Interesting thread. I understand and trust that Rng is just rng.
But how? I mean randomness is not really randomness right? When I roll a dice, it’s theoretically possible to calculate what the outcome will be (posture of the hand, speed etc.)
How it’s possible that rng does exactly rng things? Is there something like an absolute randomness without any influences?
Sorry I am not a coder
There is a lot of nuance to this question, and it can be answered in a number of different ways. But I'm going to try to combine them all in a not perfectly kosher way that still gets the basic idea(s).
There's no such thing as "absolute randomness." At least, there is no definition for such a thing. What we call randomness is most of the time just the notion of unpredictability. We don't know what the crystal will drop next.
What matters for lootboxes, or any other application, is sufficient randomness. What does that mean? It means we take the notion of "unpredictability" as far as we need to, in order to ensure things work they way they should in the context we're working in. So let's talk about what we need from a MCOC champion crystal.
1. Over large numbers of drops, the percentage of each result approximates the statistically predicted value (i.e. the published drop odds).
2. Given any reasonable number of observed drops, there is no way to predict what the next drop will be with better than the published drop odds.
In other words, if we make a crystal with twenty four possible drops and we design the crystal so that each has the same chance of dropping, we want the act of randomly selecting one of those drops to occur roughly equally on average. There is a precise definition of randomness that is required, but colloquially, we just want every champ to drop about the same amount of time in the long run. If over large numbers of crystals we find that one champ drops twice as often as the others, that's completely broken (because it defies the design intent of the crystal). So we need our random number generator to actually generate every possible number equally likely.
Separately, we want our random number generator to have no obvious patterns in what it generates that we could ever observe. If there's a pattern to the numbers generated, then someone watching crystal openings could theoretically detect the pattern and then use it to predict drops. We don't want players to be able to know what they would get, and manipulate what they would get by simply opening crystals at the right time.
If players knew that every champ in the featured crystal dropped about equally often, and no one could create an advantage by manipulating crystals to get what they wanted by watching openings and then picking favorable times to open them I think most people would think the crystals were "random enough." And in fact, "random enough" is essentially the test for randomness for computer random number generators and all random number applications. For example, random number generators are certified as being "cryptographically secure" when they pass enough tests for randomness that those applications need.
It is unclear if there exists any such thing as "absolute randomness" anywhere in the universe. Even lava lamps and quantum noise is not "absolutely random" in theoretical terms. Randomness is really a very special kind of unpredictability, and unpredictability comes from an absence of information. For every process that is declared "random" there is always some absence of information that, if it existed, would make the "random" thing non-random.
Or to put it another way, randomness is a special mathematical kind of ignorance. We just need players to be ignorant of what the crystals will drop, and it is possible to test a computer random number generator to see if people would be ignorant of what it generated. That's good enough for our purposes.
Interesting thread. I understand and trust that Rng is just rng.
But how? I mean randomness is not really randomness right? When I roll a dice, it’s theoretically possible to calculate what the outcome will be (posture of the hand, speed etc.)
How it’s possible that rng does exactly rng things? Is there something like an absolute randomness without any influences?
Sorry I am not a coder
Well there are mathematical formulas for calculating some degree of chance for physical objects that are pretty accurate but for coding it is different since the computer is not interacting with reality physically. It’s more so an algorithm designed not to repeat, creating a form of pseudo random effect.
All pRNGs repeat eventually. That's a natural consequence of the fact that a certain starting state can only have so many different future states before the initial state is repeated. Once it does, because it is deterministic the generator will then have to do the same thing over again.
Every pRNG has something called a period, which specifies how long it takes for the sequence to eventually repeat. The classic Mersenne Twister, for example, has a period of (I believe) 2^19937-1. That's very roughly a one followed by 5981 zeroes. Kinda big.
The idea is to use generators that might theoretically repeat, but in actual usage will never be used enough to actually repeat. If the generator repeats in theory, but you will not live long enough to see one cycle, for all intents and purposes it doesn't repeat.
The idea that computers can't generate "truly random" numbers but the rest of the universe can is one of those ideas that I think is based on a fundamental misunderstanding of quantum mechanics. People informally think quantum mechanics is "truly random" so it is possible to construct a random number generator that generates perfectly random numbers, but because computers are deterministic computational devices they obviously can't. However, there's a thought experiment that calls this into question.
