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Games Science

The Science of Game Strategy 136

Posted by samzenpus
from the high-score dept.
First time accepted submitter JacobAlexander writes "Writing in PNAS, a University of Manchester physicist has discovered that some games are simply impossible to fully learn, or too complex for the human mind to understand. Dr Tobias Galla from The University of Manchester and Professor Doyne Farmer from Oxford University and the Santa Fe Institute, ran thousands of simulations of two-player games to see how human behavior affects their decision-making. From the article: 'In simple games with a small number of moves, such as Noughts and Crosses the optimal strategy is easy to guess, and the game quickly becomes uninteresting. However, when games became more complex and when there are a lot of moves, such as in chess, the board game Go or complex card games, the academics argue that players' actions become less rational and that it is hard to find optimal strategies.'"
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The Science of Game Strategy

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  • by Anonymous Coward

    They found out about QWOP.

  • by Anonymous Coward on Monday January 14, 2013 @01:39PM (#42583903)

    Isn't that the whole point?

    • by smitty_one_each (243267) * on Monday January 14, 2013 @01:50PM (#42584045) Homepage Journal
      The point of doing social science research? Yes. Anybody can "argue that players' actions become less rational and that it is hard to find optimal strategies."
      It takes an academic to lay the argument out in a paper so Byzantine that it's hard to find optimal reading strategies.
      This triggers the writing of more papers, until an entire academic research field springs from a single seed of "Duh".
    • by Anonymous Coward

      Recently, scientists found that something complex is more difficult to learn, and that there are things so complex that you just can't learn them and you need to improvise a little... Really? Is that what government funding goes towards?

  • by xevioso (598654) on Monday January 14, 2013 @01:41PM (#42583929)

    As in Magic the Gathering? The card game with 12,000+ individual cards? In my honest opinion, it's the greatest game ever made. It's incredibly complex, and yet still understandable.

    It's always amazing to be playing at a multiplayer table with a bunch of other folks, each player with a field full of cards, sometimes hundreds of cards on the table (in complex games) and sometimes I have to step back from the table, stare at the board position, and pinch myself that I'm playing a game where yes, everything on the table makes sense.

    • by fuzzyfuzzyfungus (1223518) on Monday January 14, 2013 @01:47PM (#42584005) Journal

      I'm pretty sure that the optimal strategy with Magic is just to wait until Wizards of the Coast is feeling a bit pinched and decides to release a new, more powerful, bunch of cards that you just can't stay competitive without buying and then go buy those...

      • With Magic as it used to be, that was more or less true. Today, competitions are usually held with this years' series, sets released the same year only. And/or they are drafting games of various sorts, where players build their decks as the first phase of the game.

        Even in the less restricted events, more likely to be for fun than for prizes, they are careful to disallow the most overpowered cards. That inevitably means older cards (learning from their best players, WotC have gained a better understanding of

      • Re:What about Magic? (Score:4, Interesting)

        by vux984 (928602) on Monday January 14, 2013 @06:44PM (#42587015)

        I'm pretty sure that the optimal strategy with Magic is just to wait until Wizards of the Coast is feeling a bit pinched and decides to release a new, more powerful, bunch of cards that you just can't stay competitive without buying and then go buy those...

        Yes, and no. Mostly no.

        You need to purchase the new cards because to be competitive, (as in participate in tournaments) you need to be using cards from the current block. The old cards, simply aren't permitted in the block.

        (Although many old cards from various old sets are reprinted in the current set, and you can play with the originals of any reprinted card if you have the original.)

        That effectively solves the power-inflation problem. This years set doesn't have to be more powerful than last years set to appeal to players because nobody is using last years set in competitions. That was, frankly, a very smart move by wotc for the overall health of the game.

        Each year the game changes, but the cards aren't on a permanent run towards ever more power. They can even print cards that are strictly inferior to existing cards and those cards can still be desirable due to what is currently allowed.

        Of course, yes, you do still have to buy this years set to play competitively which is a smart move from a business point of view. Otherwise, there'd be no reason to keep buying cards.

