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Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss, what people think should happen is that if they kill that boss X times, they should see it drop once. But the reality was of course that loot was very non-uniform. Some pieces we saw lots of times, and other pieces very rarely, despite them having the same drop chance. And the players who wanted those pieces that happened to be rare for our guild, got very, very angry. We saw the same things on the official message boards, players were furious after having spent a year killing the same raid boss once a week, and never seeing a certain piece drop for them. But simple math shows that with million of players, tens of thousands of raiding guilds, some of those will see very streaky results. These days in World of Warcraft, boss monsters drop tokens instead, and when you have X tokens, you can exchange that for a piece of armour, or a weapon, guaranteed. And noone complains about the random loot anymore.

thurn 14y ago
This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!
- henrikschroder 14y ago
  Oh yes. Our intuition is that random is fair and uniform, but it's absolutely not. I was bit by another random quirk in World of Warcraft. There was a long-running achievement called "What a Strange Long Journey it has Been", which took at least a year in real-time to complete, and you had to actively play during each of the ten or so in-game festivals and holidays, and do some quests and tasks during each. If you missed a festival, you had to wait another year to do it again, so if you were aiming for the achievement, you really wanted to do it in one go. During their version of Valentine's, each player got a bag of heart-shaped candy, and the task you had to complete was to pull out at least one each of the eight different heart candies. But you could only pull a piece of candy once every hour or so, each time you pulled a piece you had a 1/8 chance to get a certain piece, but the holiday was time-limited, so you had about two weeks to complete it. Sounds easy and fair, right? 1/8 chance, get all eight pieces, two whole weeks, easy! Except that there was one piece that I just never got. The piece that said "I LOVE YOU!". And as the time went by, I got more and more frantic, logged in more often so as not to miss any opportunity to pull a piece of candy, but no luck. So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million. With ten million players all doing the same thing, there's going to be a number of them that will hit that "one in a million" chance, which means that whoever designed that part of the achievement didn't do their homework, didn't do the math. Because intuition tells you that 1/8 chance is plenty! Hundreds of tries, of course everyone will get all pieces! Except proper math tells you otherwise, and I was one of the "lucky" outliers. (Later, they apologized and retroactively removed that part of the achievement, so I got my purple nether-drake mount without having to wait a year extra.)
  - dhathorn 14y ago
    This is an example of a problem called the Coupon Collector problem (https://en.wikipedia.org/wiki/Coupon_collector%27s_problem https://en.wikipedia.org/wiki/Coupon_collector%27s_problem). Short version is that the expected value of number of pulls you'll need to collect all of the coupons (candy in this case) is nln(n), or about 16 pulls in this case. Of course some people are just going to be unlucky (as you demonstrated).
  - deleted 14y ago
    [deleted]
  - orangecat 14y ago
    So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million. The chance of failure would be 8 times that much because there are 8 pieces you could miss, which comes to about 12.7 per million.
    - fmx 14y ago
      You couldn't possibly miss all 8 pieces. As soon as you make one attempt you'll get one piece.
      - Zakharov 14y ago
        Henrik's math calculated the chance of missing the "I love you" piece each time. The chance of missing any one other piece each time is the same.
        deleted 14y ago
        [deleted]
        martincmartin 14y ago
        Yes, but they're not independent. Given that you missed piece X, the probability that any one piece it's piece Y it's 1/7, not 1/8, so the chance of missing both X and Y it's lower than the product of their individual probabilities.
- michaelochurch 14y ago
  Real randomness is very frustrating for players! Games should be designed to not be random. This reminds me of Magic: the Gathering and the misery of mana screw. I disagree with the uniform "should be", because there are so many different design objectives. Slot machines aren't "good games" by Euro standards, but people spend a lot of money on them. (One can argue about whether that's enjoyment or addiction. I'll skip that for now.) Random payoffs can foster enjoyment, as seen in Skinner Boxes and on slot machines. Random denial makes people unhappy. What you want in most games is some degree of random windfall but no one getting "killed by the dice". Have you played Ambition, by chance? It's a trick-taking card game designed to remove card luck.
  - chimeracoder 14y ago
    > This reminds me of Magic: the Gathering and the misery of mana screw. Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even". Also, while mana screw sucks, between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distribution of card costs), it's far more fun than the alternative.
    - michaelochurch 14y ago
      Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even". Online bridge has a similar problem. Four riffle shuffles (which does not fully randomize hands) is typical in bridge games, and this means that long suits (and, thus, better hands) are more common. Early online bridge games randomized hands fully and therefore delivered crappier (flatter) hands than people were typically used to. between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distribution of card costs), it's far more fun than the alternative. When I played (mid-90s) a lot of those options didn't exist. There weren't mulligans unless you had no land. With one, you had to play it. Also, a lot of the newer mana sources didn't exist. If you drew only 2 lands in your first 10 cards, you were screwed, but you couldn't develop an interesting deck with more than 22 land.
- martinced 14y ago
  That's interesting but then we're talking about another game. If there's a pack of cards indicating dice results you can have the equivalent of a 'warm deck' and a 'cold deck'. Players can then start counting. E.g.: I know '8' came out 7 times and '6' only came out once, then it changes my strategy because there's a benefit to expand with a new settlement (or make a "city") on an '6' instead of an '8'. I'm not against it: it's interesting. But it's not really the Settlers of Catan anymore: it's a game which happens to share a lot of rules with the Settlers of Catan but which is definitely different.
  - bcbrown 14y ago
    They mitigate that by discarding without looking several of the cards, so it's not a completely even distribution of outcomes. E.g., it's possible that 4 of the '6's won't come out at all that time through the deck.
- baddox 14y ago
  I was under the impression that a uniform distribution is still considered random, but that there are simply many other random distributions. If you have a flat 1/10 chance of receiving a certain item, then sure, you might do the task 30 times without getting it. But if it were programmed such that you will always receive the item at some point within the first 10 completions of the task (i.e. 10% of players receive it after their first completion, 10% after their second completion, etc.) I would still consider that random, and not really more or less random than the 1/10 scenario. I'm not sure what you mean by "real randomness."
  - sskates 14y ago
    The distinction is between independent identically distributed random variables, where it's possible to not get the item after 1/p tries, and what you described, which the events are not identically distributed. In the case you describe, the probability you'll get an item when you have a second completion is 1/9, not 1/10. This is the distinction that the original article highlighted and gives rise to the Poisson distribution, which can have unintuitive results because it is not a uniform distribution. You are describing a uniform distribution. (A Poisson distribution characterizes the number of hits you would expect after running some number of iid random events.)
  - Dylan16807 14y ago
    I can give you one simple argument. Ten items shuffled have 10! entropy, while ten independent rolls have 10^10 entropy. How is that not far less random?
    - baddox 14y ago
      Because amount of entropy has nothing to do with "amount of randomness."
      - Dylan16807 14y ago
        > entropy is a measure of the uncertainty in a random variable
      - 14y ago
- Laremere 14y ago
  I can think of two specific examples where breaking the rules of probability resulted in better player experience: In tf2, you randomly get weapon drops, up to a limit per week. The initial obvious solution was to randomly roll if they get a new weapon every X minutes of gameplay. This lead to players getting long unlucky streaks where they got little to no gameplay. They eventually changed it to when you get a weapon drop, it rolls to see how long you have to play until you get a new weapon. Players can be unlucky still, but it's drastically better. The other example was in civilization they showed percentage chances of winning a battle. The problem is that when a player would have three battles with say a 50% chance of winning and lost them all, they would get very frustrated. So they changed it to be much more like the average person perceives statistics to be. This means actually weighting the percentages differently from what the player is told so that if a player has a third of a chance to win each of three battles, it's actually very likely they will win one of them.
  - purplelobster 14y ago
    Ah, this is what made Risk so frustrating at times. Many a good friend was lost to that game.
  - T-hawk 14y ago
    The other example was in civilization they showed percentage chances of winning a battle. ... This means actually weighting the percentages differently from what the player is told This is a (persistent) myth. None of the Civilization games actually do this. Civilization 4 is the only game in the series that displays combat prediction as a percentage chance, and the source code for Civ 4's combat engine is publicly released and well understood. (I am a developer on a Civ 4 modding project and familiar with the code.) The earlier Civ games before 4 don't display any kind of combat odds, and Civ 5 has a totally different system that isn't based on winning percentage. So, unless you're talking about some other game like Galactic Civilizations or a mod for Civilization 4, this isn't true. Your underlying point is certainly true, though: gameplay often is perceived as a better experience with "randomness" smoothed out to produce more uniformly distributed results.
- Zakharov 14y ago
  Blizzard actually did this in Warcraft 3, the chance of getting a Critical Strike or related effect went up every time you failed, and down every time you succeeded.
- b0rsuk 14y ago
