Matt Thrower: When 2 + 2 = 5
One of the more enlightened points of view that I’ve picked up from other gaming columns and blogs – regretfully I cannot now remember where – is the idea that most games, no matter how thematic, no matter how interactive, are actually carefully dressed up mathematical exercises. The difference between a board game and a logic puzzle is pretty much limited to how obvious or accessible the underlying maths is to the game players. Even extremely random games, so long as they permit some sort of element of choice, can be seen as exposing their mathematical roots in the way that players can get an advantage through shrewd statistical analysis, however simple. Even negotiation games could be cast as having both feet planted firmly in game theory. This argument doesn’t apply to dexterity games, of course, and in most games that I’d consider worth playing the mathematical roots should be well hidden under plenty of theme, but other than that I think it’s a pretty insightful observation and one that I’ll happily subscribe to and defend.
On the flip side of the coin, the extremes to which some people will push this argument never ceases to amaze me. Just because I’ll agree that games can basically be reduced to a bunch of maths doesn’t mean that you can treat games as being nothing more than a bunch of maths and draw all sorts of erroneous conclusions as a result. There’s a wide range of points between obviously mathematical games such as Power Grid and something like Magic Realm in which the maths, although present, is completely buried under layer after layer of complexity, randomising mechanics, player interaction, and various levels of awkward value judgements. Incidentally those are both games that I despise, but they make useful examples in terms of illustrating what I’m talking about. In essence the more complexity, randomness, and in particular interaction that you add to a game, the more difficult it becomes to appreciate the maths underneath the game and play along perfectly logical lines. It might be obvious in a given situation that you’re making a mathematically-based value judgement, but when the precise value of the choices before you are muddied by something as fallible as mere human psychology, which might make you particularly attached to something or somewhere on the board just because you, say, like the artwork, then there’s no way you can convincingly use a mathematical analysis to predict the outcome. When a game is full of these sorts of opaque judgements then trying to claim it can be played in a logical, “solvable” manner is just silly.
There are a small number of games that highlight this particular discrepancy because they thrive off it. The one that springs to mind is Knizia’s Amun-Re. The phases of this game literally alternate between muddy, subjective judgements and clearly mathematical objective judgements one after another. In the auction segments during the early game you have no idea how much value other players are putting on particular provinces, so you’ve got no idea how much you need to bid to secure what you want, forcing you to play partly from the gut. You then get to spend a phase buying things in which everything has a clear value and, if you make the effort, you can calculate the eventual actual worth of what you’re purchasing. You then get a sacrifice round which can be objective if everyone is playing maximally or subjective if one player decides not to bother doing the sums. It’s crazy – and from comments by fans of the game this constant tension between the types of decision-making during the play forms a big part of its appeal. So there you have it – a clear example of how making choices in a game can vary from the purely mathematical to the non-mathematical, no matter how solidly grounded in logic the basic mechanics are.
So bearing all this in mind I’m startled by the way in which people continue to use the maths underlying a game to try to prove points during discussions about gaming. It’s a particularly disingenuous thing to do in my opinion because it almost always looks so convincing – you can do a lot of analysis in most cases, the arguments may be difficult to follow (which increases how impressive they look) and in any case people seem to have a particular susceptibility to swallowing arguments which appear to be backed up by mathematical reasoning. That maths and numbers don’t always add up to an entirely convincing explanation of something can be clearly seen in the way that marketing firms manipulate statistics in order to make exaggerated and misleading claims about the stuff they’re selling. This approach has a lot of parallels with the gaming equivalent: It relies on the reader being unable or unwilling to make wider connections about the claims made and, most perniciously of all, it has a tendency to fool those who are inexperienced or unwary, so I find it particularly offensive when these sorts of arguments get put before newbie gamers who are merely trying to make an informed choice about buying game X or game Y.
Nowhere is this sort of mathematical abuse more visible and more over-used than in the endless, tiresome debates over whether Age of Steam is better or worse that Railroad Tycoon. Most gamers that I know take the sensible view that both are extremely well-designed games that will likely have some level of appeal to gamers of almost any type, and that the difference in how a new gamer is likely to feel about playing one or the other is probably going to be minimal. But these voices of sanity are drowned out by fanboys on both sides of the debate trying to use exactly the sort of logical analysis I’ve described to “prove” that one is indisputably better than another. They might not ever admit it when confronted with the question directly, but the manner and language that they use makes it quite clear that this is what they believe and that this is what they’re trying to do.