        But pre-constructed is just one format, and there are many; draft games are quite popular where you build your deck on the fly from a pool of available cards (which can new unopened packs in sanctioned tournements, to one of your friends piles of commons in an informal setting... and then play with that. Many many players prefer various draft formats both in tournaments and in private because it does to a large degree eliminate having to buy the expensive rares to be competitive.

        • they also change the rules on cards due loopholes that some people have used / tried to use.

        • by drinkypoo (153816)

          You need to purchase the new cards because to be competitive, (as in participate in tournaments) you need to be using cards from the current block. The old cards, simply aren't permitted in the block.

          Suddenly I don't feel so bad about giving money to Games Workshop. At least I can still use my first edition miniatures, which is really handy since some of them are MUCH smaller than the later models.

          • by vux984 (928602)

            At least I can still use my first edition miniatures,

            As long as they are on a current army list, and modeled with the same equipment you want them equipped with and painted using enough colours, and flocked...

            Sanctioned GW events can be pretty anal.

          • I can remember GW when they were good. Then they went a bit mad. When all the new Chaos stuff came out (with Khorn, Nurgle and the transvestite one) anything Chaos won automatically. Then it was Empire that had new figures & there was a horse-drawn tank (anyone seen the western War Wagon?) that could kill anything.

            OK, I exaggerate. The latest model didn't win automatically. You had to roll 3 or above on 2D6.

    • Without having RTFA yet, it looks like we're talking optimal strategies here. The rules for MTG are finite and can be printed, read, and analyzed. The absolute maximum winning strategy for each play, depending on what cards your opponent has in hand, in play, and in their library is not so easy to lay out for Standard play or even a single block. Strategic complexity, not rules complexity.

      • by Giant Electronic Bra (1229876) on Monday January 14, 2013 @01:54PM (#42584077)

        Well, M:tG has both 'resource complexity', there are a vast number of possible cards you can play with and they do an equally vast number of slightly different things, and it also has what you are calling 'strategic' (though I would say most of these games have strategy AND tactics) complexity. That is even if you play the same 2 M:tG decks against each other many many times the players are likely to be able to make a number of different tactical choices in each game. Actually I think the tactical depth and strategic depth of chess are a good bit higher than with M:tG, but its a fairly complex game with a huge number of setup options (IE how you make your deck). The tactical consequences of a move or the strategic consequences of learning certain lines or aspects of the game in chess are however more significant than the individual moves in M:tG, which can often be quite insignificant.

        Go of course occupies the uttermost extreme in terms of being utterly simple in form and yet so immensely complex in both strategic and tactical depth that no software yet written even approaches the better human players.

        • by Raenex (947668)

          Go of course occupies the uttermost extreme in terms of being utterly simple in form and yet so immensely complex in both strategic and tactical depth that no software yet written even approaches the better human players.

          Go software is not as far away as you think. Zen on KGS is 5d/6d, depending on time controls, and has recently beaten a pro with only 4 handicap stones.

          • Yeah, OTOH Chess programs could beat someone like me back in the C64 days at least some of the time, and its only in the last year or two they've reached that level with Go. Nothing is even close to the "unbeatable by all but the few most advanced human players" level of the current crop of the best chess programs. There are still levels of flexibility and adaptability in play that even the best chess programs lack but my reading is this is quite a bit more true with Go. Go is definitely in some sense a 'de

          • Yes, but how much of the Go software's decision process relies on scanning through thousands of professional games? Software might be good at fighting locally, but last I knew programs still relied heavily on professional games to determine where to play outside of a fight.
            • by Raenex (947668)

              Yes, but how much of the Go software's decision process relies on scanning through thousands of professional games?

              I don't know about Zen, the current strongest program, but other programs have gotten pretty far without it. It doesn't really matter anyways, since the pros learn from those who came before them. If a computer learns too it doesn't diminish the accomplishment.

              Software might be good at fighting locally, but last I knew programs still relied heavily on professional games to determine where to play outside of a fight.

