"If a statistician hands you a die insisting that 'any given roll has the same odds of rolling a one or a twenty', it means he's handing you a depleted die in the hopes of taking advantage of you. Don't fall for it!""We guarantee that each number is random individually, but we donít guarantee that more than one of them is random." A statistician can tell you that properly generated random numbers will follow a discrete uniform distribution, giving you a roughly equal chance of rolling very good or very bad numbers. They may wax eloquent about how pseudo-random numbers are generated in computers, and how dice are wonderful randomizers. A good statistician will even disabuse you of the notion that a six sided die has a 1/6 chance to land on any one side; most dice are not built to that kind of precision. (Casino craps table dice are. They're also more expensive.) But it's going to be close to even distribution, even with a cheap die. A gamer, either of the tabletop or video variety, will tell you that this is all a load of dingoes' kidneys. The characters that gamers play live and die on good or bad rolls, and even if your dice are perfectly square and uniform, even if your game uses cryptographically strong random numbers, these numbers do not follow "distributions" or "probabilities." Instead, they usually produce whatever number you really didn't want. A tabletop gamer may say that "the dice are trying to kill" him if he encounters a long set of bad rolls (e.g. broke every weapon he was carrying). Unless, of course, you know the proper way to placate the Random Number God: then the dice will smile upon you. Usually. The name of this trope comes from Angband's and NetHack's fanbases (coined in the Angband fanbase, spread by Nethack's), as a fanciful expansion of "RNG", for "Random Number Generator"; both games are partially Luck Based Missions, considering how many Instant Deaths there are, and the players of both games have been known to build altars to the "Random Number God" or curse his/her/its name. Or both. Some games try to cut out the nonsense by supplying their own Luck Manipulation Mechanic. This never works — the Random Number God is not mocked, and it'll find a way to mess with you regardless. In Real Life or certain other situations, a Two-Headed Coin can masquerade as a mere minion of the Random Number God up until The Reveal.
— Shamus Young, DM of the Rings
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- Saki proves that this trope applies to mahjong tiles as much as it does to dice. Nodoka refuses to believe in players being "loved by the tiles" and such, but other players' freakish abilities to defy all probability when playing (as someone mentioned on the page, "how much can we make a statistician somewhere cry?") pushes her into Flat-Earth Atheist territory.
- In Quick Start!!, a 4koma about tabletop gaming group, a resident powergamer Karasuyama Sachi is on RNG's bad side, despite buying dice with equal distribution.
- In Knights of the Dinner Table, related to Hackmaster, a character was once beaten to a pulp for touching another gamer's dice. He was blinded by a cupful of soda and then was on the receiving end of a flying tackle. No one (except Sara) thought that this was uncalled for, as "that's one dice squirrel who'll think twice before touching another man's dice!"
- The attacker in that scenario was the 5'3" pencil-necked Bob Herzog, and the man who touched his dice was the 6'11" ex-marine Nitro Ferguson, and every time the event is referenced (the fight itself was never shown) it is strongly implied that Nitro got hurt at least as bad as Bob did.
- In the strip, they even outlined a "dice cleansing" ritual, used to banish bad luck from the character's dice.
- Many dice superstitions are explored in this strip. Bob refers to his dice by name, keeps them segregated according to purpose and game genre. Dave refers frequently to having his section of the table "trained" the way he likes it for dice rolling. All of the Knights, even the sensible Sara, have dice rolling styles. But the most infamous incident had Brian and Bob "fame-rubbing" their dice on Gary Jackson's corpse (a "legendary RPG creator" pastiche of Gary Gygax and Steve Jackson) to charge them with good luck. This backfired because Gary, being dead, was obviously out of good luck (as Sara pointed out, someone who'd died in a plane crash couldn't have been very lucky to begin with). All the fame rubbed dice performed poorly in game play. (Or possibly because that corpse wasn't Gary Jackson's.)
- Only Sense Online has the Running Gag of Sei getting repeatedly screwed over by the "greed sensor" (the same as Monster Hunter's desire sensor, mentioned under Video Games), as the random loot distribution system in the game is almost guaranteed to hand over whatever she wants to another party member or someone who comes shortly after her, often forcing her to grind excessively or make expensive trades. Meanwhile, Yun's sheer indifference to whatever drops eventually gives him a reputation as a lucky companion, especially since he's willing to trade fairly if he got what someone else wanted.