Imagine a random number generator constructed in the "real world" using some quantum process. It doesn't matter what it is or how it works, just that it is an actual thing that actually exists in the universe. Now imagine it starts producing a sequence of random numbers. This sequence of numbers never repeats, because if it repeated in a cycle they would not be random anymore. This means, in effect, that the generator is generating information - the random numbers that are being produced is a sequence of information. The more information that is generated by the generator, the more entropy the generator must have originally contained, because it is impossible for a finite amount of entropy to produce an infinite amount of information. The longer the generator runs, the more entropy it must have somehow contained to produce it. Eventually, if you run this generator long enough, the amount of entropy that it must have started off with exceeds the holographic limit for the size of the generator. In other words, the information density implicit in that much entropy means the generator has an event horizon.
This implies that any finite size generator, using any process to generate a sequence of numbers, must either generate a finite number of values and then repeat, or it must be a black hole and everything it does is unobservable.
Comments
There's no such thing as "absolute randomness." At least, there is no definition for such a thing. What we call randomness is most of the time just the notion of unpredictability. We don't know what the crystal will drop next.
What matters for lootboxes, or any other application, is sufficient randomness. What does that mean? It means we take the notion of "unpredictability" as far as we need to, in order to ensure things work they way they should in the context we're working in. So let's talk about what we need from a MCOC champion crystal.
1. Over large numbers of drops, the percentage of each result approximates the statistically predicted value (i.e. the published drop odds).
2. Given any reasonable number of observed drops, there is no way to predict what the next drop will be with better than the published drop odds.
In other words, if we make a crystal with twenty four possible drops and we design the crystal so that each has the same chance of dropping, we want the act of randomly selecting one of those drops to occur roughly equally on average. There is a precise definition of randomness that is required, but colloquially, we just want every champ to drop about the same amount of time in the long run. If over large numbers of crystals we find that one champ drops twice as often as the others, that's completely broken (because it defies the design intent of the crystal). So we need our random number generator to actually generate every possible number equally likely.
Separately, we want our random number generator to have no obvious patterns in what it generates that we could ever observe. If there's a pattern to the numbers generated, then someone watching crystal openings could theoretically detect the pattern and then use it to predict drops. We don't want players to be able to know what they would get, and manipulate what they would get by simply opening crystals at the right time.
If players knew that every champ in the featured crystal dropped about equally often, and no one could create an advantage by manipulating crystals to get what they wanted by watching openings and then picking favorable times to open them I think most people would think the crystals were "random enough." And in fact, "random enough" is essentially the test for randomness for computer random number generators and all random number applications. For example, random number generators are certified as being "cryptographically secure" when they pass enough tests for randomness that those applications need.
It is unclear if there exists any such thing as "absolute randomness" anywhere in the universe. Even lava lamps and quantum noise is not "absolutely random" in theoretical terms. Randomness is really a very special kind of unpredictability, and unpredictability comes from an absence of information. For every process that is declared "random" there is always some absence of information that, if it existed, would make the "random" thing non-random.
Or to put it another way, randomness is a special mathematical kind of ignorance. We just need players to be ignorant of what the crystals will drop, and it is possible to test a computer random number generator to see if people would be ignorant of what it generated. That's good enough for our purposes.
Every pRNG has something called a period, which specifies how long it takes for the sequence to eventually repeat. The classic Mersenne Twister, for example, has a period of (I believe) 2^19937-1. That's very roughly a one followed by 5981 zeroes. Kinda big.
The idea is to use generators that might theoretically repeat, but in actual usage will never be used enough to actually repeat. If the generator repeats in theory, but you will not live long enough to see one cycle, for all intents and purposes it doesn't repeat.
The idea that computers can't generate "truly random" numbers but the rest of the universe can is one of those ideas that I think is based on a fundamental misunderstanding of quantum mechanics. People informally think quantum mechanics is "truly random" so it is possible to construct a random number generator that generates perfectly random numbers, but because computers are deterministic computational devices they obviously can't. However, there's a thought experiment that calls this into question.
Imagine a random number generator constructed in the "real world" using some quantum process. It doesn't matter what it is or how it works, just that it is an actual thing that actually exists in the universe. Now imagine it starts producing a sequence of random numbers. This sequence of numbers never repeats, because if it repeated in a cycle they would not be random anymore. This means, in effect, that the generator is generating information - the random numbers that are being produced is a sequence of information. The more information that is generated by the generator, the more entropy the generator must have originally contained, because it is impossible for a finite amount of entropy to produce an infinite amount of information. The longer the generator runs, the more entropy it must have somehow contained to produce it. Eventually, if you run this generator long enough, the amount of entropy that it must have started off with exceeds the holographic limit for the size of the generator. In other words, the information density implicit in that much entropy means the generator has an event horizon.
This implies that any finite size generator, using any process to generate a sequence of numbers, must either generate a finite number of values and then repeat, or it must be a black hole and everything it does is unobservable.