  This is a gross oversimplification. Randomness in games is like a knife. It can be used to make nice things, or to hurt. Wesnoth is a good example of a game which is frustrating for many people. I think the reason is that it has random outcomes of decisions. Suppose you order a unit to attack another one. There's a base 0.6 chance to hit. The unit has 3 attacks each dealing 12 damage. What is the expected damage output ? - 0 damage: ~ 6% - 12 damage: ~ 28% - 24 damage: ~ 43% - 36 damage: ~ 21% ...so, if you're planning for the most common event - 24 damage - you're a fool, because it occurs only 43% of the time, less than half ! A bit like democracy, which is sometimes called tyranny of the minority. The example I used is actually simplified. In Wesnoth, each strike of an attack is followed by a counter-strike from the attacked unit. Not only the attacker's damage varies wildly, you can easily lose the unit without having it deal any damage. And such a random result when you make a good decision. Counterexamples: Neuroshima Hex (board game), Seasons (board game), Mission in Space: Lost Colony (flash game). In all of these games randomness is used to improve variety. In MIS there's actually little randomness and it feels more like a puzzle. The most visible effect of randomness in the game is randomly chosen alien spawned. All 3 aliens have the same HP and movement speed, so it's not a big deal. Seasons is a card and dice game, but an unusual one. Each side of dice gives some options to choose and there are no good or bad sides, there only good or bad sides at this very moment. The cards you start with are not really random either, because the game uses draft mechanic: you take one card from your hand and pass your hand to your neighbor on the left. Neuroshima Hex is essentially a game with hexagonal cards. Randomness only determines what cards you draw, and once you do you place the hex-cards on the board. Once the battle resolves, it's deterministic. The bottom line: I noticed that I much more enjoy games where randomness is used not to determine success/failure, but instead options available. That is, as long as the options are balanced relative to each other. Heroes of Might and Magic 3 has randomly selected spells and skills at levelup, but they range from awesome to pathetic. The result is frustration. All of the games I mentioned (Except Heroes 3) are free. You can actually play both board games online, too.
  - vacri 14y ago
    24 damage happens 64% of the time, not 43%. Given that you can't use your spare attack elsewhere, the 3x damage even includes the pathway of the 2x damage event. Another classic example of this randomness-pain is earlier versions of the Civ series, where you could lose tanks against pikemen or other ancient unit types. Not likely, but it hurt when it happened.
joe_the_user 14y ago
Yeah, And you know, it is always possible in those situations that there is a broken pseudo-random number generator involved. But of course, that's really hard to tell too because real randomness is so unrandom seeming.
- YokoZar 14y ago
  Another Blizzard game, Diablo 2, actually had a random number generator bug that went unnoticed for years. Essentially, any random chance in the game of the form 1 to n could only ever be 1 to n-1, I think with n-1 being twice as likely. This went unnoticed since most random rolls were over fairly large ranges and it didn't seem to hurt much, however it did explain why one particular subtype of loot literally never dropped.
anonymoushn 14y ago
These days in World of Warcraft, boss monsters drop tokens instead, and when you have X tokens, you can exchange that for a piece of armour, or a weapon, guaranteed. And noone complains about the random loot anymore. This bit is not correct. All of the most desirable items (except darkmoon trinkets and tier sets) drop directly from raid bosses, and people still complain about the outcomes of random loot.
tzs 14y ago
On the other hand, sometimes it turns out the players are right when they suspect something is biased against them. In Everquest when you cast a spell, there was a chance the spell would fizzle. Occasionally, someone would get a streak of fizzles. Many argued this was just the normal streakiness you expect when you are do repeated independent trials. Some insisted that fizzles streaks were more common than you'd expect based on that model. Finally, a statistician who also played EQ spend some time gathering data, and determined that fizzling was not independent. Your fizzle chance was an increasing function of the length of your current fizzle streak, up to a cap. Things like that give a game character.
6ren 14y ago
A market would also fix this, in effect averaging over the entire population. Given players' anger at pieces not dropping as often as they "should", the market would converge approximate the true ratio between drop frequencies of different pieces.
- jrajav 14y ago
  Final Fantasy XIV did this very well in my opinion. They designed for the economy right from the start, and everything revolves around that (and the amazing graphics, music, and exploration), rather than spells, grinding, and raids.
- endtime 14y ago
  Except that the most desirable loot was invariably soulbound: http://www.wowwiki.com/Soulbound http://www.wowwiki.com/Soulbound
ChuckMcM 14y ago
Too bad the WoW random number generator was flawed, somewhere in there it had the clause if (item == tier2.druid.pants) return (item = plate-wearer-loot()); Of this I am certain.
- Zenst 14y ago
