't even played the game. On forums visited by actual players, nobody complains about this at all.

        Sure, there are a bazillion complaints about other trivial things :), but people are generally interested in figuring out how to beat each other, as there certainly isn't a "one build order to win them all".

        • Actually, only a handful of people complain about this, and mostly those that haven't even played the game. On forums visited by actual players, nobody complains about this at all.

          That's because we've been chased off, or just play single player now.

          I've enjoyed Heroes of Might and Magic III the most I think. Turn based helped showcase the strategic aspect a lot more.

    • by Fahrvergnuugen ( 700293 ) on Tuesday November 02, 2010 @08:09AM (#34099822) Homepage

      The matchmaking system in SC2 is very good at matching you against someone with the same skill. In fact, it's almost too good.

      In SC1, 1 or 2 out of 10 games would be close. The other 8 would be a blowout by one player or the other. In SC2, 9 out of 10 games are close. It can be very exhausting.

      I wish they would put a little wander in the matchmaker giving you a wider variety of games (some easy, some hard, some close). You can learn a lot by watching a replay where you get destroyed by a higher level player.

      • by Alioth ( 221270 )

        Perhaps it is for 1vs1, but in over 80% of my 3vs3 games, the other team always has "advantage" or "slight advantage". It is very rare that the teams are equal or we have the advantage.

    • by daid303 ( 843777 )

      The single player in SC2 is quite good. I bought the game just for the single player (after a 7 hour trial someone gave me). Each mission is different, and fun in it's own way. I ran trough the game on normal difficulty, which took me 14 hours to complete the campaign I think. Only having to restart a few missions.

      But that is not the end of it, the game has 3 achievements per campaign map. 1 "complete all objectives" achievement, which is easy to get, unless you miss a bonus object. 1 achievement for "norma

    • Starcraft 2 has a matchmaking system that pits you against people that are as good (or as bad) as you are.
      Newsflash: If you don't have good builds memorized, neither will your opponent. There are many many people in the lowest league, so don't think that Starcraft 2 will only be taking loss after loss.

  • How would you evaluate for fitness?

    If you create X units of type Y - and the opponent has created units specifically to counter them, then its going to be 'unfit' - even though that it might have worked under other circumstances.

    I think that the fitness function changes too rapidly during the game in order to be properly used. Also since GA take lots of time to properly function (which may include a lot of garbage) - I don't see this reacting fast enough to changes in tactics either.

    So its an awesome idea -
    • Re:The problem is... (Score:4, Informative)

      by Ruke ( 857276 ) on Tuesday November 02, 2010 @03:07AM (#34098758)
      If you read TFA, the fitness function defined as distance (in time and resources) from having a desired set of units. The example provided is having 7 roaches. The GA isn't scoped to fight battles or develop a strategy; the programmer defines the desired end-state, and the GA finds an optimum path to get there. It's a tool for developing build-orders, not an AI to play the game for you.
    • The optimization might come up with a solution to this problem, through exploiting resource consumption rates and build times, so that even if you started building the counter units immediately, you would not be able to resource and construct them quickly enough to avoid being overwhelmed.

      EG, it calculates how quickly (maxiumum) you can develop your harvesters, evaluates the maximum rate of resource accumulation, and determines the optimum attack strategy by choosing units that are quick to produce, cheap,

  • Choose my build order. Rock, paper, or scissor?

  • Day Traders (Score:4, Interesting)

    by Danathar ( 267989 ) on Tuesday November 02, 2010 @06:58AM (#34099420) Journal

    I've often watched my brother who is a multitasking jedi play WoW, SC2, etc and I've often asked him why he does not go into day trading. The skill sets of managing a quickly changing massive amount of information and evaluating probabilistic results for gain is EXACTLY what real time traders do.

    Computer games, role playing games (with emphasis on the statistical portion), war games, RTS...

    When it comes down to it, it's nothing more than statistical simulations.

    If some game company can overlay something like WoW or SC over a real time stock trading system,...well...we will see what happens when a bunch of people who spend hours every day optimizing probabilistic statistical systems to their advantage has on world financial markets.

    Probably would make a good Sci-Fi Novel if nothing else

    • I've often watched my brother who is a multitasking jedi play WoW, SC2, etc and I've often asked him why he does not go into day trading. The skill sets of managing a quickly changing massive amount of information and evaluating probabilistic results for gain is EXACTLY what real time traders do.

      The psychological effects of risking your own money strongly affect most people's performance when day trading: the hard part in daytrading is to be able to come out while you're winning (instead if remaining in pla

  • This is not necessarily original. Douglas Lenat used EURISKO (http://en.wikipedia.org/wiki/Eurisko) to win the Traveler RPG (http://en.wikipedia.org/wiki/Traveller_(role-playing_game) "Trillion Credit Squadron" championship in the early 1980's. Lenat got the attention of DARPA and later formed the company CyCorp (http://www.cyc.com/).

Every nonzero finite dimensional inner product space has an orthonormal basis. It makes sense, when you don't think about it.

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