Just Your Luck

February 17, 2008 at 4:14 pm (Game Balance, Game Design, Philosophy) (, , )

Though the phrase “games of chance” tends to refer to gambling, random elements show up to a greater or lesser degree in many other games.  In fact, in many genres, they are so ingrained that it is difficult to imagine playing the game without them.

On the face of it, this is rather odd.  Games are fundamentally about making decisions–whether strategizing or just “playing around”–and adding in random outcomes can only reduce the amount of control the player has.  Why would so many games engage in such an apparently self-defeating behavior?  Other than the ones that are doing it to get your money, I mean.

Well, I think there are three significant reasons a for game to include randomness…

The Spice of Life

Randomness can be used to help ensure the game is different each time you play.  Confronted with a given situation, many players will repeatedly make the same choice–partly out of habit, but mostly because what seems like a good choice the first time will probably continue to seem like a good choice (in the absence of strong indications otherwise).  If the player is presented with a different choice each time he plays, or if a single choice leads to different outcomes, then the player is more likely to have an original experience.  In short, randomness can add variety, or generate content.

If this is the only purpose, then ideally, the randomness doesn’t affect the game’s difficulty, just it’s “flavor.”  However, it’s difficult to ensure that all outcomes present equal difficulty to the player.  More importantly, randomizing the success (or degree of success) of an action is often the easiest way for the designer to add randomness, so sometimes that is used to add variety (through cascading effects on the game state and player strategy) even though it primarily affects how favorable the game is to the player.  With a large enough sample of random inputs, the overall affect on difficulty may be fairly predictable.

Of course, players don’t always make the same choices–especially if those choices didn’t work out so well last time.  Players who are competing with one another are especially likely to vary their choices in an attempt to out-guess each other.  So even if the rules of the game don’t explicitly include random variation, there’s usually some introduced by the players themselves.

Risk Management

A related reason that designers may introduce randomness into the results of players’ actions is simply to complicate the game’s strategy.  Managing risk is a basic but fairly complicated task; the more uncertain players are of the results of their actions, the more they need to think ahead and plan contingencies.  Instead of simply determining the strategy with the best outcome, players need to weigh risks and consider an ever-widening array of eventualities.  This increases the cognitive complexity of the game and provides a good way to make the player lose.

Note that it’s still not actually necessary for some random outcomes to be strictly better than others, just for them to be contextually better.  The appearance of a red stone is better for me than the appearance of a blue stone if I’m prepared to use the red stone (but not the blue one) to my advantage, even if there’s nothing inherently better about one or the other.  To a certain extent, players can orchestrate their own risks if they merely have the tools (and the strategic incentive) to wager on one outcome or another.

And again, this type of variation doesn’t necessarily need to be built into the game.  Players who are competing with one another generally need to anticipate each others’ future decisions–and there’s usually some uncertainty about how your opponent will choose to act, even if the rules themselves are completely deterministic.  However, this relies either on hidden information (your opponent makes a choice without full knowledge of the game state, or you don’t learn of his choice until some time later) or upon player mistakes.  Perfect players with perfect knowledge of a nondeterministic game will always act the same way (though figuring out what way that is may have as much complexity as preparing for random choices).

Fuzzy Wins

The final reason I can see for randomness–and really the only (principled) reason for some random outcomes to be strictly better for the player than others–is to reduce the chances that the better player wins.

That may seem like a very bizarre goal, but it makes a lot of sense if you think it through.  Games are often very complicated and involved activities, and we often want to emphasize the game’s subtleties and variations, but at the end of the game we reduce the player’s entire game to one bit of information:  either they won, or they lost.

Naturally, we expect the better player to win.  But what happens if you play again?  Do we want the same player to win every single time–even when the players are very closely matched?  Do we want the best player in the world to have a 100% win rate against the second-best?  That doesn’t really seem fair; it certainly doesn’t seem representative.

Imagine we’re trying to gauge the relative skill of two players by who wins or loses.  If the better player always wins, then we can tell who’s better, but not by how much.  The loser could be almost the winner’s equal, or he could be the worst player ever to live, and we couldn’t tell the difference.  By reducing a lot of information (the entire game) down to a single bit, we lose a lot of data.  This is called quantization error; we’ve changed the average value of a signal (who plays better) in the process of compressing it.

The solution to this problem is called dithering.  You can get a much better average result if there’s some randomness in the outcome of the game; instead of the better player always winning, we want him to usually win, and to win more consistently the greater his skill.  We can determine that player A is much better than B but only slightly better than C if he beats B 95% of the time but only beats C 60% of the time.  Even though the individual games where A loses seem unfair, in a larger context, they give us a more accurate picture of how well each of the players are doing.

And really, a game is much more interesting if there’s a chance of an upset.  There’s not much excitement in watching a game when you know the outcome; there’s not much satisfaction in winning if there’s no risk of defeat; and most players probably won’t play very often if they’re certain of losing.  Introducing a little noise into the outcome makes the game more interesting all around.

The amount of noise you want is really a stylistic choice; as the outcome of a game becomes more random, the difference of player skills it accommodates increases (you can play better/worse players with the same chance of an upset), but the harder it is to play the game competitively–for a serious competitor, to play better and still lose can be extremely frustrating.  Therefore, you generally want more randomness in a game meant to be played casually, and less in a game meant to be played more competitively–but you don’t want to go too extreme in either direction.

Now, it might be objected that players are generally not perfectly consistent in how well they play; even in relatively simple and purely deterministic games, such as chess, there’s a lot of uncertainty in the outcome of a game between two similarly-skilled players.  This is entirely true–you can’t completely get rid of randomness in most games, even if you want to.  But that doesn’t necessarily mean you shouldn’t introduce more.

And there’s another principled reason to want dithering, even if players’ performance is already random–it would be nice to be able to measure the difference not only between players, but between strategies.  If strategies A and B both lose to strategy C, we haven’t learned anything about which is better, and we can’t say that the person who uses A against C played better than the person who used B (or vice versa).  If strategy A wins 40% of the time and B wins only 10% of the time, then we can say that strategy A is a better response to C than B is, even though A still usually loses.  And being able to say that is useful not only for analyzing the game, but for learning it, too–it means players can see that moving from B to A is an improvement.

So it’s not so surprising that lots of game include randomness, and even randomness that affects little besides the outcome of the game:  despite appearances, it can actually make the game more fair overall, even though a given play may seem less fair.

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3 Comments

  1. Jordan (JJ10DMAN) said,

    Another good feature of randomness is that the worse player (or player losing vs. the system) can get better through experience more easily. I always lose at chess, but I can’t tell by how much I’ve lost because a few moves might have made all the difference. With a massive loss record, any small change in this non-random game creates no perceptible difference in my win:loss ratio, and I end up fumbling around in the dark rather than approaching a more perfect strategy.

  2. Gussiexj said,

    well done, dude

  3. The Icy said,

    Kinda late posting here, but I’m going to anyway. I think randomness can make a game more memorable to the players. Sure you might have played a perfect game a chess, with every move exactly how you planned it, and then won. However, how much more exciting (and maybe this is just my perspective) is a game where someone comes from behind, gambling on the hail-mary play, and wins through sheer, dumb luck. People instinctively cheer for the underdog and it is usually that randomness factor that leads to hilariously successful plays that never should have been. And maybe, when making a game, that sort of thing is something you want.

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