  May be the case that it was coded with one version of a programming language and upgraded later and the newer version changed the handerling of rounding. Believe python from 2.0>3.0 had some difference along those lines and whilst on the surface may not mean much they can add bias into what you get dropped as rounding and somebody adding .5 will never get the low value with some rounding as it will always round 0.5 or > to 1 as apposed to some which demand at least be > than 0.5 . Yes there are standards, but they advance and evolve over time and we all know intergers are completely different from floats. Last thought, if there was a truely random number generator then why do fruitmachines have control systems to monitor the distribution and with that what is paid out to maintain that x% payout to comply with laws that say x% of money taken has to be payed out. Mostly 70-80%, but does vary and whilst the legal min may be say 70%, some casino's and the like will generaly have a higher % payout in a promenant place, just so people think it's even higher.
  - lutusp 14y ago
    > Last thought, if there was a truely random number generator then why do fruitmachines have control systems to monitor the distribution and with that what is paid out to maintain that x% payout to comply with laws that say x% of money taken has to be payed out. That's easy to answer -- to comply with rules that require a certain outcome some x percentage of the time, one need only take a truly random generator's output and filter it by x: outcome = (rn * 100 <= x); If rn is a float, lies between 0 and 1 and is truly random, then the above trivial filter will produce the required distribution in the long term.
- cheald 14y ago
  Nah, the game just used up all its Druid loot luck in Molten Core. Those frickin' salad shoulders.
cheald 14y ago
It's also worth noting that Blizzard recognized this and "fixed" it in their questing system by progressively improving the drop rates of quest items for players, which provides a natural upper limit on "bad streaks" for quest drops, as a means of reducing player frustration without removing all randomness from the system. http://www.shacknews.com/article/57886/blizzard-details-secret-world-of http://www.shacknews.com/article/57886/blizzard-details-secr...
_casperc 14y ago
I have another anecdote from WoW regarding randomness. The raid boss Onyxia (a great big dragon in a cave, which you could only kill once a week as i recall) had a phase where she would take off and fly above the raid. Once in a while she would then do a deep breath, a fire attack which had a high chance at killing you if it hit you. Now, all sorts of tactics emerged on how to handle the fire attacks. One that stuck for a very long time was that the number of DOTs (Damage Over Time) would lower the number of deep breaths you got. I'm sure there were other theories as well, but this one stuck for years with raid leaders yelling at warlocks, the class with most dots, to add more dots and even stacking the raid with warlocks to get as many dots as possible (we need at least 4 warlocks to take her). In the end there was a developer (or just Blizzard employee) who admitted that it was in fact random. This story pops back in my head once in a while because I think we do this a lot on larger scales too without realizing it: See some phenomenon caused by randomness, come up with a theory, and because it is not easily refuted (after all it works most of the time right?) it becomes common knowledge that everyone follows.
Too 14y ago
That's interesting, because in WarCraft 3, by Blizzard, randomness is designed to be "fair". They use a special word for it but i can't remember it at the moment. For example, there are certain items that can give you a chance to blow a "critical hit", a critical hit multiplies your damage with X. Say an item gives you 30% chance to do 2X damage. However, the randomness has memory and is designed to distribute the critical hits evenly by gradually increasing the probability for every non critical hit and resetting it for every critical hit. So the first time you hit the chance isn't actually 30% but more like 10%. If you miss 3 times the chance of the fourth hit being a critical is more like 40-50%. The hit after that will be back on 10% probability. (Just picking numbers out of the blue to illustrate the concept, I'm sure there's some more thought through math behind it) As the nr of hits goes towards infinity, 30% of them will still be critical but the chance of getting streaks of non-critical or streaks of critical hits is very low. In practice it works very well from my experience. It is however not completely exploit-proof, you could for example go and increase your probability of initially blowing a critical hit by first making a few hits on NPCs and then go to battle against a harder enemy. But that's more of a hypothetical exploit as the time and risk of doing this simply isn't worth those few extra percent.
- Too 14y ago
  I guess applying this concept on item drops available to every player on a whole MMO-server isn't as simple/fair as remembering the outcome of hits for a single player.
- ufo 14y ago
  I see most people refering to that as a Pseudorandom Distribution, although this is Dota terminology so I'm not 100% sure its the same word.
emp_ 14y ago
During the first long raid (Molten Core) the loot table had a weird deviance of being very similar depending on the player that created the raid, Blizzard said that was impossible but in reality guilds would just rotate the raid leader until they hit someone that "would", for example, drop the legendary bindings and stick with that RL for a while -- it worked for many people and 4 or 5 years later one dev finally answered the big question: "Is loot defined when you kill the mob" or "is loot defined when the raid is instanced" which is the second option, the sum of these plus some weird bug that they might have fixed silently at some point might have caused the RL rotation hoax.

