On RNG – Lies, Deceptions and Misinterpretations

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:

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  1. Which one was definitely generated by a RNG generator and which one was deterministic?
  2. 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:

  1. We don’t know for sure.
  2. 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:

  1. Cut into a canvas of X times Y number of boxes.
  2. Each box has a chance to contain either a dot or no dot.
  3. 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.

Capture

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:

  1. Any pattern can be generated by a true RNG generator.
  2. It does NOT show that every pattern is generated by a true RNG generator.
  3. It does NOT show that there are no RNG generators that are inherently shit.

 

Now consider two sequences:

  1. 0101010101010101010101010101010101010101010101010101010101010101
  2. 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:

Capture

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:

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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.
    • [False]
  • 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.
    • [True]

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:

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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?

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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:

  1. If an occurrence is more common, randomness becomes lesser of a factor.
  2. 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.

Capture.JPG

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.

Capture

 

So the final TL;DR:

  1. A true RNG generator has an equal likelihood of producing both images.
  2. RNG generators can be tested for randomness using many methods including statistics, transformations, string complexities, etc.
  3. The left image is more likely to be generated by a true RNG generator than a deterministic or partial RNG one.
  4. The right image is more likely to be generated by a partial RNG generator than a true RNG one.
  5. None of the above actually matters. In other words, the reddit thread posting that image was a red herring.
  6. What does matter is the frequency of RNG dice rolls and the frequency of success in each dice roll.
  7. 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.
  8. 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?

 

Market Bonus vs Valk’s Cry

If there is one thing we are absolutely sure about in the current Value Pack mayhem is that PM_Jouska directly stated that Valk’s Cry would not be added to our version due to the advantage it gives players.

For those who are confused, Valk’s Cry is a cash shop item that can be used up to 10 times to grant 10 bonus failstacks. It is a P2W mechanic that is not currently available in NA/EU.

Here is a link to the thread: http://forum.blackdesertonline.com/index.php?/topic/100020-clarification-valks-cry/

Capture

Because this is an official stance by Daum, we can safely conclude that it is objective in the context of BDO and without a doubt that anything providing more advantage than Valk’s Cry would also have no place in our build.

Valk’s Cry does not allow you to buy cash shop exclusive BiS gear. Valk’s Cry does not allow you to bypass RNG. Valk’s Cry does not allow you to catch up to a no-life player if you hardly play the game. What am I getting at? The simple fact that none of those are prerequisites to being P2W despite what some people might think. Daum themselves confirmed this.

In more simple terms if you still have trouble understanding, anything equal to or granting more enhancement advantage than Valk’s Cry is automatically classified as Pay To Win. It doesn’t matter what you think is P2W and what you think is not. Daum makes the calls on what’s P2W, not you. Simple logic dictates that the underlined statement is objectively true in context of BDO as it follows from a Daum official statement.

Now that we have an objective and irrefutable definition of P2W, we can proceed to doing the maths and determining how P2W 30% market bonus really is.

Here are the expected tries for +16->+20 gear and TRI->PEN jewelry using the methodology outlined in this post.

Untitled.jpg

Some basic inferences about how Valk’s Cry would be used:

  1. You would not use Valk’s Cry at say 0 stacks, because that’s a waste of money. You would probably not want to upgrade anything expensive with less than 25 stacks anyway. Valk’s Cry is reserved for at the bare minimum 25 stacks even if you’re very credit card happy.
  2. You are of course free to use Valk’s Cry for items you would enhance with less than 25 stacks, but that would give you negligible benefit. Go ahead and waste Valk’s Cry to enhance base Bares necklace if that’s your cup of tea.
  3. The effect of Valk’s Cry proportionally is highest at lower stacks. This is because of the diminishing returns on failstacks.

Below is a graph taking the expected tries at each failstack value and dividing by the expected tries with 10 bonus stack. Using that we can measure the proportional increase of Valk’s Cry. We will start the graph at 25 stacks because any equipment you should be enhancing at under 25 stacks cost too little to truly matter; you will not save much money wasting Valk’s Cry on them.

Capture

As you can see, the effect of Valk’s Cry is less than 10% for realistic upgrades. This means Valk’s Cry will save you up to 10% of your resources if you P2W every single gear enhancement.

We will now examine market bonus. Value pack as of right now gives 30% bonus to market income, which means you will make 30% more profit from selling items in the market.

  1. We know that the silver you spend on gear is directly proportional to how good your gear is, with some fluctuation due to RNG.
  2. RNG does not change the fact that more silver means better gear, because having double the silver means you get double the tries on enhancement. This will improve your overall RNG and give you a higher likelihood of successful enhancements.
  3. There is no longer an excuse to claim silver is useless now that secret shop is in the game. The existence of secret shop directly means that you can progress to max gear with just pure silver and nothing else by sitting there rolling all day long.
  4. The “it’s all RNG” argument is irrational, because Valk’s Cry is also RNG yet it is objectively considered P2W. Therefore RNG does not exclude bonuses from being considered P2W.

Therefore we can use silver income as a model for gear enhancement. If the value pack 30% market bonus proves to be more than 10% total silver income then value packs are objectively more P2W than Valk’s Cry.

There are two main ways to make silver in BDO:

  1. Grinding.
  2. Crafting.

For a grinder, approximately 40% of your income is in sellable items, the other 60% is in junk items;the latter is unaffected by market tax. This means 30% market bonus is worth 12% increase in total income if you only grind.

[Edit] Reddit user BadsLiteYear brought up the fact that group grinding will bypass market, which is true. However it is also true that group grinding is very inefficient for money because loot is split 5 ways without increasing killing speed by 5 times. For reasonably geared players, you will make more money solo than group even accounting for the tax. How you choose to interpret this fact is up to you.

For a crafter, approximately 100% of your income is in sellable items. This means 30% market bonus is worth AT LEAST 30% increase in total income if you only craft.

To elaborate on crafting, your income is calculated by the equation:

NetIncome = MarketSale – MaterialCost

With value pack, your income is calculated by the equation:

NetIncome = MarketSale * 1.3 – MaterialCost

Crafting is not worth it unless your material cost is lower than the market sale. When material cost is zero, you will make 30% extra profit with value pack. When material cost is equal to market sale price after tax, you will make infinite % extra profit with value pack.

Most players are a combination of both, hence the value of 30% market bonus fluctuates between 12% to infinite % depending on your activity distribution. Even quoting the lowest number in that range, value packs surpass Valk’s Cry in giving an advantage.

 

We can now seal this debate with a single logical syllogism.

Premise 1: Valk’s Cry is considered objectively P2W by Daum because of the advantage to enhancement. Anything with higher advantage to enhancement must also be P2W.

Premise 2: Value pack 30% market bonus has a higher advantage to enhancement than Valk’s Cry due to disproportionately high increase in silver acquisition.

Conclusion: Value packs are objectively P2W and allowing its existence contradicts Daum’s own philosophy on the subject.

There are no valid objections to this reasoning because both premises are objective, and the conclusion logically follows from the two. Premise 1 is directly taken from Daum’s official stance, and Premise 2 is a mathematical truth.

You may now hold one of three viable opinions:

  1. P2W is not OK, so value packs are not OK.
  2. I want to P2W, so value packs are good.
  3. I don’t care about P2W, so I don’t care about value packs.

 

Even the official promotion artist subconsciously knew this.

20160720_en

Invest what? Hmm…

Success… you mean winning?

What a Freudian slip.

:^)