No, the dice rolls are not broken Human intuition on randomness is flawed, and here is an attempt to explain why Roll20 has a page to show how random the rolls are.
The thing about randomness that people don't often get, is that streaks" of "good or "bad" luck is to be expected. Truly random
doesn't feel random. But there is something bugged about the way the rolls are distributed over a short period, like 200 rolls That is unlikely, but expected to happen to someone, at times, given the large number of rolls made on Roll20. You know how there exist people who have got hit by lightning more than once, or have won the lottery more than once? It's unlikely to happen to any given person, but the chance of it happening to someone , given large enough pool of samples, is extremely large. The chance of something happening even at small scale is something we don't have an accurate intuition about, for example the Birthday paradox , which is the statistical oddity that with a random group of 23 people, it's a 50% chance at last two people share a birthday. Math & Science behind randomness Gambler's Fallacy - wikipedia Law of Truly Large Numbers - wikipedia - "With a large enough number of samples, any outrageous (i.e. unlikely in any single sample) thing is likely to be observed." Independence of Events Probability, Random Events, and the Mathematics of Gambling - 20 pages Then there is also the fact that when the results are given instantly, it feels less random than if we see numbers flutter a bit before they appear. Slot machines and gambling games likely uses this trick of slowly showing the result to feel more random and increase the anticipation for the result Psychology behind randomness (and why we're bad at perceiving it) Randomness is Random Numberphile video on how humans think randomness looks like Reddit thread discussing Apple making their playlist shuffle less random so it would feel more random Why random hero selection doesn't feel random - LoL wikia rambling Humans have hard time with randomness - Daily Mail article The Near Miss Effect - Wired - why seeing near misses feels better(and why physical dice might feel more random) If you watch the "Randomness is Random" video, it demonstrate quite well how we think streaks of "good" or "bad" luck are longer and more prevalent than if we'd try to make a random sequence of numbers ourselves. That's why some random shuffle features on music playlists aren't always completely random, as they might prevent longer streaks of songs from appearing in their original order, or bias the system to try not to have too many songs from the same artist/album to play back to back. Previous Forum Threads on the topic This come up every now and then, and is repeatedly explained every single time. Here is a fairly long comprehensive list of previous discussions on the topic: Random Rolling numbers maybe not so random? Roll20 Dice are not True random (Pro forums) How random is quantum roll random number generator Dice results broken? Spring Update: Meh (users comments how pseudorandom where good enough even before Quantum Roll, and think it's overkill) Multi-dice rolls averaging out? Three Critical Failures In A Row! Dice Rolls - Come in Three's fix die roller Questions about Quantum Roll "Quantum" rolls aren't. Dice roll randomizer (6 years ago, from before Quantum Roll feature, but explain why normally created randomness is already pretty good) Random dice roller (6 years ago, same as above) TL;DR: Humans have a bad intuition on what is or isn't random, and this have been debunked every time it's been discussed here.