              No, the real revolution came several years ago from monte carlo approaches, and one of its main strengths is it has an innate sense of direction without having to be told.

    • by fredprado (2569351) on Monday January 14, 2013 @01:48PM (#42584015)
      I think it is a matter of taste, but a game that purposely allows for unfair circumstances based on the cards you own or not does not seem to be a good game for me. I am also not very found of the idea that complex (and in Magic's case Encyclopedic) rules are a good thing for a game.

      Great games, in my opinion, would be Chess or Go, for example. Games that have incredibly simple rules and still lead to incredibly complex situations and strategies.
      • by dido (9125)

        Reminds me of my own sig quote at the moment, which, more fully in English goes: "God, however, has chosen the most perfect, that is to say, the one which is at the same time the simplest in hypothesis and the richest in phenomena." --Gottfried Wilhelm von Leibniz. Discours de métaphysique (1686).

    • by gauauu (649169) on Monday January 14, 2013 @01:50PM (#42584041)

      As in Magic the Gathering? The card game with 12,000+ individual cards? In my honest opinion, it's the greatest game ever made.

      In my opinion, any game where a higher budget gives players more strategic options, is immediately disqualified from being the "greatest game ever made." I might be able to play the game with a $10 investment in a starter pack, but I will lose 100% of the time against players with a bigger budget, no matter what my skill level is.

      That's great in terms of profit for the game producer, but pretty weak in terms of actual gameplay.

      (That's not to say I don't think Magic is a decent game. It is. But the collectible nature weakens the game in terms of pure gameplay.)

      • by xevioso (598654)

        This is only if you play competitively. There's nothing stopping you from printing your own cards and playing with your friends. The rules of game play are the same either way.

        In addition, and most important, the "budget" issue goes away in multiplayer games. Your nifty 100$ planewalker or $5000 power 9 deck is pretty easily handled in a multiplayer game where the chances of a number of players having cards to deal with your crap is increased 3 (or more)fold

      • Re:What about Magic? (Score:4, Interesting)

        by Momomoto (118483) on Monday January 14, 2013 @02:57PM (#42584705) Homepage

        I agree 100%. A lot of people will say that you don't have to spend a lot of money to make a deck that wins. Those people are kidding themselves! Sometimes, you've just gotta pay the money to get the good cards.

        Luckily, there are formats that are designed to reward skill more than the size of your bank account: sealed deck and booster draft. Both require participants to buy unopened packs and use them, but paying $15 or $25 every once in a while is far less expensive in the long run.

      • I will lose 100% of the time against players with a bigger budget, no matter what my skill level is.

        The so-called "Sligh Deck" by Paul Sligh and Jay Schneider in the late-90s disproves your point. That deck came from folks that were frustrated by the complex and expensive decks they were running up against, so they built a cheaper, faster deck to compete with. It dominated the magic scene for years.

        • A bigger budget gives you more options. A person with an infinite budget can build any deck (including a sligh deck), and a person with a small budget can only build decks within the budget. If the best deck happens to be very inexpensive, then hooray, even poor magic players can have the best deck. This is pretty unlikely as MTG is a business and there are bound to be at least a few really powerful cards that are rare, and therefore going to be expensive.

          A well crafted deck will always beat a deck that

          • Why would most of your deck be land cards? Sounds like a great way to have a terrible deck.

            • I didn't say that every single one of those would be in your deck. I said that they would be available to you. Moxes and dual lands are just plain better than basic lands in 99.9% of circumstances. If you have a deck with 20 basic land in it, it can be made just plain better with a lotus and a mox if you use 1 color. If you use more than one color, then dual lands and more moxes will make your deck better by an even greater margin.
      • I agree completely, but luckily there are alternative formats to Constructed decks, in particular Sealed and Draft tournaments. Everyone puts in their entry fee, then builds decks right there from sealed, virgin packs, so there's no "more money = more wins" mechanic. It's the only way I'd ever consider playing in an environment other than casually with friends.