It usually goes like this: Some poor, unsuspecting new gamer will blunder into a forum and unwittingly light the tinder under this particular box of fireworks by innocently commenting that they’ve heard both games are based on essentially the same mechanics, so they want to get only one and which should it be? The length of time it takes for an extremist of one camp or the other to jump in and start the argument is usually shorter than a New York minute, but the mathematical approach to the debate is usually started by someone from the AoS camp – understandable as AoS is the more obviously mathematical game, so is likely to attract more obviously mathematical people – who will put forward a bunch of logical arguments to prove that AoS is the better game. These vary in scope and form. One runs that the auction phase in AoS is superior to that in RRT because it determines player order rather than just first player and because the advantages of going first in RRT are minimal at best. Another runs that Tycoon cards make RRT inferior because they force a player into a strategy which might be suboptimal given other in-game conditions which are largely beyond his control. The fact that AoS has a smaller board and is therefore more competitive and cut-throat because players are forced to interact will inevitably get mentioned. After this, someone from the RRT community will usually respond in-kind with the same sort of arguments. These will wind back and forth, getting into ever more minute details of the mechanics and maths of the two games (too much detail for me to repeat here) and, usually, ever more bad-tempered at the same time. There’s usually no winner, and the person who loses is the poor sap who started the discussion in the first place because he’s left none the wiser about which, if either, he’d likely prefer.
I’ve seen this done to death with a number of games; another particularly tedious one is the interminable discussion about whether base War of the Ring is balanced or not. I find a lot of things objectionable about these lines of argument: it’s confusing to new players, it’s condescending, it’s reinforcing the geek stereotype, it is, as we’ve already discussed, wrong-headed. But what particularly bugs me is that it has an underlying assumption that the only reason to play games is for the mathematical challenge they offer, that the quality of a game can be determined in a calculated and definitive way by the amount of logic required to play the game well. This is pure and abject rubbish. People play games for lots of reasons. Some people like games to be a simulation of something. Some people enjoy the sheer excitement of largely random games, the manual challenge of a dexterity game, or the verbal and social challenge of a negotiation game. Some people enjoy the only partly-mathematical manoeuvre element in a game. Some people like games because it gives them something to focus on when their friends pop round for the evening. Some people simply prefer lighter games because they find them more engaging and relaxing. Some people place more value than others on the physical components of a game or have differing opinions on what sorts of artwork suit a particular kind of game. Most people, I suspect, have a wide taste in games which encompasses all these aspects from time to time – and yet the underlying assumption that the most important aspect when it comes to judging the quality of a game is the level of logical thought needed for success has become so pernicious that no one even seems to challenge it any more. Anyone who wants to ask about lighter fare seems to feel forced to prefix their opinions with qualifiers like “I know it’s sad, but ...” or pointed comments about how they spend more time playing with family and friends than proper gamers.
At the heart of the assumption is, I think, a staple of geek culture: that intelligence and logical reasoning is an essential lynchpin of what makes someone worthy. It’s rarely stated in that manner of course, but if you think about it, it makes sense. Sadly, in many cases, intelligence and logic are the only things geeks tend to have a lot of that is of value in the wider world. People appreciate good computer programmers and engineers – they’re less appreciative of an encyclopaedic knowledge of the works of JRR Tolkien. So it’s no wonder that we put these things on a pedestal. But the fact is that it’s become pernicious and problematic. If we can’t begin to understand that there are many more things to value in the experience of playing a game than the mental workout that it offers, then we’ve trapped ourselves in a prison of our own making.
I argued not long ago that trying to get non-gamers into gaming was pretty much a waste of time. But if you really, really, want to get your friends and family gaming, then you’ve got to rid yourself of this presumption that games are all about mathematical analysis. Lose it, then go on to challenge it whenever you see it raise its ugly head. It might be that that’s what you look for in a game but that doesn’t mean it’s what everyone looks for, or even what the majority of hobby gamers look for. You might find that the people around you become rather more accepting of the games you want to play and, you never know, you might find that you manage to broaden your horizons and find more enjoyment in games you’d previously dismissed. And what greater goals can there be for gamers that those?
