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Randomness: Blight or Bane?

The following is the presentation I gave at GDC Austin '09.

In general, we tend to think of randomness in games as a bad thing.

Our sense of fiero or accomplishment at winning a game depends on the feeling that we have, in some sense, mastered it, and either that we out-played our opponents, or at least, in a soloplay game, overcame the challenges it posed by dint of hard work and skill. If, instead, we feel that we just got lucky -- or, worse, that someone else won even though we were obviously the smarter player, because they just got lucky -- we're likely to think less of the game.

But clearly many, many games have some random elements, and some are highly luck-dependent, and yet people continue to play them. What really is the role of randomness in games, and how can designers work to harness it to beneficial effect?

Magical Thinking

Randomness has been part of games since their earliest inception -- and when I say "earliest inception," I mean deep into the unwritten Neolithic past. Game scholars sometimes point to The Royal Game of Ur as the earliest known game, and in a sense it is -- but we also know of games from any number of Neolithic cultures that survived into the modern era, many of them documented by Stewart Cullin in a series of books for the Smithsonian, published in the early 20th century.

The simplest games, variations of which exist in innumerable cultures, are what Dave Parlett (in the Oxford History of Board Games) calls race games, and what others may think of as track games. Lines are drawn in the dirt with sticks to represent the spaces of the game. Binary lots -- cowrie shells, acorn cups, almost anything that can fall easily on one side or another -- are tossed. Some simple algorithm is used to determine what a particular number of up-lots versus down-lots means; players advance their tokens along the track in accordance with the lots thrown. The first player to reach the end of the track wins.

Needless to say, games of this type exist in modern cultures too, many of them deriving directly from Pachisi, an ancient and popular game in India: Parcheesi, an American commercial variant; Ludo, a British commercial variant; Sorry!; Trouble; and so on. Typically, these games add some element of strategy -- blocking, sending pawns back to start, etc. -- but the line of descent -- from track games that seem to exist in almost every Neolithic culture to modern Pachisi variants -- seems clear.

For Neolithic cultures -- and for some people in modern society too -- randomness is not merely a feature of gameplay: It has a magical, in some cases religious aspect. A random test is viewed as divinatory.

In reality of course, "luck" is not an external force. Randomness is randomness, and nothing more; in a sequence of random tests, occasional streaks will show up, but there is no real significance to this fact. It's simply how randomness happens. It's not a consequence of mystical forces.
Ancient cultures, of course, had no concept of statistics, and humans by nature tend to find patterns in things and ascribe meaning to those patterns even when there is none. Hence the very concept of "luck."

The Romans played dice games not merely for the thrill of gambling -- but also as a means of testing their favor with the Gods. Many Neolithic cultures use binary lots or other forms of random number generation as a means of divination, ascribing predictive value to the results. Very likely, track games arose not as entertainments, but as a means of recording the results of a series of divinatory casts. And Cullin documents a number of cases in which games are used by Neolithic cultures as part of their religious practices.

And even today, some people continue the practice: the Ching is a "oracle" consulted via the throw of binary lots, the Tarot uses randomly selected cards in divination. They are not games in themselves, obviously, though games have certainly been devised that use the Tarot deck, and one could, I suppose, make a game of the Ching if you so wished. Though if you take the Ching seriously, I suppose you might be reluctant to mock it thusly.

In the French noir movie Bob le Flambeur, the protagonist, who is a professional gambler, keeps a slot machine in his hall closet. Before going out each day, he inserts a coin and operates it once. If he wins, he considers that he is "lucky," and cheerfully goes off to a day at the casino. If he does not, he finds something else to do with his time. As did the Romans, as do Neolithic cultures, he is using a game for divinatory purposes, and ascribing a magical aspect to its results.

Most of us, of course, scoff at the notion that there is anything significant about the outcome of random tests. And that perhaps is the main reason why serious gamers, at least, tend to view games that are excessively luck-dependent as poor games by nature; unlike primitives, or the superstitious, we see no significance to the outcome of random processes, and therefore no sense of triumph at winning a luck-dependent game. We do not have the favor of the gods, the mystical forces of nature are not aligned in our favor, it is not an omen that our endeavors today will likewise be met with triumph. It was just a game, over which we had no real control, and therefore not a very interesting one.

Skill vs. Chance
The law, at least, divides games into two categories: games of skill and games of chance. Games of skill are always legal. Games of chance, if played for money, are generally illegal, because gambling is viewed as an addictive and destructive vice. Although if that's true, it's hard to reconcile government's suppression of gambling with the promotion of government lotteries; a libertarian would say that government suppresses other forms of gambling because the state doesn't like competition. But perhaps a more accurate statement would be that we have, somewhat confusedly, adopted toward gambling the attitude that some people think we should also adopt to other vices, like recreational drugs and prostitution: People are going to gamble whatever you do, so better that we permit gambling but tax and control it carefully, to limit the damage it does and to prevent organized crime from earning the proceeds. In this light, advertisements for the lottery are an example of a somewhat confused government, part of which wants to limit gambling and part of which wants the revenue it generates.