thurn 14y ago

This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!

henrikschroder 14y ago
Oh yes. Our intuition is that random is fair and uniform, but it's absolutely not. I was bit by another random quirk in World of Warcraft. There was a long-running achievement called "What a Strange Long Journey it has Been", which took at least a year in real-time to complete, and you had to actively play during each of the ten or so in-game festivals and holidays, and do some quests and tasks during each. If you missed a festival, you had to wait another year to do it again, so if you were aiming for the achievement, you really wanted to do it in one go. During their version of Valentine's, each player got a bag of heart-shaped candy, and the task you had to complete was to pull out at least one each of the eight different heart candies. But you could only pull a piece of candy once every hour or so, each time you pulled a piece you had a 1/8 chance to get a certain piece, but the holiday was time-limited, so you had about two weeks to complete it. Sounds easy and fair, right? 1/8 chance, get all eight pieces, two whole weeks, easy! Except that there was one piece that I just never got. The piece that said "I LOVE YOU!". And as the time went by, I got more and more frantic, logged in more often so as not to miss any opportunity to pull a piece of candy, but no luck. So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million. With ten million players all doing the same thing, there's going to be a number of them that will hit that "one in a million" chance, which means that whoever designed that part of the achievement didn't do their homework, didn't do the math. Because intuition tells you that 1/8 chance is plenty! Hundreds of tries, of course everyone will get all pieces! Except proper math tells you otherwise, and I was one of the "lucky" outliers. (Later, they apologized and retroactively removed that part of the achievement, so I got my purple nether-drake mount without having to wait a year extra.)
- dhathorn 14y ago
  This is an example of a problem called the Coupon Collector problem (https://en.wikipedia.org/wiki/Coupon_collector%27s_problem https://en.wikipedia.org/wiki/Coupon_collector%27s_problem). Short version is that the expected value of number of pulls you'll need to collect all of the coupons (candy in this case) is nln(n), or about 16 pulls in this case. Of course some people are just going to be unlucky (as you demonstrated).
- deleted 14y ago
  [deleted]
- orangecat 14y ago
  So, I did a quick bit of math. You can pull one piece every hour for two weeks, but sleeping, not playing, missing days etc, meant that I effectively pulled ~100 pieces. The chance of missing a certain piece is 7/8, so missing a certain piece 100 times in a row is (7/8)^100, which is roughly a little bit more than one in a million. The chance of failure would be 8 times that much because there are 8 pieces you could miss, which comes to about 12.7 per million.
  - fmx 14y ago
    You couldn't possibly miss all 8 pieces. As soon as you make one attempt you'll get one piece.
    - Zakharov 14y ago
      Henrik's math calculated the chance of missing the "I love you" piece each time. The chance of missing any one other piece each time is the same.
      - deleted 14y ago
        [deleted]
      - martincmartin 14y ago
        Yes, but they're not independent. Given that you missed piece X, the probability that any one piece it's piece Y it's 1/7, not 1/8, so the chance of missing both X and Y it's lower than the product of their individual probabilities.
michaelochurch 14y ago
Real randomness is very frustrating for players! Games should be designed to not be random. This reminds me of Magic: the Gathering and the misery of mana screw. I disagree with the uniform "should be", because there are so many different design objectives. Slot machines aren't "good games" by Euro standards, but people spend a lot of money on them. (One can argue about whether that's enjoyment or addiction. I'll skip that for now.) Random payoffs can foster enjoyment, as seen in Skinner Boxes and on slot machines. Random denial makes people unhappy. What you want in most games is some degree of random windfall but no one getting "killed by the dice". Have you played Ambition, by chance? It's a trick-taking card game designed to remove card luck.
- chimeracoder 14y ago
  > This reminds me of Magic: the Gathering and the misery of mana screw. Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even". Also, while mana screw sucks, between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distribution of card costs), it's far more fun than the alternative.
  - michaelochurch 14y ago
    Incidentally, apparently people complain about the online versions of the game providing a land distribution that's "too even". Online bridge has a similar problem. Four riffle shuffles (which does not fully randomize hands) is typical in bridge games, and this means that long suits (and, thus, better hands) are more common. Early online bridge games randomized hands fully and therefore delivered crappier (flatter) hands than people were typically used to. between the fact that you can decide whether or not to begin with a certain opening hand and the fact that you can design your deck around such circumstances (mana fixing, proper distribution of card costs), it's far more fun than the alternative. When I played (mid-90s) a lot of those options didn't exist. There weren't mulligans unless you had no land. With one, you had to play it. Also, a lot of the newer mana sources didn't exist. If you drew only 2 lands in your first 10 cards, you were screwed, but you couldn't develop an interesting deck with more than 22 land.
martinced 14y ago
That's interesting but then we're talking about another game. If there's a pack of cards indicating dice results you can have the equivalent of a 'warm deck' and a 'cold deck'. Players can then start counting. E.g.: I know '8' came out 7 times and '6' only came out once, then it changes my strategy because there's a benefit to expand with a new settlement (or make a "city") on an '6' instead of an '8'. I'm not against it: it's interesting. But it's not really the Settlers of Catan anymore: it's a game which happens to share a lot of rules with the Settlers of Catan but which is definitely different.
- bcbrown 14y ago
  They mitigate that by discarding without looking several of the cards, so it's not a completely even distribution of outcomes. E.g., it's possible that 4 of the '6's won't come out at all that time through the deck.
baddox 14y ago
