Dissection of Randomness in Games

Over the years there's been ongoing discussions about the use of randomness in games. I'm happy to have seen a lot of progress in game design with this topic. These discussions have usually mostly centered around the value of randomness, about how "good" or "bad" it is, and what constitutes these good or bad results. I think this is good and in the end helps us create better games, however, these are also ultimately subjective discussions surrounding the topic making value judgments. I'd like to take a look at randomness from another angle, I'll be trying to dissect randomness from an objective view using definite and robust terms, and move away from value judgements. I'll be dissecting the measuring tools for randomness, the figurative barometers we have to analyze randomness and then make those value judgments. To do this, we'll be looking at the distinct variables of every random element in games.

Delta of Randomness

The first, and possibly most important aspect of random outcomes in games is this, which can be defined as the difference between the best and worst game states possible from a random outcome. For those familiar with physics and math (hello fellow game devs!), delta denotes a state function which is independent of varying states other than the first and last positions. In our case, we're looking at the maximum and minimum values of a random occurrence which is independent from the other possible outcomes. A high delta of randomness, means that there's a higher potential for the game to be decided and affected by chance. An example of high delta of randomness would be a coin toss determining whether a player wins or loses (as in the children's card game "War"). A low delta of randomness meanwhile allows for an expected value to emerge more clearly (more on that later).

There's not much to this. An easy example is the delta of randomness on the damage values of an attacker for example where an attack for example deals 35-38 damage. The delta of randomness here is 3 damage per attack. You'd also have to factor in the delta of randomness in how it relates to emergent properties. Following the same example, those 35-38 damage attacks could have absolutely no impact on how many attacks it would take to deplete the health of a unit with 50HP because in both cases, it would be 2 attacks, so while there is a delta of randomness on one layer, there isn't any on the emergent layer.

Randomness Information Delay

Categorized as "Input Randomness vs Output Randomness" by designer Keith Burgun, this variable of randomness tells you how much time a player has to react and play with the outcome of an occurrence. Output randomness as the name suggests comes along with little or no time for a player to influence. Think of dice rolls to determine hits or misses, critical strikes and random targets of a spell in a digital card game. These are all examples of output randomness, randomness that is determined at the end of a game function. Most of the time when players and aficionados talk about randomness, they're talking about this. Input randomness, on the other hand as the name suggests, comes as input for the player to utilize and influence. Randomly generated maps in roguelites or strategy games are examples of this type, with the player having a lot of time to process the result and inform their other decisions.

As you would expect, this is not a binary and is better though of in terms of a spectrum or variable, and is why I prefer to call this "Information Delay" which is more measurable. Input randomness just denotes a high information delay compared to output randomness which has a very low (almost zero) information delay.

Randomness Complexity

In game theory "complexity" refers to the amount of interlocking and combinatorial states. Borrowing from that term: randomness complexity means the number of possible outcomes a random occurrence can have. The card draw mechanic in card games for example has a complexity equal to the number of unique cards remaining in the deck. Pretty straightforward. Layering on emergent properties here, we can take that example and think about drawing a full hand of 5 cards. The complexity now is much higher due to the combinatorial nature.

What's important for game designers to consider is that a low complexity means that players can possibly think through all possible outcomes while a high complexity means that players might not even be able to know what possibilities there are. These have different implications for the game's design. If we want players to avoid calculations in play, then we can try to overload the cognitive load through increased randomness complexity. On the other hand we might want to allow for more player skill expression in the form of them considering the different random outcomes.

Expected Value

Another very important aspect, this criteria is about how one can evaluate the statistical value of a random occurrence. It's the value a player reaches when considers an outcome's average, variance, median and mode, often expressed as just the average. In a sense this is a compound value made up of the above variables I named. A lot of critics, designers and gamers point to this when talking about randomness, that randomness can be looked through this lens, consider randomness as calculating probabilities and while this criteria exists, it is merely one component of it, an important part for sure.

What has to be taken into consideration though is whether or not these statistical variables even can be evaluated and give an expected value. For example think about games with a character selection phase (like fighting games or MOBAs) with the "pick random" choice, in this case you really don't have any expected value of the outcome. It should be pretty evident that this is highly related with the previous criteria as a higher number of possible outcomes can both make statistics like averages more meaningful, but also a high number of outcomes can mean it's harder to determine what you're going to get which is especially more game-changing if the outcomes aren't necessarily valuable numerically. For example in a randomly-generated roguelite, if there are a lot of possible different rooms, then the player probably won't have a proper idea of what they're getting themselves into when they enter a new room.

But for the numerical valued example, let's say in Magic-style card game a card effect summons a random monster with a 3-mana cost, assuming the previously mentioned averages and statistics line up (the median, mode and average are all close) then you can expect to get a monster with a certain value (like 3HP/3ATK).