      • by Afty0r (263037)

        But there is a ceiling to how much "budget" you can assign to the game... the "best" decks for most tournaments are either almost unchanging over time (the expensive, Legacy decks) or are limited to a few hundred quid (Standard Decks). It's also fair to say that as soon as you move from even remotely casual play to basic competitive play, EVERYONE has the cards they need - while some players might have had to pay out some money to meet that minimum competitive level, there are few to zero players who sit at

    • by vlm (69642)

      If MtG is Turing Complete (and it is, see link below) that would imply there is theoretically no optimum strategy because you could have two turing machines playing an arbitrarily complicated program against each other and the only way to solve the halting problem is to run the game... correct or not?

      Or maybe another way to phrase it is two Turing machines could play an unsolved / unsolvable problem, like maybe a hard AI algorithm, against each other using MtG cards?

      Of course proving an unsolvable strategy

      • by oreaq (817314)

        If MtG is Turing Complete (and it is, see link below) that would imply there is theoretically no optimum strategy

        Depends on your definition of optimal strategy. The existence of a Nash Equilibrium, i. e. a set of strategies, one for each player, such that no player has a incentive to unilaterally change his action (because changing would increase loss/ decrease win), can usually be proven without actually finding theses optimal strategies for each player. Examples: Every finite game has Nash Equilibria (obv!). Every game with compact strategy sets and continuous utility function has Nash Equilibria (Kakutani FP Theore

      • The Turing completeness of magic is referring to specific configurations of the game where automatic effects from cards can cause a certain conclusion depending on a the starting conditions. This is independent of strategy of individual players or trying to win. If you set up a carefully crafted magic game in progress (with many cards, tokens, life points, etc already on the table), and you start the game, the process of resolving all the automatic effects can be used to make computations.

        This is just an

        • by vlm (69642)

          There are some things turing machines can't compute, like solving the halting problem.

          Zactly and the fastest way to test a halting type problem is to run it. So its possible to specify a program inside MtG that cannot be solved other than running it. So at least theoretically (however impractically) there exists uncountable strategies that can only be tested by running them... so there is no simple solution to finding an optimal strategy. A weak proof to be sure, but interesting.

          • OK I see what you are saying. When you said "solving the halting problem", I immediately thought "you can't do that". But if by "solving" you mean running the program and determining that for that program and input, the program halts (if it does) and finding out nothing if it doesn't halt, then yes you can do that.
          • Also, if I am not mistaken, it is only certain specific combinations of cards on the the table that are turing complete. I have a feeling that the vast majority of games do not involve decks that contain the cards necessary to constitute a turing machine. So I think most magic games are solvable (they have an optimal strategy that is computable).
            • by vlm (69642)

              I would agree with this completely, obviously in the extreme limiting decks to two or three types of cards simplifies the game immensely.

              The problem with a game having 16000 different cards or whatever is it seems to devolve into natural language processing. MtG isnt just written in free prose, but itself is sorta a language. So now you're stuck with the equivalent of proving there exists an optimal "winning" solution to free form paper and pencil RPGs like DnD or Pathfinder. Kind alike a Turing test var

              • While the magic cards are written in something like natural language, they seem almost like source code that has been translated into natural language by hand. It would probably be less work to translate the magic cards back into source code rather than writing a program to do it. Also there are many ambiguous cards that have had their text meanings clarified by some magic rules authority, this would be hard for an automated text->meaning analyzer to deal with properly. Also, I believe the actual rule
    • by Hatta (162192)

      As in Magic the Gathering? The card game with 12,000+ individual cards? In my honest opinion, it's the greatest game ever made. It's incredibly complex, and yet still understandable.

      Yes, it's very understandable that you're being used as a cash cow. What I don't understand is why anyone would play a game where the rules are continually adjusted to whatever makes a private company the most profit.

      • by xevioso (598654)

        You realize you don't have to buy magic cards to play magic?