I was under the impression that a uniform distribution is still considered random, but that there are simply many other random distributions. If you have a flat 1/10 chance of receiving a certain item, then sure, you might do the task 30 times without getting it. But if it were programmed such that you will always receive the item at some point within the first 10 completions of the task (i.e. 10% of players receive it after their first completion, 10% after their second completion, etc.) I would still consider that random, and not really more or less random than the 1/10 scenario. I'm not sure what you mean by "real randomness."
- sskates 14y ago
  The distinction is between independent identically distributed random variables, where it's possible to not get the item after 1/p tries, and what you described, which the events are not identically distributed. In the case you describe, the probability you'll get an item when you have a second completion is 1/9, not 1/10. This is the distinction that the original article highlighted and gives rise to the Poisson distribution, which can have unintuitive results because it is not a uniform distribution. You are describing a uniform distribution. (A Poisson distribution characterizes the number of hits you would expect after running some number of iid random events.)
- Dylan16807 14y ago
  I can give you one simple argument. Ten items shuffled have 10! entropy, while ten independent rolls have 10^10 entropy. How is that not far less random?
  - baddox 14y ago
    Because amount of entropy has nothing to do with "amount of randomness."
    - Dylan16807 14y ago
      > entropy is a measure of the uncertainty in a random variable
    - 14y ago
Laremere 14y ago
I can think of two specific examples where breaking the rules of probability resulted in better player experience: In tf2, you randomly get weapon drops, up to a limit per week. The initial obvious solution was to randomly roll if they get a new weapon every X minutes of gameplay. This lead to players getting long unlucky streaks where they got little to no gameplay. They eventually changed it to when you get a weapon drop, it rolls to see how long you have to play until you get a new weapon. Players can be unlucky still, but it's drastically better. The other example was in civilization they showed percentage chances of winning a battle. The problem is that when a player would have three battles with say a 50% chance of winning and lost them all, they would get very frustrated. So they changed it to be much more like the average person perceives statistics to be. This means actually weighting the percentages differently from what the player is told so that if a player has a third of a chance to win each of three battles, it's actually very likely they will win one of them.
- purplelobster 14y ago
  Ah, this is what made Risk so frustrating at times. Many a good friend was lost to that game.
- T-hawk 14y ago
  The other example was in civilization they showed percentage chances of winning a battle. ... This means actually weighting the percentages differently from what the player is told This is a (persistent) myth. None of the Civilization games actually do this. Civilization 4 is the only game in the series that displays combat prediction as a percentage chance, and the source code for Civ 4's combat engine is publicly released and well understood. (I am a developer on a Civ 4 modding project and familiar with the code.) The earlier Civ games before 4 don't display any kind of combat odds, and Civ 5 has a totally different system that isn't based on winning percentage. So, unless you're talking about some other game like Galactic Civilizations or a mod for Civilization 4, this isn't true. Your underlying point is certainly true, though: gameplay often is perceived as a better experience with "randomness" smoothed out to produce more uniformly distributed results.
Zakharov 14y ago
Blizzard actually did this in Warcraft 3, the chance of getting a Critical Strike or related effect went up every time you failed, and down every time you succeeded.
b0rsuk 14y ago
This is a gross oversimplification. Randomness in games is like a knife. It can be used to make nice things, or to hurt. Wesnoth is a good example of a game which is frustrating for many people. I think the reason is that it has random outcomes of decisions. Suppose you order a unit to attack another one. There's a base 0.6 chance to hit. The unit has 3 attacks each dealing 12 damage. What is the expected damage output ? - 0 damage: ~ 6% - 12 damage: ~ 28% - 24 damage: ~ 43% - 36 damage: ~ 21% ...so, if you're planning for the most common event - 24 damage - you're a fool, because it occurs only 43% of the time, less than half ! A bit like democracy, which is sometimes called tyranny of the minority. The example I used is actually simplified. In Wesnoth, each strike of an attack is followed by a counter-strike from the attacked unit. Not only the attacker's damage varies wildly, you can easily lose the unit without having it deal any damage. And such a random result when you make a good decision. Counterexamples: Neuroshima Hex (board game), Seasons (board game), Mission in Space: Lost Colony (flash game). In all of these games randomness is used to improve variety. In MIS there's actually little randomness and it feels more like a puzzle. The most visible effect of randomness in the game is randomly chosen alien spawned. All 3 aliens have the same HP and movement speed, so it's not a big deal. Seasons is a card and dice game, but an unusual one. Each side of dice gives some options to choose and there are no good or bad sides, there only good or bad sides at this very moment. The cards you start with are not really random either, because the game uses draft mechanic: you take one card from your hand and pass your hand to your neighbor on the left. Neuroshima Hex is essentially a game with hexagonal cards. Randomness only determines what cards you draw, and once you do you place the hex-cards on the board. Once the battle resolves, it's deterministic. The bottom line: I noticed that I much more enjoy games where randomness is used not to determine success/failure, but instead options available. That is, as long as the options are balanced relative to each other. Heroes of Might and Magic 3 has randomly selected spells and skills at levelup, but they range from awesome to pathetic. The result is frustration. All of the games I mentioned (Except Heroes 3) are free. You can actually play both board games online, too.
- vacri 14y ago
  24 damage happens 64% of the time, not 43%. Given that you can't use your spare attack elsewhere, the 3x damage even includes the pathway of the 2x damage event. Another classic example of this randomness-pain is earlier versions of the Civ series, where you could lose tanks against pikemen or other ancient unit types. Not likely, but it hurt when it happened.