Just as government is confused about whether it wants to restrict or promote gambling, however, government is also confused about what gambling is. Games like Roulette or Craps (at least when played with honest wheels and people who don't try to manipulate the dice) are indeed pure games of chance, but the same is not true even of all casino games. Blackjack has at least some element of skill, and some Poker players will tell you that their game is absolutely a game of skill. (The claim is, however, not entirely true, as I'll explore later.) And some forms of gambling, such as betting on the horses, are almost entirely a matter of skill.

Horse racing bookmakers use what's called a parimutuel system of betting. In a parimutuel system, the posted odds are dynamically adjusted as bets are made. By contrast, in a game like Roulette, the house earns its money by having some numbers on the wheel (0, and in some cases 00) that do not fall under the conventional bets of even/odd and black/red; and the payoff for betting on a single number (36-to-1) is lower than the actual number of slots on the wheel (37 or 38). Consequently, over repeated spins, the house is guaranteed to come out ahead.

In a parimutuel system, however, the house simply ensures that, regardless of how the horses come in, the total payout, based on posted odds and bets received, will always be smaller than the amount of money bet. As new bets come in, the posted odds are dynamically adjusted. Consequently, the house doesn't care if one bettor is a better "player" of the horses than another, or has some scheme that lets them consistently win; the house's rake is guaranteed.

In fact, it's possible to make a living betting on the horses, and some people do. It isn't easy; it requires a lot of work, and considerable self-discipline. The way to do it is to study the horses, pore over statistics of their performance, learn which do well or poorly in different track conditions, and then pay careful attention to the posted odds. Most bettors are naïve, and will not have the same expert knowledge as you; consequently, you will have a better sense of the likelihood of different outcomes than they, and when a spread opens up between the posted odds and your actual expectation of outcomes, you can take advantage of that by betting against the mass of naïve bettors. It's a form of arbitrage, in other words.

In truth, the outcome of a horse race very rarely depends on chance; it depends on the characteristics of the horses involved, and the condition of the track on which they run, and perhaps more subtle variables; but, pace quantum mechanics, it takes place in the Newtownian phenomenological world, and a sufficiently advanced student of the horses can win consistently, because posted "odds" are not based on actual odds, but on the pattern of betting.

The only element of chance that intrudes, really, is that unexpected events can happen in a universe as complicated as ours; thus, a horse can stumble and fall, say. This isn't 'chance' either, of course, but it's the kind of event that no student of the horses can anticipate -- it's the sort of thing we'd simulate in a game by introducing a chance element.

The common dichotomy between "games of chance" and "games of skill" therefore is something of a false one; there are pure games of chance (such as Roulette) and there are pure games of skill (such as Chess), but almost everything else is some mixture of the two.

Different Aesthetics

Different games appeal to different aesthetics. People who love story-driven Japanese CRPGs will tell you how much they loved the story of Final Fantasy X, while others, blind to this genre, will characterize the game as "interminable cut-scenes separated by boring and repetitive gameplay." A more broadminded gamer may see truth in both viewpoints -- the Final Fantasy games do provide interesting characters, well-written stories, and gorgeously-rendered cut scenes, and players do come to care about the characters surprisingly deeply; yet there's far less variation in moment-to-moment gameplay, and in terms of strategy and puzzle-solving, than in almost every other game genre. Final Fantasy X is a wonderful story, and is also characterized by dull and repetitive gameplay between story elements.

Part of my objective in general is to foster the aesthetic of a "broadminded gamer," able to see what people find appealing in any game; but that's because I'm a game designer and pretentious "ludeaste" (a word I just coined by analogy to cineaste). Most gamers prefer to find games that they like, and often look down on ones they don't, even if enjoyed by others. My games rock; your games suck, and never the twain shall meet. If you don't like Final Fantasy, you're obviously an idiot, or conversely, sucked in by the story and don't really understand what games are really about. This is a short-sighted view.

But to return to the question of randomness, in light of the idea that there are different, and equally valid, aesthetics of "the game." One sort of game aesthetic says: Games should be won by skill and not luck. Hence any recourse to randomness by a game is bad.

Curiously, it's an attitude held by two sorts of gamers who otherwise have very little in common: Fans of abstract strategy games, and fans of first-person shooters.

To an abstract strategy gamer, games like Chess and Go are the n'est plus ultra of gaming: mechanically simple but strategically profound. You can, and people do, spend a lifetime studying and mastering these games. To a serious abstract strategy gamer, a game like Risk is a trivial and even appallingly stupid waste of time, a mere die-rolling exercise; and even something like Backgammon, a game of no little strategic depth in its own right, is inherently suspect, and inferior, because of its reliance on dice. The ideal is a game that pits mind against mind in a clean contest of strategic planning and anticipation of the opponent. Anything that involves even the slightest degree of randomness is inferior, because victory should come through mastery of the game and superior play. The notion that someone might win through luck is almost repulsive. Never mind the fact that factors external to the game itself, such as one player's third margarita the night before or another's existential despair over the affair her husband is having might affect their quality of play; within the magic circle itself, everything should be pure.