Posted by Matt Thrower on Nov 17, 2008 at 01:00 AM in Columnists, Matt Thrower / 1598
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I actually played with a guy this weekend that said that the games we were playing felt like math class, we pretty much laughed it off. But thinking a little bit about it, isn’t everything in life connected to mathematics? Everything, even that gut feeling is somehow connected to an equation. Posted by Tiago Nunes on Nov 17, 2008 at 07:21 AM | #
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You want math class? Play Age of Renaissance. Posted by Peter Stein on Nov 17, 2008 at 08:52 AM | #
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I think the argument cuts both ways. I’ve played Power Grid with new gamers who enjoyed the economic aspect of the game and would have been put off by a conflict/fantasy/sci-fi theme. You really have to know your audience. “Gateway game”, although a flawed term, is useful to describe a game that is basically un-offensive to the average non-gamer. They shouldn’t be viewed as a means to getting your in-laws to play Age of Steam, but they can be enjoyable in their own right. Posted by David Wiens on Nov 17, 2008 at 09:50 AM | #
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I believe this comic applies to gaming as well. Posted by Jon Theys on Nov 17, 2008 at 11:24 AM | #
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While some of the arguments you cite in the endless AoS vs. RT debate don’t seem very mathematical to me, Matt, I agree that the numbers arguments are tiresome and their practitioners even more so. However, the people I really wonder about are the nimrods who post a question on the Geek saying “which game is better?” or “which of these games should I buy next?”. Of course what follows are all the usual suspects screaming out about why *their* favorite should be favored, irrespective of what the OP might prefer. More often than not, the poster gives no clue as to where his preferences lie, so the question is really inane. Posing such a question to one’s Geek Buddies, who presumably share your tastes, makes sense; asking the Gaming World at large, including those who carry the banner for their favorites at every opportunity, does not. Posted by Larry Levy on Nov 17, 2008 at 11:27 AM | #
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Yes, it’s a good point. Asking “which is better” and providing no sort of criteria to help people help you is pretty much asking for trouble wherever you choose to do it! Posted by Matt Thrower on Nov 17, 2008 at 11:31 AM | #
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I’ve developed a citeria for judging games for my high school club: how often does th group burst into commentary/laughter/etc… due to each game. If it can frequently spawn such discussions, it’s probably a good game. Posted by Matt J. Carlson on Nov 17, 2008 at 01:30 PM | #
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@Larry - the thing about your comment Larry is that I think people who ask questions are just trying to get their feet on the ground. I hate when they seem to get driven off or pounced on because they asked an “inappropriate” question. Maybe they don’t have any geek buddies or even know about them. Maybe, they are legitimately, just wondering, what others think about the game. I don’t see how that is inane. Yes, many times there is little information to go on, so try and draw out their interests I say. I think so often those of us who are well ingrained in this hobby take too much for granted. That people would have a baseline knowledge of what is or isn’t a worthy question to post is such an example.
@Matt and re: Math
So perhaps we get back to different personality types at the core of this. Those who enjoy math for maths sake, and those who enjoy gaming despite the math. The layers of abstraction make gaming fun for me. Posted by vandemonium on Nov 17, 2008 at 03:00 PM | #
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Van, you’re absolutely right and I should have distinguished between the newbies trying to find a first title and the experienced gamers looking for a next purchase. It seems to me that the latter case is much more prevalent, which is why I made my comment. But I can’t say anything bad about a newbie innocently asking which games are good ones, because they have no way of knowing that they’ve just wandered into a hornets nest. Posted by Larry Levy on Nov 17, 2008 at 07:45 PM | #
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The basic operation in a game is determining value (real or perceived) and so manipulating those values as to win. As Matt says the values may or may not have objective basis, a player may just like the art on the tile or the name on that figure, but they can all be assigned values as factors in the decision making process. At this level it is all just logic (or math) albeit with some suspiciously subjective operands but very discretely objective operators. But it depends on what you are looking for. Some are looking for that sort of discrete systemic analysis and that is quite simply what games are for them and quite correctly, that is how they see all games. For them that is actually all games are and there should be no surprise that they discuss games in accordance with their own perceptions. It is really just a bias. Others have different values and thus different priorities, no better or worse, no more