- The Bible says in Proverbs 16:33 that man casts lots, which were a form of chance equipment like dice, if not dice, but the result comes from God, making Jehovah/Yahweh the literal Random Number God.
- Priests from ancient Israel also used an Ummim and Thummim, which apparently were stones in a bag to be picked in random, for court trials and was controlled by God Himself.
- In the back of the Hackmaster 2nd Edition rulebook, there's actually a list of various dice rituals that are prescribed for the game, including rubbing the dice clockwise for higher rolls and counter clockwise for lower rolls.
- A number of bizarre good luck superstitions have arisen in the Warhammer 40,000 community, such as never calling missile launchers by their proper name (it has the word "miss" in it), the idea that painted models are luckier than unpainted modelsnote , and the practice of occasionally muttering prayers to the Emperor. Never taken seriously, but often endearing.
- Don't ever say "anything but an X." The more important the roll is, the higher the chance that you will get that X. Most players have lost more games by saying "anything but an X" than by bad strategy.note
- Also worth mentioning are the Chaos gods' chosen numbers. Chaos players used to get bonuses for fielding units of a certain size based on which god you were using. Slaanesh was 6, Nurgle 7, Khorne 8, Tzeentch 9, the idea being that the Chaos god makes the characters more lucky as long as they spend time in their chosen number. Modern versions of the game, for the sake of simplicity, have removed this rule.
- The 40K rule book advises players who are rolling large numbers of dice to take out the dice that failed and continue rolling the successful onesnote . Players will tell you the exact opposite: NEVER reroll the successful ones immediately afterwards, because they have just used up a good roll.
- A player will say, "I never seem to roll as well as I just did." A statistician will say, "Well, duh. Regression to the mean. You just had a lucky break, so the same entirely random process is very likely to produce a lower value simply because most possible values are lower." Both are correct. The player will usually retort, "Whatever," and produce another fifty dice. 40K players always have enough dice, just never enough dakka.
- Ork players are advised to use green dice for standard rolls ("green iz best"), red dice for moving through terrain ("coz da red ones go fasta"), and blue dice for critical rolls ("da luckiest"). Buy in bulk.
- It is also recommended, as the melta is one of the most powerful anti-armor weapons a troop can carry, that it never be referred to as such, as firing a melta weapon is an exercise in comedic inaccuracy. Simply referring to which model is firing should suffice. And never use Meltaguns against infantry. They might be great for blowing up tanks, but against infantry you're guaranteed to roll a 1.
- Some Eldar players mutter prayers to Khaine, or to Cegorach if using Harlequins. Chaos players, meanwhile, invoke the Dark Gods, and Ork players just shout "WAAAAAGH" when shooting. Or charging. Or at random intervals.
- The Rogue Trader spin-off RPG made off with the old idea of the Chaos gods' favored numbers by making 9s occasionally have special effects on rolls - especially those related to psychic powers. Yes, this means that Tzeentch, the god of Sorcery and Change, is implied to be the RNG that is out to get you.
- In the Wuxia RPG Weapons Of The Gods, observed good or bad luck with the dice can be utilized as a game effect, discovering that the character is under a curse or blessing which can then be either increased to add actual bonuses or used to create a balancing effect of the opposite type.
- The system itself also features the River mechanic, designed to mitigate the influence of the RNG. You can take dice results out of a role and store them for later use, so if you make an awesome roll on a trivial task, or roll two sets when you only need one, you can set some aside and break them out later when you screw up something important.
- The Red Dragon Inn provides an in depth (and tongue in cheek) tutorial on how to make the dice roll high numbers.
- Referenced by name in Hoyle's Rules of Dragon Poker, where players are afforded infinite mulligans if they've angered the RNG.
- Blood Bowl features a literal example of this in-universe, in the form of Nuffle, the game's patron god. This trope is also very much in effect for the players, since one of the keys to a successful game is rolling your dice as seldom as possible while forcing your opponent to roll dice as often as possible.
- This concept is taken to extremes in Kingdom of Loathing, where the RNG is a conscious entity that has its own account and frequents the various chat rooms. Those who please the RNG in some way may find themselves "Blessed by the RNG", whereas those who annoy it (especially by begging for a blessing) may find themselves "Cursed by the RNG" (both of which are active character effects). Because KoL game mechanics rely heavily on random number generation, and because KoL effects are rarely explicitly defined, there is still a significant debate over whether or not the Blessing and/or Curse actually affect a player's RNG-based "luck" in the game, or if it's just a red herring.