Similarly, for an FPS player, winning a deathmatch involves mastery of the interface, perfect knowledge of the level layout and the location of spawn points and power-ups, and superior knowledge of (and ability to perform) tactical tricks of the trade, such as the bunnyhop and the rocket jump.

Chess is about as different a game as you can possibly get from Quake: one is a game of mental domination, and the other a "twitch" game, a game that depends almost entirely on the mastery of a limited set of physical skills.

No Chess player ever leapt from a board shouting "Woot! Ph34r my l33t sk1llz!", and "pwned" is not likely to become synonymous with "checkmate" anytime soon. Yet Chess players, too, prefer to feel that it is their "l33t sk1llz" that bring victory, not any random element.

Gamers often divide games into two categories by the type of skill they require: "player skill" games, like Counter-Strike, depend on physical mastery, while "character skill" games, like Final Fantasy, depend primarily on the characters' stats and the player's choice of special actions to determine outcomes. To a serious FPS gamer, character skill games are obviously inferior; all they take to win is perseverance, while player-skill games reward those who work to master the gameplay.

And yet, if you look under the hood (that is, at the source code) you'll find that weapon damage in FPSes is partly random; typically, weapons do some set amount of damage (X) plus some additional amount of damage determined randomly and linearly between 0 and another factor (Y).

This fact isn't normally perceptible to players, who may assume that any variation in damage is a consequence of variation in accuracy or range; and indeed, in actual play, the randomness of FPS damage has little impact on ultimate outcomes. Except perhaps in very marginal circumstances, it's not enough to let an inferior player beat a superior one. Nor is it particularly clear why id (Quake's developer) felt it necessary to make variable damage part of the game: in the soloplay game, most monsters are killed with a definable number of shots from particular weapons, and the randomness isn't enough to cause any surprises; in deathmatch play, there's enough variability in a system of chaotic fireplay to prevent a non-random system from becoming dull. I suspect the random element of damage derives not from a conscious design choice, but from an unconscious and automatic adoption of a game mechanic -- variable weapons damage -- that stretches back into the tabletop roleplaying and miniatures gaming prehistory of the videogame.

But miniatures gaming, certainly, and tabletop roleplaying, to a lesser degree, need a degree of randomness to sustain player interest. Why might that be?

Value in Simulation

Let's start by examining Little Wars, H.G. Wells's landmark miniatures rules, the first commercial rules published for gaming with toy soldiers. It does not rely on chance, at least on the surface. Infantry may move such-and-so many inches per turn, cavalry somewhat farther, artillery less far. Melee combat is resolved according to a simple, non-random rule: if the two sides are equal, everyone on both sides dies. If unequal, the inferior force is eliminated, doing damage to the inferior force according to this formula:

Thus, if the inferior force has 4 units, and the superior one 6, the superior force loses 2 units: doubling the inferior force gives us 8, and subtracting the superior force of 6 produces 2.

No randomness here.

Artillery fire is, however, resolved in a different way. The rules to the game assume that both players have what Wells describes as "spring breech-loader guns." You slide a stick into the cannon, depress the spring, and aim the cannon, then release the stick. If it strikes an opposing figure, that figure is lost.

It seems clear to me that without this second rule, for artillery, Little Wars would be a very dull game indeed. If melee combat was all it permitted, you could almost predict before play begins who would win: The side with the greater strength, of course. Only poor play by the superior side, or brilliant play by the inferior one, could prevent that outcome.

Artillery changes the equation, however. It's still non-random, in the sense that the effectiveness of your artillery depends on your ability to aim it, your feel for the power of the cannon's spring, and of course your ability to maneuver your troops to leave clear lines of sight from your cannon to opposing units. But all of these are tricky things, not as cut-and-dried as the rules for melee. In the Newtonian universe, they are not random elements -- but they provide, in this context, the sort of variability of outcome essential in any true wargame.

Why do I say that variability of outcome is essential in a wargame? For a simple reason: wargames are supposed to be simulations. They are supposed to represent, with greater or lesser fidelity, a real or hypothetical military conflict. There has never yet been a general who can confidently predict the outcome of battle.

Part of the reason for that is, of course, fog of war; at the inception of battle, both sides generally don't really know how strong the opposing side is (something few games do a good job of simulating). But even if they knew what they were up against down to the last man and piece of equipment, they could not be certain of the outcome. So much is dependent on the actions, or failures, of individual men on the field; so much on vagaries of weather and lighting; so much on improvisational genius or confusion and sloth.

As von Moltke says, "No battle plan survives contact with the enemy." The phenomenological world may be Newtonian, and hence in principle calculable, but thousands of men in desperate struggle is a messy, incalculable situation. "For want of a nail, a kingdom was lost" -- an extreme statement of the situation, but illustrative. You can't know; all you can do is plan, take your best shot, and hope things work out.

