Perceiving Randomness
“It’s like ten thousand spoons when all you need is a knife…” — A. Morissette, Ironic.
In Finland where I live, gambling is legal and slot machines are in every shopping mall. They are usually played by senior citizens, but I knew a young guy who had a full-proof plan of how to win. He would lurk around the machines, waiting to spot another player give up after a long sequence of futile attempts. The guy would then jump un the machine that was free now and start to play, sure that after a long sequence of lost games the machine was bound to throw a winner. Eh, he never won big, and he lost more than he had won, but he still remembers only those times that he won anything. I bet he is still waiting for his big win, which surely after all these years of playing must be coming any day soon. Right?
Of course, the math doesn’t work that way. The probability of you hitting a jackpot doesn’t actually grow each time you lose. Still, good luck in trying to explain this to some people. The reason why people believe in this stuff is profoundly tied to the way how our brains perceive randomness. We perceive randomness in a way that is fundamentally flawed yet rooted in a solid survival strategy.
Video games can harbor randomness in various places. As a game designer, you will eventually going to use it, so it pays off to understand how players are going to perceive it.
Randomness in nature
A brain is a pattern recognition organ. Any brain in any kind of animal. The purpose of the central nervous system is to ensure the survival of the organism. We, like any other living creature, live in a chaotic, random world. This randomness is driven by something fundamental to the nature of the universe, and we do not quite understand it. In order to deal with the ever-changing environment living organisms have adopted two broad strategies. Some, like plants, or fungi are happy to stay anchored to one spot ready to suffer whatever calamity the elements throw at them. Others have chosen to stay mobile, constantly searching for a source of food or trying to get away from potential danger.
These movements are inevitably guided by some sort of a nervous system. Boiled down to its most basic essence, there is only one question that even the brain of the simplest animal on this planet needs to answer at each moment in life; Will things be better if I move over there than if I stay over here? In order to answer this question, a brain needs to be able to predict the future. Not in a sense of guessing the movement of the stock market but in a sense in which a sparrow brain is able to predict where the tier of an oncoming car is going to be in the next three seconds.
In order to do so, the brain needs to spot patterns, patterns of movement of objects, patterns of colors, patterns of lights, and sounds, patterns in any sensory input. Brains hate randomness. True randomness has no pattern. There is nothing to be learned from randomness. Quite the opposite. For a creature with a brain, it is better to assume that there is a pattern where no pattern exists than to assume that things are just chaotic and miss picking on an actual pattern of behavior. That whisper in the grass could be just the wind. It could also be a cat lurking.
The human brain is exactly like any other brain on this planet, only more complex. This is the reason why phenomena such as pareidolia exist. This is why we see faces in electric sockets or Jesus on a piece of toast. There is an evolutionary advantage in assuming that a pattern exists even in really random input.
KEY IDEA: Humans are hardwired to perceive patterns even if no pattern exists.
Randomness in games
Obviously, this has some very fundamental implications on how we humans perceive randomness, especially randomness in games. Imagine that you are rolling a die, a simple six-sided die. The chance of you rolling 6 is always, and at each roll exactly 1/6. This is what is known as an independent and identically distributed random variable.
However, an average human will assume that the chance of you rolling 6 increases each time that you roll any other number! Our brain assumes that there is a pattern. It is hardwired to do so. It will assume that the chance of rolling a particular number in a particular roll is somehow tied to the outcome of several preceding rolls. This is why some people believe that there is some magic system by which you could fill in Lotto numbers or increase your chances at the lottery.
Dice, bingo, and lotto are simple, they are straightforward games of chance. Videogames on the other hand can hide randomness in many places. If the pattern of the outcome of a roll does not correspond to the player’s expectation, the player will assume that the system is deliberately trying to sabotage his efforts or withhold something from him.