- A player may also be "Blessed by The RNG" by sending a gift package with an 8-ball, and a look in The RNG's display case may reveal other effective sacrifices.
- One particular area that makes players rage to the RNG: the F'c'le. In order to earn Pirate Fledges and be able to access the Obligatory Pirate Cove without wearing fairly weak equipment (the Fledges themselves are actually pretty strong), you must defeat three specific enemy types in this area, pick up their random drops, and use them. Every KoL player can regale you with stories of spending hundreds of adventures praying for the right enemy to show up, or, alternatively, having all three enemies show up in turn and give up their items in a row. The RNG in the F'c'le is an extremely fickle godling, and no one can predict its mood on a given day.
- In the Roguelike communities where the term originated, finding a very good item early in the game is a sure sign that the rest of it is going to be a hellish struggle against the wrath of the Random Number God. It's given you your one good thing, now it's going to do its damnedest to kill you.
- The ultimate item in this is an Amulet of Life Saving, which effectively gives you an extra life (in Roguelikes, if you die, that's normally it — your (one) save game is erased). If you find one of these early, rest assured the game is going to maneuver you into a situation where even instant resurrection will not help you. After all, if something is tough enough to kill you once, it can probably do it a second time... Paradoxically, "lucky finds" like this that should improve your chances of survival will just make players incredibly paranoid and even more cautious.
- Added as a character in TOME (and its parent game, Z Angband). Random Number Gods are weak, annoying, fast multiplying monsters that drop decent loot — and cause confusion.
- Players of Magic: The Gathering Online revere Grog, Goblin Shuffler.
- The RNG manifests in Billy Vs SNAKEMAN as a monster that players in a village (read: clan) can fight. While all other monsters of that class have accurate Hit Points displays, the RNG has nonsensical numbers or words to represent remaining and total life. It also shows up during The Festival, where it runs a game where you roll ten dice; anything higher than a one gets you an obscenely valuable item. The item cannot be obtained there because you only ever roll ten ones. Getting it actually requires completing an entirely different quest.
- Players who have become aware of higher-dimensional spaces may start to briefly encounter the RNG in other locations, and one of the more traumatic experiences during a quest is briefly seeing it in its true form.
- In World of Warcraft, it's customary to use the /roll command a few times before rolling for a specific piece of equipment to please the Random Number God and to get the low numbers "out of the way". In addition, there are persistent (but frequently debunked) rumors that the game seeds the random number generator according to specific criteria, including, but not limited to, the raid leader, the first person entering the dungeon and/or the number of damage-over-time spells (more dots!) on the boss.
- The developers are equally sadistic with this. Two of the Achievements involved having to get 100 on rolls to Need or Greed loot (once the system was redesigned to distribute loot drops automatically). It can take as long to get those to come up as specific, desperately wanted gear.
- The Hearthstone: Heroes of Warcraft community has taken to naming their God RNGesus. With a significant number of cards having RNG-based effects, many streamers actually ''pray'' to RNGesus when they need a random effect to go the way they need.
- Final Fantasy XIV players have adopted the RN Gesus meme from Hearthstone. Those who repeatedly fail to win his favour occasionally turn to Lootcifer in hopes of better rolls.
- Anyone who has ever played EverQuest and attempted to level tradeskills beyond a certain point knows that the RNG is a spiteful beast that hates you. There is a reason the premier crafting forum has the appropriately named Primal Scream Room...
- The Monster Hunter fandom has come to the conclusion that the series has a sadistic, psychic, "desire-based" RNG for determining how often a really rare item Randomly Drops, also known as the desire sensor. It will skew the odds out of your favor if you really want something, and the only way to end your curse is to not want it. You can't act like you don't want it, you have to actually not need it; the system is immune to reverse psychology. So if you spend hours farming the same giant monster for its armor plating, you may go through fifty corpses without seeing one, but you'll end up swimming in the stuff once you give up and move on to a different goal. The only other way to appease it may be petting the pig.