"Alea jacta est," Caesar said as he crossed the Rubicon, leading his army to Rome in defiance of the orders of the Senate; the die is cast. Surely he thought he had the power to triumph, as he ultimately did; but he knew also that he was taking a huge risk. As in Poker, military command is a matter of minimizing risks and making the best bets you can -- but as in Poker, you cannot be sure of the outcome.

To properly simulate war, therefore, unpredictability is essential, and the easiest way to ensure unpredictability is to harness the power of randomness; like Caesar, we cast the die, in our case to simulate the impact of all the multifarious factors that no commander can control.

In other words, a wargame that contains no random elements is, by nature, a poorer simulation than one that incorporates randomness. Accuracy, or at least verisimilitude -- the feeling of accuracy -- is essential to the aesthetic of the wargame: When playing a simulation of the Second World War, we want it to feel like the war, to feel that as commanders of one side or the other, we're making decisions about what to do that were within the realm of possibility for the opposing sides. If things happen that strike us as ludicrously infeasible -- like, say,

Sweden conquering Russia in 1943 -- then it's clear that the game is flawed. To a wargamer, at this point it doesn't matter whether the game system is strategically deep, or provides an interesting narrative, or satisfies any of the other aesthetic criteria that some bring to games: it's a bad game, because it's a bad simulation, and for a wargamer, value as a simulation is a major part of his aesthetic.

The notion that randomness is bad is an aesthetic one, and appropriate to games characterized a spartan commitment to pure strategy; but that is only one valid aesthetic lens. A wargamer might, in fact, consider a game like Chess too dry, too moldy in antiquity, and ultimately uninteresting because of its lack of color, aesthetically unsatisfying because of its severe divorce from anything real. It simulates not, neither does it spin (the dice).

The use of chance as an element in heightening the realism of a simulation isn't unique to wargames; indeed, almost any game that purports to simulate real world phenomena uses chance to a degree. In Roller Coaster Tycoon, when one of the little people wandering about your theme park completes their current action, the game chooses a new action for them to perform that is partly dependent on the character's current stats and partly based on a random factor. In SimCity, the paths taken by individual "sims" through the city are determined semi-randomly. In Kremlin, whether or not one of your geriatric Politbureau members dies this year is determined by a die-roll. Just as war is too complex to simulate accurately through an entirely non-random system, so are almost all real-world phenomena, at least addressed at a high level, and thus a degree of randomness increases the simulation's fidelity.

When Chance isn't Random: Regression to the Mean

In reality, the reliance by games on chance does not necessarily mean that the game's final outcome is random. In a game with chance elements, there will typically be dozens or hundreds of random tests over the course of the game -- many, many times in which dice rolled, or an algorithm that uses a random number as an input applied.

Paradoxically, the greater the number of random tests, the less effect chance has on the outcome. Over time, random systems regress to the mean.

Consider a single die-roll: there is exactly a 1/6th chance of each possible result. Now consider a 2D6 roll (that is, rolling two six sided dice and summing the numbers rolled): There is a 1/6th chance of rolling a 7, but only a 1/36th chance of rolling a 2 or 12. A single die-roll produces a flat curve, with all outcomes equally probable; a 2D6 roll produces a bell curve, with numbers toward the center of the curve more probable, and the extremes less likely. Adding more dice increases the sharpness of the curve.

In other words, the more random tests, the lower the likelihood that the outcome will be at one extreme of the bell curve, and the more likely that it will be near the center.
Suppose that the outcome of a game is based on a single random test that can go either way -- 50/50 odds. In this case, I will win 50% of the time, and you will win 50% of the time. The outcome of the game is purely random.

Let us suppose instead that, over the course of the game, we have 100 random, 50/50 tests -- but in addition to those tests, there's an element of strategy -- in a wargame, the element of strategy might depend on choosing where and how to maneuver, taking advantage of terrain, deciding where to follow up success and where to retreat, and so on. Over the course of the game, the likelihood is that I will win roughly half of those random tests, and you will win roughly half. It's possible, though highly unlikely, for me to win every one, and therefore the game, purely by luck. It's far likelier that the random tests will give no player any strong advantage, and that instead, strategy will dominate -- that victory will, as in a purely non-random game, go to the superior player.

Or to put it another way, if a game contains even a small element of strategy, then as the number of random tests approaches infinity, the outcome of the game is more and more likely to be dictated by strategy than by chance. The point at which strategy begins to dominate over randomness depends on how much effect strategy has -- in a game where random elements are small and strategy vital, strategy dominates with even a handful of random tests, while if strategy is a relatively modest dictator of outcomes, then many random tests are required before strategy dominates.

But the net effect is clear: in a game that relies on chance to some degree, has many random tests, and also has highly strategic elements -- typical of all sorts of simulations -- the outcome will only in very rare cases be dictated by chance.