or less correct—and that puts the kibosh on my lead paragraph. My initial paragraph is only true if it aligns with your values. Matt Carlson above says that he picks games that cause commentary and laughter. That’s fine—those are his values and biases, those extra weights he inserts in his value-determination process—but that’s a poor behavioural selection criteria for me. I select games which prompt fascination (with or without commentary or laughter) and would be unhappy if I tried to pursue (either) Matt’s values. At this level some games are indisputably simply better than others. Age of Steam is just a better game than Railroad Tycoon and it is that simple—for my values. More honestly Railroad Tycoon is a great game ... for people who like that sort of thing. But that doesn’t mean I’m one of those people. My son adores the Crayon Rails system and they are great games for him and his values. I’m less impressed but then I don’t have his values. I seem to be saying that a lot lately: “That’s a great game for people who like that sort of thing.” Recently Dominion and Agricola have been holding that aphorism throne. Both are games I find no possibly enjoyment in for me but there are clearly people who greatly enjoy and value them and their game-value systems support that. While it applies to a lot more than just game selection: pick a set of values and stick with them. The arguments that are backed with numbers and pseudo logic that Matt so decries are simply battles of value systems. The number/logic chanters aren’t really talking about those particular games, they are championing their world-view of games, their values, their biases. They are apostles for their faith, their gaming world-view, out seeking converts and recruits. Perhaps if you look at those discussions that way, as actually discussions of competing religions and world-views, you may find them more useful. Posted by J C Lawrence on Nov 20, 2008 at 04:09 PM | #
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I think there’s a false split here. I don’t play on BSW for example, because part of what makes games playing for me is with a group of friends, in the pub, at someone’s home, or at a convention (the small, friendly, open gaming sort) in an atmosphere which is open to socialising. But simultaneously, with the right sort of game, I’m using a mixture of analysis, experience (of this game, and of games in general) and intuition (which is something you develop, not something you are born with fully functioning) to work out, estimate, or guess, which action - and which plan that action is part of - will get me the best rate of return on my limited actions, money or whatever for victory points or whatever else is the object of the game. And for whether a game is any good, it’s also all of the above. I haven’t played chess for twenty years, as it just had too much analysis that I didn’t want to do, and not enough fun. But I also don’t play many games that are too random and while appearing to offer analysis, it’s mostly a waste of time. (Today’s Board2Pieces is exactly my judgment of Cavum after one turn at Spiel. Premature judgment, maybe, but my wallet stayed closed.) But a good dice game, with radomness must either with a “play the percentages” or “chance your luck” element I enjoy, if it’s not too long. Can’t Stop for example is one of the all time greats. And my most recent purchase (not yet played) was Battlestar Galactica, that I certainly wouldn’t have purchased without the themeing. Maths? Fun? Theme? (And that’s not all.) I’ll take them all please, ideally in the same game, but failing that, I’ll mix my games (though the bias is strongly towards the high rated multiplayer games on the Geek, with exceptions both ways of course). Posted by Christopher Dearlove on Nov 20, 2008 at 06:45 PM | #
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Thanks for your comments JC - in the past I’ve not agreed with many opinions I’ve seen you put forward, as I’m sure you can imagine, but that’s well thought out, fair and very perceptive. I can’t help but feel that everyone would be a lot better off it people making these sorts of arguments - and this applies to all sides - made it clear that they were arguing about value systems rather than putting things in terms of black-and-white fact. But I suppose that goes against the grain of human nature, sadly. Posted by Matt Thrower on Nov 24, 2008 at 05:00 AM | #
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The “maths” argument is a red-herring. Ask a group of Trekkies which is the best Star trek movie and you’ll get the same vitriolic arguments. (Or maybe not, everyone knows Wrath of khan was the best.) Board gamers are no different. We are all the same in one respect: we fail to realize that everyone is different. Tastes differ. Motivations differ. People differ. Maybe you play games to have socialize. Maybe someone else plays games to escape from reality. A third plays because his ego is based on his win percentage. Who knows? But you fall into the same misogynistic trap when you denigrate people who like mathy games and who enjoy analyzing mathy games. Fans of a particular game may try to argue their case out a need to justify their own tastes, but again, they shouldn’t bother. JC has it right: “… if you like that sort of thing.” By the same token, the reader of an argument thread about AoS or RRT can probably come away with a good idea which game he’d prefer, because of all the discussion points raised, he can determine which of those resonate with him personally. I don’t like games with tons of player chaos or random elements. I prefer deep, invigorating strategy games. I do not like Fluxx. Or broccoli. Or peas. Or romantic comedies. And no amount of brow-beating, cum peer pressure is going to change that. Posted by Tim "out4blood" Seitz on Nov 25, 2008 at 02:28 PM | #