joe_the_user 14y ago

Yeah, And you know, it is always possible in those situations that there is a broken pseudo-random number generator involved. But of course, that's really hard to tell too because real randomness is so unrandom seeming.

YokoZar 14y ago
Another Blizzard game, Diablo 2, actually had a random number generator bug that went unnoticed for years. Essentially, any random chance in the game of the form 1 to n could only ever be 1 to n-1, I think with n-1 being twice as likely. This went unnoticed since most random rolls were over fairly large ranges and it didn't seem to hurt much, however it did explain why one particular subtype of loot literally never dropped.

anonymoushn 14y ago

These days in World of Warcraft, boss monsters drop tokens instead, and when you have X tokens, you can exchange that for a piece of armour, or a weapon, guaranteed. And noone complains about the random loot anymore. This bit is not correct. All of the most desirable items (except darkmoon trinkets and tier sets) drop directly from raid bosses, and people still complain about the outcomes of random loot.

tzs 14y ago

On the other hand, sometimes it turns out the players are right when they suspect something is biased against them. In Everquest when you cast a spell, there was a chance the spell would fizzle. Occasionally, someone would get a streak of fizzles. Many argued this was just the normal streakiness you expect when you are do repeated independent trials. Some insisted that fizzles streaks were more common than you'd expect based on that model. Finally, a statistician who also played EQ spend some time gathering data, and determined that fizzling was not independent. Your fizzle chance was an increasing function of the length of your current fizzle streak, up to a cap. Things like that give a game character.

6ren 14y ago

A market would also fix this, in effect averaging over the entire population. Given players' anger at pieces not dropping as often as they "should", the market would converge approximate the true ratio between drop frequencies of different pieces.

jrajav 14y ago
Final Fantasy XIV did this very well in my opinion. They designed for the economy right from the start, and everything revolves around that (and the amazing graphics, music, and exploration), rather than spells, grinding, and raids.
endtime 14y ago
Except that the most desirable loot was invariably soulbound: http://www.wowwiki.com/Soulbound http://www.wowwiki.com/Soulbound

ChuckMcM 14y ago

Too bad the WoW random number generator was flawed, somewhere in there it had the clause if (item == tier2.druid.pants) return (item = plate-wearer-loot()); Of this I am certain.