Mind you, this analysis presupposes that each random test has roughly the same impact on the game as every other such test; there are cases when this is very much untrue. It might be that a handful of random tests are critical. As an example, in Jim Dunnigan's Empires of the Middle Ages, the players' success is critically affected by the military, administrative, and diplomatic capabilities of their monarchs, each represented by a number from 1 to 9. When a monarch dies -- which happens only a handful of times during a game -- the new monarch's stats are randomly generated. Being lucky in monarch generation is so important that it overwhelms almost every other factor of the game; strategy still plays an important role, but if one player has a 9-9-9 monarch for most of the game, he's very likely to win, almost no matter what the other players do.

Dunnigan would doubtless argue that in this regard, Empires is an accurate simulation of conditions in the Medieval era, that the characteristics of monarchs were critical to their nations' success or lack thereof; and indeed, the color and historicity of the game are sufficient to make the game enjoyable despite its largely random path. But considered as a game qua game, as opposed to a simulation, this is undeniably a design flaw: if you have bad luck, it's frustrating to play, and if you have good luck, it's hard to feel a sense of accomplishment at winning.

Empires is, however, an outlier in this regard; most wargames are consciously designed to take advantage of regression to the mean, in order to preserve the simulation value of randomness in a military context, while also ensuring that the game remains strategically interesting to the players.

The point remains: the criticism by strategy-purists of games that involve some degree of chance is not wholly valid, not only because random tests can improve other aspects of the game, such as fidelity of simulation, but also because if chance is used sufficiently frequently, and with sufficient care, strategic elements will still dominate outcomes. Thus, strategy and not luck will remain the most important factor in play.

Poker: Strategy as the Epiphenomenon of Randomness

Poker is a perfect illustration of this point. On the surface, Poker appears to be an entirely random game: cards are allocated randomly, and the best hand wins. Hard to get more random than that.

Of course, we've described only two of the game's mechanics: card distribution, and hand comparison. What transforms Poker from a random game to one that is highly dependent on player skill is, for the main part, one thing: betting strategy.

Versions of Poker vary, but in all cases, there are multiple rounds of betting before hands are revealed. Each round, some information is revealed to the players; in Draw Poker, after one round of betting, players may discard some cards and request more, and the number of cards discarded by your opponents gives you a bit of a clue as to what they hold. In Stud, cards are dealt out to the players each round of betting, with some displayed face-up. In Texas Hold'Em, "community" cards that are shared by players are revealed over several betting rounds.

Thus, in all cases, players gain information during the hand that, while imperfect, gives them some sense of the odds. They know what they have, they have some clues as to what the other players may have, and they can drop out after any round of betting. And of course, there's also the information provided by the facial expressions and body language of the other players.

The trick, then, is to minimize your losses when the cards are against you, while maximizing the pot when you have the cards. One typical strategy is "fold early, and bet aggressively;" don't hold onto weak cards, and if you have a strong hand relative to what you see on the table, work to maximize your potential win.

Let us imagine a game between several average players and one superior player -- a player who knows the odds backwards and forwards, and reads other players well. If only one hand is played, the outcome of that hand -- in terms of who wins -- is wholly random. The flow of money in that hand is not; in all likelihood, the superior player will fold early on a weak hand, and ramp up the betting to win substantially on a strong one. That's only "in all likelihood," however; the superior player could have a Flush (an excellent hand in most versions of Poker), bet aggressively, and still be beaten out by an inferior player who, this hand, just had the luck to get a Full House. In a single hand, the superior player has an advantage, but the advantage is modest.

Poker is almost never played for a single hand. It's typically played for many hands in succession. The superior player's edge in a single hand is modest, but over time, that modest edge means that, all things being equal, the pile of chips in front of him will grow, while the piles in front of the other players will shrink.

Random tests regress to the mean. The superior player can be beaten by luck over a small number of plays, but over a lifetime of play, he will dominate.

As with the horses, there are people who make their living playing Poker, and as with the horses, doing so requires work and commitment, and either the ability to calculate odds quickly on the fly, or a strong gut feel for odds learned by long-time play. In this regard, Poker players and racetrack bettors rely on something very similar: for the horses, the arbitrage opportunities opened up by naïve bettors in a parimutuel system; for Poker, the opportunities created by the inferior strategies of more naïve players.

Is Poker a game of skill or chance? If Roulette is the measure, it is unquestionably a game of skill. Yet even in, say, a typical Texas Hold'Em tournament, with a single buy-in and a relatively limited number of hands, a perfect player can still be defeated by the luck of the draw. Poker is a mix, but over the long term, strategy beats luck.

And, please note: the strategy of Poker is based on its randomness. Without random card allocation, it would be an entirely different, and inferior game. The strategy of Poker lies in understanding the statistical nature of the game, and managing statistical outcomes. That's true, to a lesser degree, of many other games that rely on random factors; in a board wargame, for example, you always know the probabilities of different outcomes before you commit to an attack. But Poker is almost unique in its pure reliance on probability as the creator of real strategic depth. Poker in particular belies the abstract strategy gamer's idea that randomness is in opposition to strategy: in Poker, strategy is an epiphenomenon of randomness.