- Given that the engine knows the characters' profiles, quests, recipes and any discovered players' paths, the implementation of a sadistic "you'll always get stuck with only nineteen bear asses" drop routine is easy. In fact, it would be a usual semi-random drop with reversed adjustments. So the question is whether it's really that random, or not.
- Due to the nature of the makers (and fanbase) of DragonFable the RNG is nicknamed the Rude (or Reall) Nasty Gnome. He sits on a floating pile of all of the gear in the game and throws items at heroes who finish quests. Those heroes that 'amuse' him, get a better item thrown at them (albeit faster).
- One of the main cons in Dragon Ball Xenoverse. Everything that is not the storyline is virtually dictated by the RNG, from the skills you want, to the clothes you wear and even the mentor you want and it even extends to the missions themselves. All missions have bonus objectives that have you fight more or the same enemy twice after clearing the mission quick enough, but even activating the bonus parts is controlled by RNG. That's right, you can literally curbstomp everyone around you with having lost any of your teammates, and you still will not get the bonus objective, despite fulfilling it. Even worse is when you're trying to get certain items or skills to drop and they simply refuse to, no matter how hard you try.
- Much of the mechanics in Summoners War: Sky Arena, but most notably the summoning mechanics, are handled by the RNGeesus. Players have formulated theories on how the system works, how to influence the RNG to grant them that elusive Olympus Mons, up to the weird rituals one could do to 'surely' get a natural 4* at least.
- In the The Sims community, the term "sado-random" (a slightly more accurate form of "pseudo-random") is popular, referring to how even when it doesn't glitch somehow, the game's RNG always manages to give you exactly what you don't want whenever you don't want it. Specific opportunities for unfortunate randomized outcomes vary throughout the series, but the cussedness of the RNG is invariable. For instance, the base odds of a Sim being abducted by aliens are incredibly low, so it'll only happen if they've snuck off to stargaze at the worst possible moment for them to get whisked away by little green men and probed to within an inch of their lives. Likewise, you've got pretty good odds of finding any given job in the newspaper, but if it's exactly the one you're looking for, it always somehow manages to take much, much longer. Fortunately, the cheat console gives you various ways of interfering with most randomized outcomes.
- Fallen London: It plays a huge part, since the entire game is based on stat checks, along with the occasional card that's entirely up to chance. Nothing like raising your scandal to huge, unmanageable levels because you failed an 80% success chance five times in a row. It got so bad the players actually got an apology card (and a pair of dice as a make-up gift) from the RNG during one of the Christmas events. It's that sort of game.
"We've had our differences. But this is Christmas. Best wishes, the Fallen London Probably Random Number Algorithm."
- Fire Emblem has plenty of RNG-related stats - during attacks, whether they'll land and\or be a critical hit; during level-ups, what will be improved. And often it screws the player and\or helps the enemy, to the point a Let's Play of Fuiin No Tsurugi was named "Let's plumb the depths of the RNG's spite in Fire Emblem: Sword of Seals!"
I do not know what sorcery is at work here, but I'm sure as hell not complaining.
Itís possible the RNG gods were pleased by your previous sacrifice.
Or maybe all the levels in my LP are going to start sucking. I think thatís how the RNG works.
- Touken Ranbu is highly dependent on this, especially for the crafting of new swords. This means if the RNG is not on your side, you'll never get certain swords unless you commit lots of in-game resources and lots of hours to just make them.
- In Pokťmon, the Random Number Arceus has a habit of trolling you by, for example, giving you critical hits when your opponent is one hit away from fainting anyway. Or when you're trying to catch something and you know your next attack won't make it faint, but a critical hit will. It also heavily favors the computer when it comes to things like accuracy, paralysis, confusion, etc. Enjoy getting hit with Sand Attack once and whiffing your next 3 or 4 attacks, while they can be hit with Sand Attack 5 times and be paralyzed, but still manage to attack every turn and land them all. Of course, every so often it will decide to Throw the Dog a Bone and give you a ridiculously lucky turn or two. Just so you don't get too suspicious of it.
- It's even worse when playing competitively. It is rare for RNG to allow either side's schemes to work ideally. Many matches are determined by the number of consecutive turns a paralyzed Pokemon won't move, and finishing off the opponent is often made less trivial by repeated missing from attacks with accuracy upwards of 80%.
