Perceived Randomness: A Guide to Chance in Games

(As a primer, I’d suggest checking out Psychochild’s post about “good” and “bad” randoms, as well as my previous post about the role of chance in RPGs. This article digs a bit deeper than those two and tries to arrive at general guidelines for when chance and randomness fit into game design well.)

Perceived randomness has nothing to do with true unpredictability. True randomness is completely opaque: a perfect random number generator would generate a sequence of numbers that, when taken as a whole, has no discernable pattern. Its results would be completely unpredictable. We approximate true randomness through rolling dice, and this approximation of randomness is satisfactory to our perceptions as long as the dice are “fair”. When you roll dice, though, the result is not truly random. You can do some extraordinarily complex math, if given enough time, and figure out what face of the die will face up when the die comes to rest based only upon the force exerted on the die by your hand when you throw it and the composition of the die. We accept the outcome of a die roll as being random because, in common perception in the time-frame of the die rolling, we are incapable of forming and executing a process that will allow us to presage the side that will face up when the die has come to a halt.

Perceived Randomness as the Result of Theory-absence

On the level of abstraction on which a human being operates throughout his daily life, nothing is random from an objective view. For any event we can trace causes and effects into and beyond the conceivable and perceivable past.

If we’re diligent and use all the tools at our disposal, we can reliably form useful theories about events (e.g. theories that can predict the outcome of events given inputs we can gather from our perceptions) . In the course of your life, you will rarely have the time to be so diligent—you do as little work possible to establish theories about the world that are as effective as possible in the context of your everyday life.

When you can’t investigate the causes of an event and you cannot conceive of what the causes might be (or you don’t have the time to conceive of causes), you perceive the event as being random. We usually ascribe meaning to events that we perceive of as random because we do not like to feel as if we’re at the mercy of cast dice—it does not sit well with our teleological sensibilities. From this fact all superstition has grown. The seemingly insurmountable role of chance in life can also lead to hopelessness if taken too seriously. If all events rely on an external factor over which we have no effect (chance, in this case), why should we bother trying to effect certain outcomes with our actions? If some talentless hack can stumble into riches while I slave for my entire life for barely any money and recognition, why should I bother working so hard?

Perceived Randomness as Uncertainty

We know with varying levels of certainty how specific parts of the world work. If we don’t know well-enough how something works, we will perceive the outcome of that something as random.

If I’m certain that an outcome will result from some event, that outcome cannot be random with respect to that event in my perception. I know what is going to happen—the pattern is determined so the result is clear.

If I have no information about how what outcomes will result from some event (e.g. I am completely uncertain as to the outcome of the event), the outcome of the event is indistinguishable from a the event randomly determining an outcome.

If I have some moderate degree of certainty about the outcomes of an event, I still can perceive the event to be random, but with well-defined outcomes of limited variety.

This is a restatement of perceived randomness as theory-absence, but in simpler terms.

Gauging Perceived Randomness

Four elements that lead us towards perceiving an event or outcome as practically random:

• How much agency do we have in determining outcomes? If I have no perceivable say in the outcome, it might as well be determined by chance.
• What do we know about the process, abstractly? If I don’t understand how certain outcomes result from certain situations, those outcomes might as well be determined by chance.
• How much information do we have about this particular execution of the process? Even if I understand the process, if I cannot perceive details about this specific execution of the process, I still have no hope of making a prediction, so the outcome might as well be determined by chance.
• How remote in time and space is the outcome? The further away, the more uncertain, the more “random” the result will seem to us. As subevents resolve, the likelihood of the main event resolving in a certain way will become more and more easily perceptible and seem less random.

We can use these four elements to decide what parts of a game are best suited towards being procedurally or randomly determined.

• If the player has no say in some event’s resolution or introduction, that event is well-suited towards having elements of randomness.
• In Europa Universalis 3 there are some relatively fine-grained events that can happen within your kingdom that the player would have no way to cause or prevent, these events are introduced randomly as the game progresses.
• If the player has no way of gaining knowledge about how a specific event actually happens, it makes sense to allow some randomness in how that event unfolds.
• The player has no way of knowing how each magical item in Diablo II was made, so the player isn’t shocked when there are a wide variety of effects in a wide variety of magnitudes that are applied seemingly at random to items.
• In Civilization games, the actual tactics of individual units in combat are entirely skipped over, so it makes sense for there to be randomness in the resolution of combat.
• If the specifics about some particular event’s occurrence cannot be reliably shown to and understood by the player, randomness can play a role in deciding the result of that action.
• Dungeons and Dragons’ combat resolution engine generally does not care about how a sword is swung under relatively normal conditions. To represent the minor variations of the PC’s swinging motion and the opponent’s defensive maneuver, it makes sense to use randomness.
• Most RPG combat systems don’t make you worry about how exactly a spell is cast or a sword is swung. So we see a bit of randomness in the results of such actions.
• What happens very far away, very long ago, or very far into the future does not need to be resolved with the same level of detail as what the player is currently doing. Some randomness can reasonably be used to stand for that detail.
• In a TBS game like Civilization, a war between two far-off nations who are beneath fog-of-war for the player can be simulated more easily through a more liberal use of randomness. No need to move units individually when the player can’t see, for example.
• In AI War, the AI’s production and resource gathering operations occur in another galaxy that is inaccessible to the player. The game doesn’t actually simulate this universe’s specific resources and the construction of ships and structures as the game shows the player’s resource gathering and construction. AI War warps AI ships into the player’s galaxy based on some heuristics and some randomness.