I don’t feel like actually tagging Salty because I’m not exactly looking to drag her into this, but what she said is exactly what Akots’ math proved. Her conclusion is wrong and if the devs believe the RNG has a tendency to streak in the short term they should fix it because it is unfair to individual players and implies that not all players are equal.
Asterisk: an RNG is a volatile thing, and in general small trials are not a good way to measure it. I will address this further below. The problem here is applying “common sense” instead of “the kind of mathematics you spend more than four years working with to get a degree”.
The concept of “an RNG can look streaky in the short-term” is incorrect in the wide sense of how we expect an RNG to work. We expect that if 5,000 players flip a coin 10 times:
- Half of the players will get 5/5.
- 25% of the players will get 6/4.
- 12.5% of the players will get 7/3.
- The other 12.5% will get either 8/2, 9/1, and 10/0.
What a player has proved, via statistical analysis that has been accepted by people with math doctorates for at least a century, is that the GoW RNG displays a bias in the short term that works out in the long term. The test used in this particular case was specifically designed by math academics to figure out from small trials if a sequence displays abnormal out-of-expectation streaks while still displaying the expected curve in large trials.
This can be an undesirable quality in an RNG if you expect it will be frequently used for short streaks, like “a player opening 10 chests”. Imagine if 5,000 players flip a coin 10 times but:
- 30% of players get 5/5.
- 30% of players get 6/4.
- 21% of players get 7/3.
- 10% of players get 10/0.
- The remaining 9% of players will get either 8/2 or 9/1.
- If you add up all of the results, you’ll find them very close to 25,000/25,000.
- (These numbers are imaginary and meant to indicate what “streaky short-term but OK long-term” might look like. Akots proved the GoW RNG does this in a post I linked above, and Salty admitted it. [Though I think Salty meant to “confirm a common sense opinion” which is incorrect, not “confirm a developer design goal”.])
This is a curve that streaks in the short-term, but works out in the long term, and it is unfair. In the original setup, exactly 50% of players get “lucky” or “unlucky”. In this setup, 70% of players are “lucky” or “unlucky”, with no guarantees about which side the RNG is tilting towards. It turns out, in this case, if you got the expected probability of 50%, you’re not lucky because you theoretically had a higher chance of better than 50%. But if the numbers shake out just right, if you look at “all pulls from all players” like the devs do, the RNG looks fine. 50,000 coins were tossed, and 25k were winners. Who cares if 70% of the players won, right?
That’s why the assertion above is very wrong. “It works out over 100,000 pulls” does not reflect that the 100,000 pulls are technically thousands of players’ individual trials. I don’t get to take some of Mithran’s lucky pulls to “make up” for my bad pulls: if I get 2 wins and 8 losses then I lose and that is permanent. So accepting “over the short-term it has a tendency to streak” means you are admitting that “it is designed to be unfair in the most common use case”.
So in a way, Salty just pointed out if you are getting the published probability in your pulls, you are unlucky because technically you should expect to be most likely to get something 2 steps away from the published rate, be it lucky or unlucky. The only way this could balance out for players is if we were able to open “as many keys as we want”.
But they’ve always fought hard to keep us from opening keys except in short batches. And you can only open chaos portals in short batches of 10. You can only open chaos orbs in short batches of roughly 1-4. But it’s OK, because the RNG is only unfair in short batches. Funny how that lines up, right? Weird how “it’s only rigged in short trials” and short trials are the only thing we can do.
This is why a lot of people hate math. Common sense does not apply. There are different rules, and it can take years to unlearn common sense so you can truly understand how probability works.