- The RNG is also what determines a Pokémon's ability, nature, I Vs, and by extent, shininess.Note Because of how diverse the range is for all of these (excluding abilities, which are limited to two at most [apart from hidden abilities]), it is very difficult to get a perfect Pokémon for your party. For instance, it is very likely that the shiny Pokémon you just encountered has poor enough stats to serve as nothing more than a trophy, or that Pokémon you found with the ability you want is severely crippled by its IV-altering nature. Conversely, it is possible for a good ability to perfectly compensate for a bad nature, and a shiny Pokémon could be just enough to carry you a long way as a trainer. The fact that Generation VI now includes Super Training and Pokémon Amie, two surefire ways to efficiently EV train your party to Game Breaker status helps alleviate some of the RNG's flaws.
- Don't let its adorable aesthetics fool you, Animal Crossing's entire gameplay revolves around randomness. Who your village starts out with, what your native fruit will be, who moves in, who wants to move out, where and what things will spawn, what items will appear in shops... the list goes on and on. After all, real life isn't exactly pre-planned, now is it?
- This◊ Dork Tower strip was the beginning of an arc about scheming dice that started behaving only when the cats got a hold of them.
- Sometimes, the power of the dice can get a little out of control. Efforts at appeasing the dice may meet with failure.
- There's a sort of Double Subversion to this concept, detailed in the annotations to this Darths & Droids strip, which involves "rejecting that superstitious nonsense" and instead using the laws of probability distribution:
- Take 1000 or so 20-sided dice.
- Roll each and every one of them once.
- About one-twentieth of these will have rolled 1s. Take these fifty-odd dice, and roll each of them again, once.
- Two or three of these dice will now have rolled 1 twice in a row. Statistically, the odds of rolling the same number three times on a 20-sided die is 1 in 8000, so now these dice have the 1s "rolled out of them"
- Place them in a special padded container so that they can't roll around, and you may now safely bring them out in emergencies for use for a die roll in which you really don't want a 1.
- This is of course patent nonsense; no matter how many times in a row you get a 1, the odds of the next roll getting a one are always 1 in 20, even if it seems "overdue" for a different number.
- Darths & Droids also goes as far as to Lampshade the trope with a link in the annontations of the strip mentioned above that links to this very page.
- This strip demonstrates this strategy in action: The prerolled die yields a natural 1 but the Random Number God's true believers don't waver. They reason it will simply be even more lucky next time.
- Full Frontal Nerdity carries this to a ludicrous extreme when Lewis attempts to dispose of a 'cursed' die that can seemingly only roll 1s. The die rises from the grave and the curse is so strong that every random number generation device in the world becomes incapable of generating any number other than 1.
- Lampshaded in this Dilbert comic strip when he's touring a layer of hell known as Accounting.
- In the Erfworld comic intermission, a Luckamancer discusses the mechanics behind luck-manipulation with a young Wanda :
"Now here's an important thing, though," said Clay, pointing at the die. "Where did those 4s come from?"Wanda looked down at the little brown enchanted pyramid and shook her head. "From you. You cast upon the die."Clay grinned slyly. "So you're saying my juice had a physical effect on the way the die rolled.""Yes.""Yes and no," said Clay, grinning more broadly now. "It's not a direct effect, you see? The 4 is a Number. It had to come from somewhere."
- In Larry Leadhead, the God appears as capriciously as you might expect. Larry's dice rolls are renowned, for all the wrong reasons.
- A College Humor sketch about Tetris called "The Tetris God" involves the eponymous character manually choosing which piece will be next.
"Thou art a cruel and angry God!!"
- Ribbon of /tg/ explained series explains◊.
- Often invoked on Tabletop. In the Elder Sign episode, Wil Wheaton claims that the dice are trying to kill him. They succeed.
- Critical Role is...strange. On the one hand, it's a livestreamed D&D game, so absolutely nothing is staged. Chance should be king. And yet sometimes the dice seem to obey the Theory of Narrative Causality in that players are prone to getting Natural 20s at the best possible times. Examples include Percy rolling a crit on a save against a fear effect after one of his homemade bombs successfully explodes, Vax rolling a crit to prank Grog by shaving his beard, and Vex rolling not one but two crits in succession when Vax is downed by the Briarwoods. On the other hand, Wil Wheaton has a brief guest spot, and maintains his streak of absolutely miserable luck known as "the Wheaton dice curse", rolling five or less an absurd number of times.