Randomness as a Way to Break Symmetry

Chess and Go, the abstract strategy games par excellence, are almost perfectly symmetrical: both players have equal forces, with equal positions and equal capabilities. The only element of asymmetry is their turn-based nature, which gives one player a turn-order advantage -- in both of these games, the first player has a slight advantage, but in some other games, the last player, or some other player in the order, may have some advantage.

Symmetry, at least in terms of starting position, is common, though not universal, in virtually all games that involve two or more players. In multiplayer games, players prefer to feel that they begin on a level playing-field, and the easiest way to ensure that they do is to start them off equally.

Symmetry is also a real danger in any game design. Symmetry can lead to a host of ills. Symmetry works in Chess and Go because these are games of enormous strategic depth, and symmetry is quickly broken by the moves or placements of the players.

Contrast this with John Nash's Hex or Alex Randolph's Twixt (which, despite minor variations in tessellation and play, are extremely similar games). The object of both games is to build a connected line from your side of the board to your opponent's, with the opponent trying to do the reverse, with neither player able to play through the other player's line.

At first, this may appear interesting, but in actuality, the game has an optimum strategy -- a fact mathematically proven up to 9x9 Hex grids. Given optimum play, the first mover wins. The problem with Hex is that it has nothing like the strategic depth of Chess or Go; symmetry never gets broken.

Games in which all players pursue the same strategy result in a win by the player who makes the fewest mistakes -- or, if none, by the player who has the player-order advantage.

This is dull.

To make a symmetrical game interesting, you need to break the symmetry as quickly as possible. You need to put the players into somewhat different positions, so that they have different concerns to think about, and different strategies to adopt. Chess begins symmetrical, but with a single exchange of moves, it begins to open up; your first pawn move opens a line of potential attack for a bishop, while my first move signals a potential castling. Immediately, it's a different game.

Chess can pull this off because of its strategic complexity. Chess has been refined over centuries, pondered by millions of minds. Good luck to you in devising a game of equivalent depth.

How else can you break symmetry? One way is by providing slight asymmetry in starting positions. Puerto Rico does this by having different players start with different plantations, and by forcing players to adopt different actions each turn. But one easy way to break symmetry is to provide a degree of randomness -- and in fact, almost every Eurogame does so.

This seems paradoxical on the face of it: the Eurogame aesthetic prizes strategy and disparages luck, and yet at the core, many games in the genre depend on some degree of randomness.

In Settlers of Catan, for example, new players are advised to set up the board as per a diagram in the rules that provides a balanced, symmetrical arrangement of terrain -- but more advanced players are encouraged to lay out the board in a random fashion. Discs with different numbers are distributed semi-randomly across the board's hexagonal tessellation, and dice are rolled each turn, and compared to those numbers, to see which areas produce resources. The players begin with symmetrical resources, but the asymmetry of the board, coupled with the random nature of resource production, quickly produce asymmetries as players settle different areas of the board.

Or consider Torres, which at heart is a purely symmetrical abstract strategy game -- but breaks the symmetry by giving players "action cards," each of which provides some special benefit. Different players hold different action cards, and the opportunities they offer therefore provide them with an incentive to adopt slightly different tactics during play, opening up what would otherwise be a pretty dull game.

Similarly, in Ticket to Ride, players begin with a number of "route" cards, and the victory points they earn mainly (though not exclusively) come from completing routes (e.g., New York to Los Angeles). Played without the route cards, Ticket to Ride would be a dull exercise in trying to complete the longest rail lines first; with the route cards, each player is striving for different objectives in an asymmetrical landscape, and therefore the game has far greater strategic depth.

The danger with the use of randomness as provider of asymmetry is that the game becomes too chance-dependent, which in a genre like the Eurostyle is a flaw, since the aesthetic of the genre prizes strategy and planning. There are, however, three ways to harness the virtues of randomness without falling into the trap of allowing randomness to determine the winner: Regression to the mean, as we've discussed; ensuring that random elements are "balanced;" and ensuring that random elements face all players with the same opportunities.

Let's start with "balance," a term I used advisedly: it's an awkward term to use, because "balance" can mean many different things in the context of a game, depending on exactly what you're talking about. In this context, what I mean is that if randomness is used to open up different possibilities to different players, thereby fostering different approaches to the game, but if all opportunities opened up are of roughly equivalent game value, then the random element does not unbalance the game, that is, make it luck-dependent.

As an example, the action cards in Torres allow players to do different things but, at least a priori, none of the actions they permit is obviously better or worse than the others. In addition, to draw a new action card, a player must forgo taking some other action in the game, so the question of whether or not to draw a card becomes a strategic concern. Chance is not entirely eliminated through this scheme, however; in a particular strategic situation, drawing a new action card might provide you with an ability that is precisely what you need at this moment, or something that is of no immediate benefit -- and so luck continues to play a role.

