Here’s a fun little trivia fact that you probably already know: Computers can’t really *do* randomness. A random number is usually generated by pulling outside data that appear to have an unpredictable pattern, shoving them through equations, and then outputting something that has the *appearance* of randomness. It’s not actually truly random, though; technically, the same seed for randomness would produce the same result. You can even use this in various ways (authentication dongles and apps work off of that basic principle).

Despite that fact, randomness or the appearance of randomness is baked into lots of MMOs, since it was baked into lots of single-player games and so on back down the line. And this ties into a lot of other issues within games, the sort of things that weird nerds who enjoy thinking about this stuff (including me) tend to enjoy talking about. So today, let’s share some random thoughts on… random things.

### Single-roll vs. multi-roll systems

Here’s a fun question with two different answers. Say that you have a 100% chance to hit a target, a 20% chance for a critical hit, and a 20% chance for a solid hit, and the target itself has a 10% chance to evade. What is your actual chance to land a normal hit? The answer depends on how the game handles those odds.

*World of Warcraft* classically used a single-roll system for this. *Final Fantasy XIV* uses a multi-roll system. And it’s interesting to understand how the two interact because different systems produce different results.

In a single-roll system, you have only one random roll determining what happens when your ability is used. This means that you have a priority system for how likely certain outcomes are to happen. Tanks relied upon this back in the day to ensure that a boss couldn’t critically hit or land a crushing blow; by stacking up defensive values high enough, they could ensure that both of those impacts were pushed off the potential hit chart.

In this scenario, your chance of landing a normal hit would be 50%. Your base chance to hit is modified by a 20% chance to crit, a 20% chance for a solid hit, and a 10% evade. 90% of the time you’ll land a hit, but 40% of the time it won’t just be a normal hit.

By contrast, a multi-roll system rolls each chance separately, meaning that you have a different roll to determine if you hit at all, then if you score a critical hit, and so on. Using a multi-roll system, you have a 57.6% of landing a normal hit when all is said and done (since you have a 90% chance to hit at all, an 80% chance to not get a critical hit, and an 80% chance to not get a solid hit).

So which system is superior? Well… the real answer is “they’re both superior for different things and different goals.” A single-roll system is useful when there’s going to be one result as opposed to multiple particular results; for example, a piece of gear dropped from a boss can be only one of a specific number of things, but it’ll only ever be *one* thing for a given drop. On the other hand, multi-roll systems are good for other pieces of loot, like determining whether said boss also happens to drop a mount that might not show up every time.

In combat terms, the single-roll system has the advantage of being a little more immediately straightforward to understand. If your crit chance is 20%, you know that means you will crit one out of every five hits without any additional elements. However, the multi-roll system has the advantage of being able to layer effects; in the above scenario, you’ll have around a 4% chance to get a critical hit and a solid hit at the same time, presumably for even more damage. It also means not having to deal with chances being modified by circumstances in the same way (“yes, technically you have a 30% chance to crit, but this character’s defense pushes that down to 15%”).

### Loot and drop rates

So hey, let’s go ahead and segue to talking about loot. How do drop rates work? The answer is not “a 10% drop rate means you’ll get it in 10 runs.” In fact, the answer is really “it varies,” but it’s useful to drop this down here in the “later reference material” column.

Generally, things dropped by random creatures in the world follow a multi-roll system. The specifics vary by game, but conceptually it’s pretty easy to understand. This enemy drops between 0-3 items; only the third slot can be a worldwide valuable drop. Or the enemy has a chance to drop three items, each separate from one another. Or it rolls for one drop, then what the drop is, then to see if there’s another… it’s not really all that complex.

However, we tend to *make* it complex because it’s easy to kill two dozen wolves and have *none* of them drop fangs, and *what’s wrong here?!* And the answer, in short, is that we don’t really understand the way that statistics for things like drop rates actually *work*.