- Even their failures are oddly appropriate for the narrative! In Whitestone, the lingering undead atmosphere causes the entire party to need to make saves against "corruption" once a day. The only person who has failed the saves so far is Percy, who is already acting more violent and being corrupted by the smoky entity from his dream.
- There are some calculations scientists perform that require truly random numbers, such that the slight predictability inherent in a computerized system is too large. For these cases a "True Random Number" generator can be purchased, which is effectively a small radio telescope tuned precisely to the frequency of the Cosmic Microwave Background radiation, as produced by the Big Bang.
- Radioactive isotopes can also be used - set up a Geiger counter and a numeric counter, then stop the counter whenever the Geiger meter goes "beep". The time between successive radioactive decays is random, so your numbers are random.
- Noisy diodes are also truly random, and as a benefit for computers, binary. Similarly, overdriving a transistor into overheating so you can read thermal noise from it.
- http://www.random.org/ generates random numbers using atmospheric noise.
- For many microcontrollers, reading an input off an analog-capable pin that is "floating" (not connected to anything) will return a truly random result as the pin will (or won't!) respond to electronic noise, the actions of other pins on the chip or other things in the local environment. This random result can then be used as a seed for a pseudo-random number generator.
- Actually getting a random number out of a truly random source is far from trivial in itself - you have to build a device that doesn't introduce any bias.
- As this 2015 video explains, cheap dice have dull edges because they were polished in a rock tumbler. The resulting imperfections change the die's center of gravity and make it easier to roll over some edges than others. So there is a scientific explanation to this phenomenon, and a way to prevent it.
- It also makes reference to one of the classic ways con artists can rig games: "shaving" the edges on a die (usually a casino die, since they have sharp edges to begin with). You trim off a tiny bit on the edges of whatever's opposite the side you don't want to land on. So for example, if you don't want to roll a six, you'd shave the edges of the one face. The die expends less energy rolling over the shaved edges, which skews the probability way below 1/6. (Incidentally, if you find an actual casino die that's been shaved, you could be rewarded by the state gaming commission. They take fair odds seriously. Outside of a casino, though... just remember the page quote.)
- Another common method of messing with die odds is to cook them. You take your plastic die, put it in the microwave with the side you want to show face up, then nuke it for a couple of seconds, no more than five. The nuking causes the plastic to melt downwards a bit(thus making the die more likely to stop on that edge, since it's heavier). Done right, it's almost undetectable at casual inspection.
- Most computer software use a Pseudo random number generator Often, a programming language's library will provide it, but for early games and applications, bugs in the implementations of pseudo random number generators caused biases. C's built-in random library is actually notable for allowing programmers to use it incorrectly and introduce biases to the numbers generated by it. Problems with how the random number seed is picked can also cause the numbers to be predictable.
- Since random number generators are used by many security applications, their predictability can lead to serious security vulnerabilities. Which makes computing with serious security need another area of use for the aforementioned true random number generator devices.
- It is difficult to keep correct uniform distribution when picking more complicated random events, even while the actual random number generator has a good distribution. For example, consider picking a random point inside a disk, as is needed in certain games (usually some variation of bullet spread). Programmers without prior knowledge, specially amateur ones coding for a game mod can implement this random point generator in a way that there is a bias towards the center of the circle or towards its limits.
- One particularly notable random number generator, known nowdays as RANDU, was noted as being, in the words of Donald Knuth, "truly horrible". It has since become a textbook example of a bad PRNG, due to many, many undesirable properties. note (On the plus side, if your system is newer than the second half of the Reagan administration, and doesn't involve FORTRAN, it's highly unlikely you will suffer under this particular misguided PRNG.)
[On RANDU]: "One of us recalls producing a 'random' plot with only 11 planes, and being told by his computer center's programming consultant that he had misused the random number generator: "We guarantee that each number is random individually, but we donít guarantee that more than one of them is random." Figure that out."
- Many versions of Linux have a very good PRNG as a system resource with a seed that depends on many hard-to-access and fast-changing internals of the system, making it difficult to guess what the next value will be, even if you have many recent values and normal programmatic access to the system.
- Apple rewrote the "Shuffle" program on their newer iPods so that no two songs from the same artist are close to each other, if possible. Turns out people want high entropy from a shuffle, not random entropy.