The route cards of Ticket to Ride, and how they have evolved over the course of the game's expansion, are particularly interesting here. In the original game (set in North America), your original draw of route cards has a huge impact on your likelihood of winning or losing. If you have cards that involve nice, high-value, long-haul routes that overlap to a high degree, so that you can complete them with a relatively few number of rail car placements, you are likely to win. Conversely, if you are stuck with short-haul routes in the central US that do not lay the groundwork for later long haul successes, you are most likely screwed.

Alan Moon, the game's designer seems to have recognized the problem here; subsequent versions of the game, such as the European board and the "Mega Game" that replaces the original North American card set, are designed to ameliorate the problem. On the European board, all players are guaranteed one long-haul route with their initial route cards; and the Mega Game provides players with a choice of more cards initially, making it less likely that you will be stuck with duds, while also giving bonus points to the player who completes the most routes, providing more benefit to the short-haul route cards. Both games are far more balanced, in the sense that initial card distribution is less likely to determine the outcome.

The concept of "balance" in this context assumes that the game's random elements apply to individual players; but it is possible to have random elements that offer the same opportunities to all players. Think of these elements as akin to the weather; you and I are equally subject to the rain.

Consider Reiner Knizia's Medici; in this game, competing Medieval merchants bid on lots of luxury trade goods. At the beginning of each round, counters representing the trade goods are placed in a cloth bag. On his turn, a player draws between one and three goods from the bag, and these become a lot on which all players bid.

Clearly, there's a random element here, because goods are drawn blindly, that is, at random. Yet all players are bidding on the same lot of goods; the distribution of goods does not, in itself, offer any immediate advantage or disadvantage to any player. Though this is random, the randomness does not in itself have any immediate impact on the game's outcome.

In Medici, you earn points both for the raw value of the goods that are shipped -- but also for shipping more goods of a particular type (say, spices) than other players. This is, in fact, how Knizia breaks the symmetry of an otherwise perfectly symmetrical game with perfect information: different goods suddenly become more valuable to you than others, because you have previously purchased or shipped goods of a particular type. But this in itself is not chance dependent -- it depends purely on your decisions, that is, on what lots you bid on.

Randomness isn't being used here as the key way to break symmetry -- Knizia does that with his scoring system. Instead, randomness is being used to ensure that players cannot predict what goods will be auctioned next, and to ensure that each auction is likely to be somewhat different from the previous one, thus preventing the game from becoming static and predictable.

In summary, adding a random element to any game creates a risk that the outcome will depend on luck rather than strategy; but it also helps to break open a symmetrical game, which is essential to prevent it from degenerating into strategic gridlock.

Too, designers can adopt strategies to minimize the impact that luck has on outcomes, such as balance among random elements, exposing all players equally to random elements, and/or regression to the mean.

Leveling the Playing Field

In children's games, in particular, randomness is often used as a way of leveling the playing field -- that is, of ensuring that everyone has an equal chance of winning, regardless of age or skill.

Please note that we're talking about yet another game aesthetic here: for most styles of games, and for most gamers, the idea that everyone should have an equal chance of winning regardless of skill is tantamount to saying "this is barely a game." You might as well roll a die to see who wins. Why even play?

Suppose, however, that you are a parent with a small child, with whom you want to play a game. You could choose Chess, I suppose, but unless you purposefully play badly, you will beat your child every time. And very likely, will wind up trying to comfort a crying child who will never, ever, want to play a game with Daddy again.

Consider Snakes and Ladders, a classic and centuries-old game of childhood (popularized in the US as the commercial title Chutes and Ladders). Everyone begins at square 1, and strives to reach square 100, in a 10x10 matrix of squares numbered sequentially. Each turn, you roll a die (or use a spinner), and advance your token as many spaces as the number generated. At various points on the board are "snakes" (or "chutes") that cause you to slide from one square to a lower one -- or "ladders" that cause you to advance from one square to a higher one. The first to square 100 wins.

A moment's thought will show that there is no strategy to the game; the outcome is purely dependent on chance. This fact is not readily apparent to a small child, however, who may well experience a moment of fiero when landing on a ladder, and momentary annoyance when landing on a chute -- and will be gleeful if and when she beats her Dad.

From the perspective of an abstract strategy gamer, say, Snakes and Ladders is nugatory, a degenerate game, not worth the time to play. But it is actually perfectly suited to its niche in the ecosystem of games. Playing Snakes and Ladders, a child learns how to take turns, make moves, experience some of the emotions that games evoke, gains practice with counting -- and also learns to internalize the "magic circle," the idea that what happens in the game stays in the game, that you strive to win but loss has no consequences external to the game and is therefore not to breed ill feeling.

Examine almost any halfway decent game designed for small children, and you'll find the same factor at work. Candyland, 3D Labyrinth, and the innumerable forgettable licensed "track" games that appear each year are all, in the final analysis, dependent wholly on luck. And even games aimed at slightly older children are generally mostly a function of luck, thought they start to add strategic options: Go Fish, Sorry, Uno, Parcheesi, and Ludo all have minor strategic elements, but luck is the main determinant of outcome.