        • by Hatta (162192)

          No, I didn't realize that. Where do I get free cards? Are those free cards as good as the cards that people play for?

          • You make them yourself, perhaps using regular playing cards or just your own stiff paper. The actual function of the cards (and even the art) is entirely online with no legal encumbrance, so you're paying for basically tournament-legal decks / decks that a random opponent will accept, time saved, and small-scale art.

            • by drinkypoo (153816)

              You make them yourself, perhaps using regular playing cards or just your own stiff paper.

              So the answer is no, they are not as good as the normal cards. They also aren't free, because the materials cost money and/or time, and time isn't free even if you don't charge yourself for free time because you don't get it back.

          • by xevioso (598654)

            You get free cards by printing them. You won't be able to play them in sanctioned tournaments, but you can play them with your friends, if they will let you.

          • Your standard run-of-the-mill desktop printer. If you really want to go all out, then you can use nice thick glossy paper or even get even the rarest cards printed at Kinko's for a pittance.

            That said, cheap decks can be officially paid for and still be strong. Unless you want to be a top tier tournament player, I guess. You might need to invest a bit more to have that hobby. It doesn't invalidate the whole game however.

    • Magic is not the greatest game ever made. It's not a bad game. I used to play it (1994 - 1997), and I had a lot of fun, but have since moved on to other games. The game design was a pretty good design for it's time. It was the pioneer in CCGs, but it hasn't really changed for 20 years. There have been a lot of games that have come out since that have been more fun in my opinion. Maybe I just have different taste than you, but having 100 cards on the table doesn't seem like fun to me. That sounds like

      • by bughunter (10093)

        I played around the same time, and even got back into it a bit later (around 2000).

        The number one thing I learned from MtG is that the more complex a rules system, the more likely there will be a degenerate set of min/max conditions in the rules, and then the game becomes a meta-game of finding these and exploiting them to maximize gain.... many times these conditions are outside spirit of the game, and those who exploit them look down upon those players who still try to embrace the spirit of the game.

        This

        • And sometimes to combat this "abuse" it is tempting to create very strict rules to prevent players from doing abusive things. In government this is called red tape. In games it can kill creativity. You are never able to do anything that wasn't specifically considered and sanctioned by the game designer. It's a fine line.
    • by Anonymous Coward

      Race to the Galaxy is incredibly complex and fun

    • by Kergan (780543)

      As in Magic the Gathering? The card game with 12,000+ individual cards? In my honest opinion, it's the greatest game ever made. It's incredibly complex, and yet still understandable.

      May I ask how many of those cards you actually use in practice? Think hard: how often have you built a deck that used that white 1/1 banding creature card (I forgot its name...)? It's not limited to uninteresting common cards, either. When I looked into selling my shoebox full of cards, I got told that players seldom fielded Serra Angels or Thunder Spirits anymore because there were better white creatures -- whereas back when I played, you'd find a few of either or both in nearly every white deck.

      Back when

  • by DaemonDan (2773445) <dan@demonarchives.com> on Monday January 14, 2013 @01:42PM (#42583945) Homepage
    Not being able to "solve" games like chess like you can with Tic-Tac-Toe (http://xkcd.com/832/) is what makes them fun and playable. Otherwise it quickly gets boring. It's also why it isn't always as fun to play against the computer on really high levels. They can cheat and solve the next bajillion moves.
    • They can cheat and solve the next bajillion moves.

      cheat

      I do not think that word means what you think it means.

      • "Inconceivable!" You're right that it isn't really "cheating", but it is less fun (for me at least) to play against an opponent with an unfair advantage
        • I'd disagree with that premise. If I use a computer to calculate the odds of winning every next possible move and use that information to my advantage, wouldn't I be considered cheating? Why does that same logic not apply to AI opponents?
    • It's also why it isn't always as fun to play against the computer on really high levels.