Zenst 14y ago
May be the case that it was coded with one version of a programming language and upgraded later and the newer version changed the handerling of rounding. Believe python from 2.0>3.0 had some difference along those lines and whilst on the surface may not mean much they can add bias into what you get dropped as rounding and somebody adding .5 will never get the low value with some rounding as it will always round 0.5 or > to 1 as apposed to some which demand at least be > than 0.5 . Yes there are standards, but they advance and evolve over time and we all know intergers are completely different from floats. Last thought, if there was a truely random number generator then why do fruitmachines have control systems to monitor the distribution and with that what is paid out to maintain that x% payout to comply with laws that say x% of money taken has to be payed out. Mostly 70-80%, but does vary and whilst the legal min may be say 70%, some casino's and the like will generaly have a higher % payout in a promenant place, just so people think it's even higher.
- lutusp 14y ago
  > Last thought, if there was a truely random number generator then why do fruitmachines have control systems to monitor the distribution and with that what is paid out to maintain that x% payout to comply with laws that say x% of money taken has to be payed out. That's easy to answer -- to comply with rules that require a certain outcome some x percentage of the time, one need only take a truly random generator's output and filter it by x: outcome = (rn * 100 <= x); If rn is a float, lies between 0 and 1 and is truly random, then the above trivial filter will produce the required distribution in the long term.
cheald 14y ago
Nah, the game just used up all its Druid loot luck in Molten Core. Those frickin' salad shoulders.

cheald 14y ago

It's also worth noting that Blizzard recognized this and "fixed" it in their questing system by progressively improving the drop rates of quest items for players, which provides a natural upper limit on "bad streaks" for quest drops, as a means of reducing player frustration without removing all randomness from the system. http://www.shacknews.com/article/57886/blizzard-details-secret-world-of http://www.shacknews.com/article/57886/blizzard-details-secr...

_casperc 14y ago

I have another anecdote from WoW regarding randomness. The raid boss Onyxia (a great big dragon in a cave, which you could only kill once a week as i recall) had a phase where she would take off and fly above the raid. Once in a while she would then do a deep breath, a fire attack which had a high chance at killing you if it hit you. Now, all sorts of tactics emerged on how to handle the fire attacks. One that stuck for a very long time was that the number of DOTs (Damage Over Time) would lower the number of deep breaths you got. I'm sure there were other theories as well, but this one stuck for years with raid leaders yelling at warlocks, the class with most dots, to add more dots and even stacking the raid with warlocks to get as many dots as possible (we need at least 4 warlocks to take her). In the end there was a developer (or just Blizzard employee) who admitted that it was in fact random. This story pops back in my head once in a while because I think we do this a lot on larger scales too without realizing it: See some phenomenon caused by randomness, come up with a theory, and because it is not easily refuted (after all it works most of the time right?) it becomes common knowledge that everyone follows.

Too 14y ago

That's interesting, because in WarCraft 3, by Blizzard, randomness is designed to be "fair". They use a special word for it but i can't remember it at the moment. For example, there are certain items that can give you a chance to blow a "critical hit", a critical hit multiplies your damage with X. Say an item gives you 30% chance to do 2X damage. However, the randomness has memory and is designed to distribute the critical hits evenly by gradually increasing the probability for every non critical hit and resetting it for every critical hit. So the first time you hit the chance isn't actually 30% but more like 10%. If you miss 3 times the chance of the fourth hit being a critical is more like 40-50%. The hit after that will be back on 10% probability. (Just picking numbers out of the blue to illustrate the concept, I'm sure there's some more thought through math behind it) As the nr of hits goes towards infinity, 30% of them will still be critical but the chance of getting streaks of non-critical or streaks of critical hits is very low. In practice it works very well from my experience. It is however not completely exploit-proof, you could for example go and increase your probability of initially blowing a critical hit by first making a few hits on NPCs and then go to battle against a harder enemy. But that's more of a hypothetical exploit as the time and risk of doing this simply isn't worth those few extra percent.

Too 14y ago
I guess applying this concept on item drops available to every player on a whole MMO-server isn't as simple/fair as remembering the outcome of hits for a single player.
ufo 14y ago
I see most people refering to that as a Pseudorandom Distribution, although this is Dota terminology so I'm not 100% sure its the same word.

emp_ 14y ago

During the first long raid (Molten Core) the loot table had a weird deviance of being very similar depending on the player that created the raid, Blizzard said that was impossible but in reality guilds would just rotate the raid leader until they hit someone that "would", for example, drop the legendary bindings and stick with that RL for a while -- it worked for many people and 4 or 5 years later one dev finally answered the big question: "Is loot defined when you kill the mob" or "is loot defined when the raid is instanced" which is the second option, the sum of these plus some weird bug that they might have fixed silently at some point might have caused the RL rotation hoax.