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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

• 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).
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  • 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
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        • 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.