      What's interesting is that while computers can handily beat a person at chess, the best AI yet developed is no match against a person in a real time strategy game, or a turn-based strategy game like Civilization. While the author is quick to point out humans don't pick the most optimal strategy in a complex environment, he fails to note that humans usally beat computers in the same environments. Computers have to brute force their way through a problem, and can only find the optimal path when given paramete

  • Even for computers it is really hard to find an optimal strategy for Go. To my knowledge it's still a research topic. No surprise it's even harder for humans. Concerning how much effort was needed to research and program software, that beats a human in chess, I thought it would have been well known, that humans can't find an optimal strategy in this game either.

  • by tp1024 (2409684) on Monday January 14, 2013 @01:44PM (#42583971)

    The point of a two player game, like Go, is to beat the opponent. If you know your opponent doesn't like a certain kind of opening, or is likely to feel overconfident in certain positions, thus creating weaknesses for you to exploit - this is a viable strategy, provided it works.

    However, the better the players the more they look down upon such things - and rightfully so - because they learned the hard way that weak moves will be punished by good players.

    • Even high-level players do tend to use a bit of that kind of thing. Kasparov mentioned that was one of the odd things about playing Deep Blue, that unlike playing another grandmaster, there wasn't this human meta-game element: he couldn't intimidate the machine into screwing up.

      • Yeah, if you look at Karpov, Kasparov, Fisher, etc etc etc, you rapidly see that high level chess is rife with 'meta-game'. There are other levels of meta-game as well. Players will master different types of game and different lines, focus on different parts of the game, etc. Some players are more defensive, others more offensive, some more tactical, like Kasparov, others more strategic. One player might be a master of specific styles of opening lines, and other might be a mid-game generalist or an expert a

        • by fatphil (181876)
          I had some spare time today, and was watching a few of the live GM games in the Tata Steel tournament. The computerkibitz function was quite enlightening, even the best in the world quite often deviated from what the computer thought was best. Which doesn't mean they're wrong at all, of course, for the reasons you state.

          (Though to be honest, I'm not really a chess fan, I just wish eevn a fraction of the time, effort, and money, were ploughed into other abstract strategy games.)
    • One of the best parts about Magic is playing with multiple players, and trying to figure out the best way to deal with so many different players/approaches. You _can't_ win by beating your opponents, you need the right strategy.

      On that note, Race for the Galaxy is definitely an excellent game to explore. If you're familiar with game theory, try expanding it to three, four, or five people.

  • Makes sense. (Score:5, Insightful)

    by tool462 (677306) on Monday January 14, 2013 @01:49PM (#42584027)

    That's why they're fun. With a solvable game, you play the game. With an unsolvable game, you play the player.

    Of course, it's a lot less fun once you're playing the stock market or global thermonuclear war, but no less rewarding.
    And of course of course, they're neglecting that any attempt at predicting the behavior of a market will affect the behavior of that market such that the predictions no longer hold true.

    Kudos to anyone who can pull off the ultimate hack: invest your money based on your -unpublished- theory of how the market will respond the theory that you ARE about to publish.

    • Insider trading is the ultimate hack?
    • by dhomstad (1424117)

      Or just pay millions of dollars to get a fat pipe out of the Chicago and New York stock exchange, write a program that bases itself on the Black-Scholes equation, and take advantage of all the traders that aren't operating on the millisecond timescale.

      There's always that option too. Oh and if you're too lazy to watch kill switch connected to your billion-dollar monster, just ask that your bogus trades be cancelled when all hell breaks loose.

      source = http://www.reuters.com/article/2012/08/01/us-usa-nyse-trad [reuters.com]

  • I'm guessing "noughts and crosses" is "tic tac toe".
  • So the more complex the game, the harder it is to find optimal strategies...\ Better break out the Nobel prizes early this year.
  • [after playing out all possible outcomes for Global Thermonuclear War]
    Joshua: Greetings, Professor Falken.
    Stephen Falken: Hello, Joshua.
    Joshua: A strange game. The only winning move is not to play. How about a nice game of chess?
  • by gurps_npc (621217) on Monday January 14, 2013 @02:26PM (#42584409) Homepage
    They are not talking about the too complicated for people to play, They mean too complicated for a computer to play 'perfectly..