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It’s not a red herring and your Trek simile is misplaced. I understand that fanboys - especially geekyfanboys - will have bitter arguments about relatively trivial things. My issue is, in this case, with the form that those arguments take. I can see a lot of reasons beyond a mathematical analysis of the mechanics why a gamer might prefer AoS over RRT or the other way around. And yet those aspects are rarely mentioned - my question is: why? And what does that say about the hobby? Oh, and I fail to see why it’s only low-chaos, low-randomness games that can be deep and invigorating. (P.S. Don’t like peas? Are you crazy? Peas are great!) Posted by Matt Thrower on Nov 26, 2008 at 05:10 AM | #
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It says that the hobby is full of a bunch of geekyfanboys. I think that would be self-evident. “Oh, and I fail to see why it’s only low-chaos, low-randomness games that can be deep and invigorating.” That is the problem with your article. Low-chaos, low-randomness games are deep and invigorating for ME. It’s what I enjoy. Your tastes may differ. There’s no need to try to force other people to accept the things that you like. Posted by Tim "out4blood" Seitz on Nov 26, 2008 at 11:36 AM | #
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Heh. I’ve obviously made a bad job of getting my point of view across here, because forcing you to accept what I like isn’t what this is about: quite the opposite. I was trying to draw attention to the fact that people are prone to making statements such as “I don’t like games with tons of player chaos or random elements. I prefer deep, invigorating strategy games” which is stated in such a way as to imply that chaotic and/or random games are neither deep nor invigorating. Had you simply said “"I don’t like games with tons of player chaos or random elements” then fine - you’re stating a point of view about your taste in games and I have no argument or quibble there. Why would I? Everyone enjoys what they enjoy! What irks me is that heavily mathematical analysis games are naturally assumed as superior to other types of games - hence the second part of your comment, which would seem to imply this very thing. What’s particularly ironic about this situation is that it’s evident from the comments posted here that a lot of folks took my argument to mean the opposite - that I was actually doing down the sorts of games that I dislike. So I’ve clearly made a very poor job of it. Nothing could be further from my mind - I’m arguing for more equality and less assumed superiority when we’re discussing the relative merits of games. Posted by Matt Thrower on Nov 26, 2008 at 11:44 AM | #
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LOL. In that case, I agree with you. But then, I’d have to make a new comment: you are a bad writer. ;-) Posted by Tim "out4blood" Seitz on Nov 26, 2008 at 11:50 AM | #
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And sadly, in this case, I’d have to agree! ;) Posted by Matt Thrower on Nov 26, 2008 at 11:54 AM | #
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’people are prone to making statements such as “I don’t like games with tons of player chaos or random elements. I prefer deep, invigorating strategy games” which is stated in such a way as to imply that chaotic and/or random games are neither deep nor invigorating’ If “deep” means anything (probably something related to depth of decision trees, speaking mathematically) then chaotic and/or random games aren’t as deep as strategic games without those characteristics. Invigorating, on the other hand, certainly isn’t a characteristic exclusive to strategic games, or even necessarily a characteristic of them at all. In fact, much as my general preference is for strategic games, invigorating isn’t a word I would use to explain that preference. I would use it of, say, Cash’n’Guns, a highly chaotic and random game that I rate very highly. The point I’m making is that while a statement such as “Agricola is better than Killer Bunnies” (which is so, so, true for me) isn’t objective, you can go too far down the road of considering all to be a matter of opinion. Agricola is deeper than Killer Bunnies, and that remains true even if you hate Agricola and love Killer Bunnies (it could even be why someone had those opinions). Posted by Christopher Dearlove on Nov 26, 2008 at 03:57 PM | #
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I agree with the point you’re making. But I don’t entirely agree that chaotic/random games can’t be deep. Diplomacy can be extremely chaotic but most people would think of it as a pretty deep game. Twilight Struggle can be pretty random but most people would think of it as a pretty deep game. You’re right to say there’s only so far you can push the “opinion” argument, but I think it probably can and ought to be pushed further than it sometimes is. Posted by Matt Thrower on Nov 27, 2008 at 05:20 AM | #
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