Even in sophisticated games, the use of randomness as a leveling factor has a role to play. Poker is a good example here. Every Poker player knows that better players win more over time -- but also know that, this hand, you have some shot at winning, even if you're not one of the elite. The game's randomness doesn't level the playing field entirely, as it does in Snakes and Ladders, but it does given you a reason to play, and a hope of winning, even if you are not a studious master of the game. The leveling nature of randomness, for Poker, serves a highly important function, and one that sophisticated players of the game prize rather than despise: It keeps the suckers playing.

Wild Cards

B-17: Queen of the Skies, a long out of print game from Avalon Hill, simulates the military career of the crew of a single B-17 bomber engaged in repeated raids over Germany during the Second World War. As a game, it is a little more than a series of tables on which the player (it's a single-player game) rolls dice. Dice are rolled to determine the player's mission, what opposition in terms of German fighters, flak, and so on the crew faces during the mission, the effects of combat with enemy fighters, how successful the aircraft is in damaging its targets during bombing runs, which crew members get killed or injured, and how badly, and so on. There are almost no decisions to be made, just dice to be rolled. It sold relatively well during its lifetime (by board wargaming standards).

Part of the reason for that was undoubtedly that there are very few solitaire board wargames (a mainly two-player genre); but part of it was that B-17 was, in its own weird way, fun to play. There was some enjoyment to be gained by rolling the dice and seeing what came next.

Interestingly, I don't think a digital adaptation would be remotely popular; you'd just click "next" and see the next event. The process of operating the game system, of physically rolling the dice and looking up the results, felt something like gameplay, even though it wasn't, really. The mechanization of resolution that digital games provide would make the underlying dullness of the game obvious.

B-17 is an example of randomly-generated algorithmic content. What made it (mildly) interesting was that interesting stuff happened in the game -- even though your ability to respond to or manage that stuff was, well, essentially non-existent.
I'm not holding it out as an example of good game design; it's not. But it is a good demonstration of another utility of randomness: providing variety of encounter, a mechanism for letting "interesting stuff happen."

As an example of digital games with something of the same dynamic, consider Rogue-likes. Rogue-like games are single-character, hack-and-slash, dungeon-crawling RPGs in which almost everything is randomly generated. Each level of the dungeon is laid out according to algorithms that rely on a random seed; the level is populated with monsters and treasure generated by tables referred to with a random index. Almost nothing is "level-designed," in the sense of most digital games, though some Rogue-likes, such as NetHack, intersperse a handful of levels with designed elements among the randomly-generated ones.

Rogue-likes are highly luck dependent; you are often faced with hordes of monsters, or other problems that you cannot overcome, and can contrariwise (though not often) gain some key magic items that let you advance quickly. But they are far from devoid of strategy; they're turn-based, and every turn you typically have a choice of a wide variety of actions -- not just the usual movement and attack, but things like using spells or potions, praying to your god, locking doors behind you, and so on. There are a host of tactical tricks to learn, counters to special monster abilities, and so on. If the mark of the superior strategy game is that it makes you stop and think about your next move, then Rogue-likes qualify -- even though they are so heavily luck-dependent.

In exchange for accepting an almost perverse level of chance, Rogue-likes offer an almost unparalleled level of variety. Because they are randomly generated, no two play sessions are identical. They typically have dozens or hundreds of different monsters, magic items, and other capabilities, and quite often dozens of "verbs," actions the player may trigger. Some of the more involved Rogue-likes, such as NetHack, contain so much rococo detail, handle so many unlikely possibilities, that even after years of play you may discover new features. As an example, in NetHack, if you toss a ring down the sink, the sound the sink makes in response may give you a clue as to what that kind of ring does -- one of NetHack's innumerable coders (it's a long-standing open-source project) having a bit of fun, there.

Obviously, you cannot play a Rogue-like with the kind of seriousness that a Chess master brings to that game; no matter how experienced a player, the next corner may bring you face to face with instant death. It requires a sort of cheerful resignation, a willingness to enjoy the often humorous ways in which you die ("gnawed to death by rats on level 17 while paralyzed").

Despite the randomness of the game, the sheer variability it offers means that it is infinitely replayable. Games like Diablo -- a commercial, graphical dungeon-crawler, similar in many ways, but with designed levels -- is hardly worth playing more than once. You might try it a second time with a different sort of character, but the challenges and story elements will be the same. By contrast, NetHack is one of only two games that has been on the hard drive of every computer I've owned since I first encountered in. (The other is Civilization.)

There's a lot to be said for sheer variety of encounter, and random shuffling of game elements is perhaps the easiest way to provide it.

So. Randomness: Bane or blight? It all depends. If randomness dictates outcomes, many players will find the game unsatisfying. But there are times when a degree of randomness plays an important, and useful, role in a design.

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Copyright © 2009 by Greg Costikyan.