    No one insults a baseball player because he only hit a triple, rather than a home run. But in their definition of game play, they expect every single move to be the best one possible. That is how COMPUTERS play games, not how people do. Computers make calculations based on all possible moves. That is not how people play at all.

    Instead, people play the odds. We work in the murky world of probably rather than optimal. Which is why humans will always beat a computer playing Go, even if we lose in Chess.

    Games are not about picking the optimal move. Instead they are either about:

    Having fun

    LEARNING which moves are better and which moves are worse

    Both. That is what all play is about. Having fun, learning how to do things, or both. Knowing the optimal moves ahead of time means you can't learn and you can't really have fun.

    What they are talking about is trying to win the game for ever and ever. When we do that, we move on to another game.

    Just like when I learned how to always win at tic tac toe.

    • by Anonymous Coward

      Instead, people play the odds. We work in the murky world of probably rather than optimal. Which is why humans will always beat a computer playing Go, even if we lose in Chess.

      Actually, this is one of the most promising directions that Go programs are headed in. Putting the game into a more Bayesian framework of "what move maximizes my probability of winning". They're still not better than the best humans, but there is progress being made and I think it's a bit presumptuous of you to assume that computers will never take the lead.

      Just like when I learned how to always win at tic tac toe.

      Play against a 4 year old, or take an extra move when nobody is looking? Personally, I'm a fan of the switch-sides-in-the-middle gambit.

    • by niado (1650369)

      humans currently can beat a computer playing Go, even if we lose in Chess.

      FTFY. Go, like Chess, is theoretically solvable, since it is, after all, a game of perfect information. [wikipedia.org] Perhaps neither game will ever be truly solved, but even in Go computers are very likely to become unbeatable eventually, and probably sooner rather than later.

  • At the risk of seeming like a shill, I have to say that most of the top 10 games on Board Game Geek are worth playing, and definitely hard to master.

    Generally speaking, Agricola, and Puerto Rico are considered to be the best board games currently available. If you haven't played them, you should really try to find them, because they're very dynamic, and require a lot of strategizing, while demanding that you be able to react to both your opponents and the game.

  • The research didn't study humans and has nothing to do with humans. It studied learning computer algorithms, which are now sometimes used in economics. The researchers claim that their work suggests something about human behaviour without having studied a single human. They should have their science licence revoked.

    • From TFA:

      We assume that the players learn their strategies x via a form of reinforcement learning called experience weighted attraction. This has been extensively studied by experimental economists who have shown that it provides a reasonable approximation for how real people learn in games.

    • by chrismcb (983081)
      I RTFA, it didn't say anything about studying "learning computer algorithms.' It did mention "ran thousands of simulations of two-player games to see how human behaviour affects their decision-making."
      I'm not saying they didn't study humans, but it doesn't look like they studied learning computer algorithms either.
  • Gaia is a thing (read the book by James Lovelock). Gaia is a -result- of complexity.
    Look at the chemical operations occurring in a single cell. A cell is the -result- of a soup of chemical reactions. The cell does not initiate basic chemistry anymore than Gaia can create a new species. When a new species is created, it is within and because of all the other complexities of Gaia.

    Same with games (and anything). Add a few non-dependent rulesets and suddenly there is an amazing complexity.

    If gaia is too co
  • This 'news' does not appear to be anything more than a simple application of Gödel's incompleteness theorems. What's the point, then?

  • They become less predictable because of the large number variables behaving in increasingly less predictable ways? You mean you've never heard of tertiary and quaternary derivatives?

  • From my reading of the article, the point seems to be that people apply game theory (http://en.wikipedia.org/wiki/Game_theory) modeling to real world problems using the assumption that everyone understand the system. This is one of two of the most problematic tenants with economic modeling. The other is that people behave in their rational best interest. The emerging idea of behavioral economics (http://en.wikipedia.org/wiki/Behavioral_economics) is one way people are looking to address that. I think the ar

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