Let’s say that those fangs have a 10% drop rate. That means 90% of the time, you get no fang. So what are your odds of killing two dozen wolves and still getting no fang? Right around 8%. That’s *unlikely*, but it’s still *entirely* plausible. Because of the way that percentages multiply, even if you killed twice that number, you’d still have a 0.6% chance of getting no fangs. There’s never a point when you *absolutely* must get a fang.

For most people, drama doesn’t start around lack of random fangs, though. It starts in games like *WoW* or *FFXIV* or *Star Wars: The Old Republic* when you’re looking for that one piece of gear the game will not drop. And *that* is a different situation.

In most of these games, boss drops are single-roll systems. Kill a raid boss in *WoW* and it will drop a fixed amount of loot based on party size. That loot *can* be differentiated by slot – e.g., this boss always drops a piece of gear *and* a shoulder or glove tier token – but it can just as easy be two drops from the same master table.

The odds of a given piece dropping on a table are thus easy to figure out; if there are twelve items available, any given piece has a 1/12 chance of dropping. But we have a bad habit of thinking in terms of “well, that means that after 12 runs, I should see everything.”

But scaling percentages work there as well, because each roll is independent of the subsequent roll. After 12 runs, you you think that your number of *chances* has been multiplied by 12, but your number of *possible outcomes* has been multiplied by 12 as well. To be very mathy, your chances are not now 12/12, they’re 12/144. Or, you know… 1/12.

Some games will use a form of protection here, insofar as the percent chance of you getting *something* goes up over time, and that’s a more elaborate discussion. But just looking at math it should be clear that so long as you’re still talking about multiplying random percentages, there’s no such thing as a certainty. In order for your odds of not seeing that one drop you want for a 1/12 chance to reach below 1%, you’d need to get a shot at that item *53 times*.

And the conclusion? I don’t have one this week. It’s just random thoughts on random chance, you know?

For games, a stronger example might be procedural generation. It’s why whenever you input the same seed in a game like Minecraft or Oxygen Not Included you get the exact same “random” world.

Meaning every attempt where you don’t get the random item you wanted is an utter and complete waste of time, at least from the point of view of getting that item.

This is why, when I’m trying to decide what piece of content to play, I completely disregard random rewards; I treat the content as if anything that can be obtained randomly from it didn’t even exist, and allow myself to be pleasantly surprised when something nice drop.

The caveat is that this means I will never farm content if whichever reward I want out of it is a random drop, with the added consequence that if not farming for random drops locks me out of progressing then I will leave the game altogether; if a game wants me to keep playing for the long run, it needs to provide me with a path to progression that doesn’t depend, at all, on random rewards.

Sadly, your first fun little trivia statement is already wrong. Of course there are ways to create true randomness with computers. Hardware Security Modules for example often have true random generators. They create their randomness from using quantum mechanics, like amplifying the white noise from an open transistor amplifier and doing an A/D conversion of that signal. It does not get more random than that.

This TRNG output (T stands for true) is then used as a seed for a PRNG (a Pseudo RNG) which creates the mass random data.

If you do this – and it is not complicated to do – you have a stream of true random generated bits.

Caveat: the amount of TRNG results you can get in a given time interval before they start to get strangely correlated is finite. Which is why TRNG results are often used as inputs for not-really-random PRNGs rather than being used directly.

What it boils down to is that if you do this plus take into consideration the fact that in a RPG game server there are so many places where randomness is required and in a multiplayer game server you cannot predict the order in which the randomness is required, it is really random and there is no real means of prediction anymore. Believing that an account is bound to bad rng is nonsense (assuming no major implementation faults) and every “I always have bad luck” is just a case of pareidolia.

Yep, the very actions of the players in a massively multiplayer environment serve as a source of entropy, even in the absence of a TRNG module.

Being annoyed by bad luck, though, doesn’t require bad luck to actually exist (or, in other words, for the RNG to actually be biased). One instance of a particularly long string of bad rolls can be enough to make the game so frustrating it’s not worth playing anymore, and the existence of those can be reliably predicted when you actually have unbiased pseudo-random results or even true randomness.