Influenceability

Hardenability describes how much a steel can be hardened through the hardening process

Inspired by "Hardenability" in materials engineering, this variable of randomness determines the type of randomness by how much it can be influenced. High influenceability means that it's possible for the player to influence and change the outcome of the random process by a lot. From a logical standpoint, not necessarily a substantive one, influenceability can be broken down into three states and two types: Intrinsic influenceability, extrinsic influenceability, and no influenceability.

Having no influenceability is pretty self-explanatory, it's when the player has no choice and no decision to make to change the outcome of a random effect. Most physical dice rolls are like this, and a lot of random effects in games employ this. Your dice rolls in Backgammon are this and so are the hands dealt in Poker.

Intrinsic and extrinsic now refer to the function that rolls out a random outcome, so having intrinsic influenceability means that in the game's design and rules, other factors than the random number generator are taken in as input, like the game state, or previous outcomes of the random process. Popular in gacha games, but also in MOBAs and common in most modern games, pseudo-RNG have intrinsic influenceability because they take into account the history of outcomes. While the intended purpose of this is usually to help smooth out occurrence rates to more resemble what the expected value is and stopping the player from going onto highly lucky or unlucky streaks, players can exploit this to their advantage. If it's possible for the player to decipher how this influenceability works, then players can utilize this even further and another dynamic of increasing your odds will be added to play.

Extrinsic influenceability meanwhile is when a random effect isn't coded to take into account anything other than the RNG's result, but due to the nature of the effect, it's possible for the player to manipulate the result, by changing the timing/target/game state or other factors. For example if in a strategy game there was an ability that had an effect that would destroy a single random enemy, it would be possible for the player to lower the number of enemies before using this ability to influence the outcome by making it apply to a smaller set of targets. The opponent on the other hand could reduce the risk of a bad outcome by putting into play cheaper and expendable targets. As one might think, a lot of random effects in games have extrinsic influenceability but a lot of times it may not be immediately apparent to the player.

Another important aspect to realize is that it's also possible for a random effect to be both intrinsically and extrinsically influenceable. This may or may not give players a higher degree of control depending on whether the intrinsic factors are related to the extrinsic ones.

A Short Case Study

Alright time for an example! For this purpose I've chosen Hearthstone which is full of random effects with a lot of variance in implementation. Let's try to keep this as simple to follow as possible for those who are unfamiliar with the game. We can examine two classic cards, Ragnaros the Firelord, and Burgle. Ragnaros hits a random enemy target at the end of your turn, while Burgle adds 2 random cards from your opponent's class to your hand.

First off, Ragnaros: Since the amount of damage being dealt is fixed, it may not feel like it has a high delta of randomness, but depending on the board state, there is a big difference between destroying a powerful legendary monster with 8 health or simply taking out a cheap minion. So its delta of randomness is board-dependent and can usually be high. Next its information delay is zero, it is an example of output randomness at its finest, the dice rolls and it hits someone. Its randomness complexity, is also board-dependent, and its number is equal to however many minions its opponent has plus one for the hero. Its expected value is fuzzy. Due to the board having a limited number of minions at each time, plus how different each minion can be in terms of value to its owner, there is no particular expected value besides maybe "reduce the number of enemies by 1", which isn't saying much most of the time. As for influenceability, unless the programmers have sneakily added something in, there is no intrinsic influenceability, but there is extrinsic influenceability because it's possible to destroy enemy minions before the effect triggers, letting the player clear targets so Ragnaros' chances of hitting a higher value target increases!

Next is Burgle: The delta of randomness itself is pretty large as you can get wildly differently valuable cards from it. You could get very useless cards or very strong cards right for your situation. It also seems to have neither intrinsic nor extrinsic influenceability as it's only dependent on your opponent's class which is fixed at the start of the game. It has a very high complexity as the number of possible combination of 2 cards from an entire class is very high which also results in a very fuzzy expected value where it's hard to determine what the playing player gets out of this. It does have the expected value of offering you more cards than you would have without this card in your deck though. And finally its information delay is relatively high (at least for hearthstone), as it acts a bit closer to input randomness than output randomness like Ragnaros did, as the player now has to play with the new cards granted by this later in their turn or match.

Conclusion

We can see how randomness has many sides for it to be tackled by. It's definitely possible for a random effect to be balanced even if apparently it isn't conforming to a single design ideal. It's possible to have high delta of randomness, but have that be balanced out by a meaningful expected value. It's possible for output randomness be balanced out by low delta of randomness or high influenceability. High complexity can be offset with a solid expected value, and so on. There are many ways out there to use randomness and make it work, it's important though to think through its many different aspects and see how they fit together as.

As game designers, we have a toolbox, and the better we understand our tools, the better informed design decisions we can make.