Assume that you are making a game in which a player from time to time gets to open a chest. There are three possible items that he can find in each chest, a healing potion giving him an extra life, a piece of gold, or a bomb that can be thrown at enemies. If not otherwise communicated players will assume that the probabilities of finding any of these are equal, i.e. 1/3. They will also assume that after opening, for example, 30 chests they will have about 10 of each item in their inventory. If you design your system to be truly random, what is likely to happen is that an average player will end up with a big surplus or a big deficit of one of the items. For example, an inventory might hold 4 healing potions, 6 pieces of gold, and 20 bombs!
The value of these items in a game can be very contextual. For example, gold is cool when you are standing in front of a merchant selling weapon upgrades, but to reach that spot you need to clear a forest path of a pack of trolls and those bombs would come in handy in that situation. Player’s brains will inevitably imagine a pattern in the randomness of this system. A player running away from a horde of baddies with only half a heart, desperately searching for a healing potion will inevitably think that the system is deliberately trying to screw him over after opening the fifth chest only to find another lousy piece of gold. A while later the same player might be searching for gold cos he has 997 pieces and that slick new sword costs 1000 at that merchant’s place, and all he can find is just healing potions and bombs! Surely the system is again deliberately hiding from him just the things he needs!
KEY IDEA: Humans expect conditional probabilities even if outcomes are independent.
There are several strategies that you can use to mitigate this problem. One obvious strategy is to implement the system which would take into account the player’s expectations. For example, you could increase the likelihood of a player finding a healing potion when his energy is low, or a probability of finding bombs in chests that are close to spawning spots of enemies. This is a traditional method employed by many games for years. The pitfall of this method is that you might allow for an easy exploit. If players figure the set of conditions that makes the certain outcome more probable they might be also able to replicate them at will thus breaking the balance of your game.
The other approach is to give an illusion of control over the outcome into the hands of the player. No one is blaming dice for not rolling 6, simply because they are the ones doing the actual roll. Many games include this option. The player is required to select a box, or a card, or to choose which crate to smash. This is pure smoke and mirrors, and the success of this psychological trick depends very much on the minute details of UX and visual presentation.
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You can also try to balance out the amounts of items that the player will eventually get. For example, you could generate a list of 30 elements with 10 of each three item types and randomize the order in which they appear. You can use this list to decide the outcome of opening a chest. This will ensure that after opening 30 chests the player’s inventory will contain an equal number of health potions, bombs, and pieces of gold, resulting in a more fair game.
There is no universal solution and the choice of approach depends on what kind of a game you are trying to make.
Randomness of action
Remember the Self-Determination Theory. It is a psychological framework dealing with human psychological needs. One of three fundamental needs is characterized as competence. Simply, we as humans want to see that when we take some action the outcome of that action will produce an expected result. For example, when I kick the ball I hope it will go in an intended direction. If the ball instead veers off in some random direction I will feel frustration.
This applies to the world of video games as well. If the outcome of the player’s conscious actions is something random this is likely to cause frustration. If randomness is tied too closely to the player’s actions it will cause frustration. If randomness or the outcome is not hinted at in some way it will cause frustration. For example, a player will feel fine if he opens a chest with a big question mark painted on it and a random thing happens. He will not feel fine if he throws a hand grenade and it flies off in an unexpected direction.
KEY IDEA: People want to fight randomness and overcome it using their skills.
What players want to see instead is a random change in the environment to which they can react using their skills. The outcome of their actions needs to be predictable and in accordance with their expectations. Otherwise, they will doubt their skill, the fairness of the game and start to feel frustrated.
Key takeaways
- Brains are pattern recognition organs.
- Brains are hardwired to see patterns even if a pattern doesn’t exist.
- There is an evolutionary advantage for a brain to assume that a pattern exists even if there is none, then to miss a hidden pattern.
- Humans want to battle randomness and overcome it using their skills.
- Players will see patterns in randomness and assume that this is done deliberately to hurt them.
- Your game needs to work around and against this assumption.
Link
- Definition of independent and identically distributed random variables
- Quantum theory and randomness
- Seeing Probabilities — an interactive presentation by Brown University.
- Perceiving Patterns in Randomness
- Role of Randomness in Games
- Two types of randomness
- Veikkaus — Finnish government-owned gambling monopoly