This is why I very much prefer when my progression doesn’t rely on any kind of randomness, and in particular the randomness of loot drops. When it comes to rewards, I always assume I will get the worst possible random result, so as to be pleased when I get something better. The downside is that, since I’m assuming I will get the worst possible result, I won’t do the content at all if the worst possible result isn’t worth the effort.

That’s a common mistake in probability theory. But it’s actually less grim than that. Each time, you have a 1/12 chance to see the loot, so in order to go 12 times without seeing it, you need a 11/12 probability event to occur 12 times in a row. The probability of that is (11/12)^12, or about 35%. So the probability of seeing the loot at least once in 12 runs is about 65%.

The trick comes in because large populations in games mean lots of people will experience long-tail probability outcomes. For our 1/12 drop rate, 7% of players won’t see the loot in 30 runs. About 1% won’t see it in 50 runs. And about 2 out of every 10,000 won’t see it in 100 runs. That last seems like a small number, but it does mean that dozens of current FFXIV players (for example) would functionally never see the loot item.

And that’s for a 1/12 probability. Stuff with 1% drop rates has way longer tails. When it comes to randomness in games, variance is the soul killer.

Oh the number of times I almost quit WoW during Burning Crusade after I killed like 900 of the stupid bears in the Dranei starting area without a single effing one-of-eight tooth drop.

This is why Blizzard changed how those quest drops work. Now the more times you kill the correct mob without getting the quest item, the higher the chance of it dropping, up to the point where a drop is guaranteed.

Yes, and thank goodness they did that. Let’s talk about more reasons I don’t care about vanilla heh.

I like the way that the Warframe Wiki always shows drop rate followed by the Expected number of runs to get the thing (which is the result from calculating the Expected Value of the probability function, i.e. like getting the 10% drop after ten runs), followed again by the “Nearly Guaranteed” number of runs to get the thing, for which they use a range of values with 99% confidence as the bottom range and 99.99% as the top range.

The majority of players will end up closer to the “Expected” number, of course, because of how probability distributions work, but I feel like the “Nearly Guaranteed” number gives a good picture of how grindy something is, even clearer than raw percentages do.

The chances of killing a boss over and over and over (and over…) without ever getting the drop you want is why I favour token systems as a backup for loot rolls. If you don’t get the drop you want after 20 runs, at least you can then buy it from a vendor.

And when drops rely on the simulated randomness of equations, if that drop is also available in the cash shop then companies have an incentive to tweak those equations if they think they’ll be able to get away with it. While big name games and companies (I hope) know the consequences would outweigh the gains, I wouldn’t be at all surprised if a lot of mobile games etc. aren’t as random as they look.

Randomness on computers is not really random?

That’s another mark against loot surprise macaroni boxes. It’s not random, everything is rigged. And the house always wins.

It’s always a good practice to take Eliot’s CS claims with an unhealthy amount of salt grains.

CPU’s have had circuitry to generate real entropy (randomness) for several years (decades?) now but they can only create so much at a time so it’s better to use a different algorithm that simulates randomness. While not cryptographically secure they’re “good enough” for things like games.

So in this case his assertion is right but virtually meaningless.

I’ve often thought of randomness in games as being a way for games to simulate real life.

Real life, of course, is not random at all, its all completely governed by rules (i.e. physics). Things only seem random because we lack an understanding of the rules and of all the inputs.

Games, certainly for the forseeable future, will not be able to be as complex as real life. The rules that govern a game will always be a lot simpler than real life and that simplicity can be off-putting.

But, introduce randomness and it starts to feel more realistic. Take swinging a sword at an opponent. In real life, there is nothing random – the attacker chooses the swing, chooses their power input, chooses any course corrections, adjust their balance, move their feet etc. The defender, likewise, chooses how to react and with what speed and power. There are hundreds of small inputs into the equation, the outcome being whether the attacker hits or not.

Those hundreds of inputs in real life cannot be done within a game – our input devices just aren’t capable! But, add randomness and it starts to feel more realistic. A game may not be able to adjust swing speed, power, defender movements etc, but at a 10% chance to miss and the outcomes start to match real life.