Warning: This blog post is extremely heavy on the mathematical side and does not have much direct relevance to BDO gameplay. There were feedback that asked for more maths-orientated posts, so this is an experiment on how much demand there is on this type of content. Read this if you want to understand RNG. Do not read this if you don’t care about maths.
- RNG is by far the most misunderstood popular concept in the history of everything.
- RNG is frustrating, it makes people want to ragequit.
- RNG is without skill, and your outcome rests solely on a dice roll.
- RNG is psychologically rewarding through Operant conditioning, no matter how much you want to deny it.
- RNG is part of almost everything in BDO.
- But luckily, RNG does not actually change your fate in BDO.
I’ve wanted to write an article on RNG since I started this blog, however I never found a good way to discuss this topic in a relevant, succinct and straightforward manner. RNG is a complex issue that had been constantly misunderstood by people since the beginning of time. In fact, interpreting RNG is so hard that even scientists cannot easily explain the foundation statistical concept known as the p-value.
Today after seeing a reddit thread, I was inspired to make this blog post. Of course I was inspired because of how misleading that thread was, otherwise I’d just copy it here with credits. Nevertheless, it showed me the exact angle in which this topic should be best explained.
Look at these two pictures:
- Which one was definitely generated by a RNG generator and which one was deterministic?
- If I gave you magical sand and asked you to spread it randomly and continuously gather and spread it again, which pattern would I more likely make?
Before we start, let’s assume both pictures have the exact same number of dots.
And here are the answers:
- We don’t know for sure.
- Both are equally likely.
The first answer should be easy to comprehend. An RNG mechanism of spreading dots on a sheet can produce literally any pattern. In fact, the dots can simply create a smiley face shape or all be confined to the top left quadrant of the canvas, albeit both extremely improbable.
The answer to the second question? The picture is just as likely to spread itself into a smiley face as it is to copy the left picture exactly.
Too deep down the rabbit hole? Don’t worry, this article ends with a very simple conclusion that everyone should take home.
This can be difficult to comprehend, so let us explain this by first cutting the canvas into discrete blocks. A canvas of X pixels height and Y pixels width can be:
- Cut into a canvas of X times Y number of boxes.
- Each box has a chance to contain either a dot or no dot.
- There are n dots in the canvas.
Therefore, the number of combinations the dots can take is finite. Because this concept applies to any number of dots, I’ll simplify it by demonstrating what I’m talking about in a 3 by 3 tic-tac-toe tiny canvas with n = 3 dots.
Mathematically, we know that 3 dots on a 3×3 canvas has a total of 9 Combination 3 solutions, thus 84 possible arrangements.
Here are examples of three arrangements.
Which one is truly RNG? Which one is more likely to appear?
The answer is that all 3 can be generated by an RNG generator, and that all 3 have an equal probability to appear.
The probability to appear for each combination of black and white boxes can be calculated by the equation:
p(black total) * p(black total -1) * p(black total -2)
Which in mathematical form is:
3/9 * 2/8 * 1/7 = 1/84
Each combination has a 1/84 chance to be produced. There are 84 combinations.
To conclude partially, the above explanation shows that:
- Any pattern can be generated by a true RNG generator.
- It does NOT show that every pattern is generated by a true RNG generator.
- It does NOT show that there are no RNG generators that are inherently shit.
Now consider two sequences:
- 0101010101010101010101010101010101010101010101010101010101010101
- 1101000101011011100010101010110000011000001011110101000001000001
Which one is more likely to be generated by a true RNG generator? Still the same. But let’s ask a different question, which is more likely to be generated by a fake RNG generator?
The first sequence can be eyeballed and a pattern is already apparent. It is 01 repeated 32 times. The second sequence wasn’t generated with a pattern; I generated it with random.org.
Knowing the probability of both is not important if you want to know whether the pattern is surely random, but it is important if you want to know the odds of the RNG generator behind the sequence being a good RNG generator (i.e. closer to random).
We can now map the odds into a grid:
This is not an advanced mathematics class so I won’t go into the several methods one can use to calculate the bottom right box, all you need to know is that it’s pretty much as low as the probability of it being truly random.
In other words, the odds of:
- The first sequence is 18,400,000,000,000,000,000 to 1 in favor of fake RNG.
- The second sequence is about 1 to 1 in favor of nothing.
We can therefore make a probabilistic claim that the first sequence is not actually RNG. We cannot make that claim for the second sequence.
Let’s go back to this picture:
The same method can be applied to these pictures but because this is not an advanced maths class I will not do it step by step. The conclusion using a similar randomness approach to the above is that:
- The left side image is probably generated by RNG.
- The right side image is probably generated by a mixed RNG algorithm. It is rigged by a formula which decreases the probability of a dot being close to another preexisting dot.
- MOBAs such as DotA and LoL use something similar to the image on the right side to reduce the snowball effect of RNG streaks.
The correct conclusions to draw from the reddit thread is:
- The left side image in its exact form is more probable than the right side image to appear in a true RNG system.
- The left side image is RNG, the right side isn’t.
- [Impossible to determine with certainty]
- The left side image is more likely than the right side image to be generated with a true RNG generator compared to a partial/fake one.
The most beautiful part of all of this? None of this is relevant to BDO at all. Suppose a square X unit tall and width represents 1 hour of grinding loot, now consider these two images:
If I place the same red box on the image randomly (simulating 1 hour of grinding), which side is more likely to give me a higher number of drops?
If I place the same red box on the image randomly (simulating 1 hour of grinding), which side is more likely to give me a higher number of drops?
The answer to both is it makes no difference as long as the algorithms do not use the red box as a variable. In other words, as long as BDO RNG isn’t controlled by a temperamental gnome that hates you, it honestly makes zero difference which formula it is in the long run. However, the smaller red box is likely to give larger fluctuations in the number of loot you get. This applies no matter whether you look at the left side or right side.
In fact, we can magnify both images to simulate events with low probability of occurrence, such as obtaining an Ogre Ring…. If you’re smart you’d realize that it has the same effect as making the red box smaller.
In other words:
- If an occurrence is more common, randomness becomes lesser of a factor.
- If the RNG dice is rolled more times, randomness becomes lesser of a factor.
To summarize, I will show you two graphs.
This is the cumulative probability graph of an event tested to be 10% success chance in game over 1000 tries using a real RNG generator.
This is the cumulative probability graph of an event tested to be 10% success chance in game over 1000 tries using a broken RNG generator that has double the chance of rolling 9.
So the final TL;DR:
- A true RNG generator has an equal likelihood of producing both images.
- RNG generators can be tested for randomness using many methods including statistics, transformations, string complexities, etc.
- The left image is more likely to be generated by a true RNG generator than a deterministic or partial RNG one.
- The right image is more likely to be generated by a partial RNG generator than a true RNG one.
- None of the above actually matters. In other words, the reddit thread posting that image was a red herring.
- What does matter is the frequency of RNG dice rolls and the frequency of success in each dice roll.
- Although I have to admit if BDO uses an algorithm like the one on the right, it will smooth the progression curve at least in the early stages.
- Point 7 shows why it can actually be beneficial to have rigged RNG systems, as long as you’re not the variable being rigged against. And you aren’t, so tinfoil hats off please.
The entire point of this long blog post? The effect of RNG gets lower the longer you play. Simple right?
Min-Max your Black Desert Experience 