Luck

Ahhh, luck – that mysterious, oft-fickle force which evokes so much glee or misery. There’s no consensus opinion among players on whether luck and randomness enhances the gaming experience or detracts from it. From a designer’s perspective luck is neither intrinsically good nor bad. Because the collective gaming audience has such broad tastes a game can easily live one end of the spectrum and be completely deterministic or it can fall at the other extreme and be almost entire based on chance and either way still appeal to a vast number of people. While this does mean a game will find fans no matter how much or little it relies on luck, careful analysis must be done to guarantee the effect of luck is actually what the designers had in mind. In this article I’ll examine what “luck” means in the context of design, as well as a few common applications of it and what these do for a game.

What is Luck?

Before investigating what luck does, we first have to establish what it is. In a broad sense, luck fits under the larger umbrella of randomness, but for this article I’m going to focus on luck simply in the traditional sense of “having good luck” or “having bad luck.” This narrow focus still leaves us with plenty of material to cover, and none of us want this to end up being twenty pages long.

When faced with a situation with an unpredictable outcome, all of us will formulate some idea of what the ‘average’ result should be. “Luck” in the game design universe is when the actual results differ from these expectations due to forces outside of the control of the players. You might consider it ‘bad luck’ if you’re playing rock-paper-scissors and you choose scissors, while your opponent chooses rock, but your defeat was the result of the choices made by you and your opponent rather than the game itself. The only luck we as designers should worry about is when they’re an element no one controls – things like rolling dice or drawing a card from a shuffled deck. AI opponents in computer games are a tricky grey area because, technically, they’re just another system that lives outside of the player’s influence – but there’s a lot more to dig into with this topic so I’ll save that for another day.

Before digging into too much detail, let’s use combat damage as a simple example of what good and bad luck can look like in a game. You’re in control of a melee fighter in an RPG. We’ll say that your basic sword attack does, on average, 10 damage. If you did exactly 10 damage with it you’d say “yep, makes sense.” Obviously no luck involved there – the results matched the expectations perfectly. On the other hand, if you did 15 damage that would be ‘good luck’ and if you did only 5 that would be ‘bad luck’. Your actions might be guided by the perfect strategy, or maybe an absolutely stupid one (I’m going to first hit him with attack A, then finish him off with attack B!), but once you’ve pressed the button to attack the ultimate outcome leaves your control and enters the realm of luck.

Now that we have a established what luck is, our next task is to identify its purpose. The main effect luck has is to add suspense. This can be ‘good’ suspense (“I wonder what’s behind prize door number one… oh wow, now that’s awesome!”) or it can be ‘bad’ suspense (“Man, if I don’t roll a six here it’s all over…”). The moment when you’re anticipating the next card to be flipped over can be incredibly tense. The game which has always stressed me out the most is poker. While a big part of the suspense offered in that game is not knowing what cards your opponents have in their hand, there’s also a significant element of luck – you or your opponent might be holding pocket aces and lose to a 7-2, or you could be sitting on an extremely poor hand and have only a single out in the entire deck but still miraculously hit it.

 

So what does Luck do?

As noted above, players have very different feelings towards luck. Highly competitive gamers, in general, tend to hate any form of randomness because this sometimes leads to less skilled players winning. If you ask hardcore Magic the Gathering players what they think of the possibility of being “mana screwed” (where, due to bad luck, you don’t draw enough land cards to cast your spells) – nearly all of them will say they hate it.

At the other extreme, very casual players often enjoy games with a great deal of luck. Many won’t actually come out and say “I really like games that are completely random!” but whether they realize it or not, luck is usually taking their side behind the scenes. Players that are significantly less experienced or talented will find it nearly impossible to win games that are entirely skill-based. Very few of us would keep at it if we played 10 games against someone and were utterly destroyed in all 10. The mere luck of the draw in Magic will often lead to a complete newbie winning at least a couple of those games. This is one of the most significant reasons why Magic is constantly being revitalized with new blood, and why you can’t really say the same about chess.

Another way luck appeals to casual players is that it offers interesting surprises. If you’re not going to bother playing a game 50 or 100 times and master it, a few random wacky events help make a game more memorable. The reality is that most people only play a game a handful of times, and for this audience the fact that a game is well-balanced or highly skill-based is completely irrelevant.

One of my own experiences that serves as a good example of luck making a game memorable is one time I played the Settlers of Catan tabletop game. For those of you unfamiliar with it, dice are rolled at the start of every turn to see what resources players collect for that round. Each player has ‘ownership’ over a couple dice result combinations, and the luck tends to even out over time. However, in this particular game I went 17 (yes, seventeen) turns without getting anything. That, my friends, is the definition of bad luck. Someone did the math and I think the odds of that happening were so low I could have won the lottery a few times and been less ‘lucky.’ While I certainly wasn’t happy with Catan at the time, I’ll certainly never forget that experience, and I’m now glad to have such a ridiculous memory to share with friends. On the other hand, had that particular game been during the GenCon Masters Tournament I probably wouldn’t be laughing about it now!

The types of surprises which appeal to casual players can also be less dramatic. For example, in a game like Civilization a tribal village (aka “goody hut”) could occasionally surprise the player by giving a much larger payout than usual. This kind of bonus will excite some, but the more hardcore will often find something like this imbalancing. Neither approach is inherently right or wrong – it simply comes down to what the designer’s goals and priorities are.

 

Common Applications of Luck

One of the most prevalent uses of luck in games is when dishing out rewards. When players open up a treasure chest, they often wonder what’s inside. Will it be more boring money? Will it be a potion I can use? Will it be something awesome this time? The possibility of lucky results can tickle an almost gambling-like part of the brain.

A very polarizing mechanic that leans heavily on luck is the “grind in order to hit the miniscule chance of getting something really awesome” that many players are familiar with. For some, this ‘works’ and they might even call it fun. The tiny probability of finding a rare Pokemon, or getting an uber-epic loot drop in name-your-Blizzard-game is a major reason why those games have such a large and dedicated following. But the downside of this mechanic is the brain-dead grinding necessary to earn your shot at the big payout. While I can’t claim to have never played or enjoyed these games, one would be hard-pressed to claim that it’s actually good design and not just psychological manipulation. The only reason rewards of this sort are so satisfying is because they required spending an hour (or fifty) doing something unfun – it wouldn’t be nearly the same if it only took three tries.

In many games, combat is one of the places where luck is most on-display. Earlier in the article we looked at a simple example of randomized damage. In general, a large variance in damage reduces the value of strategy, while systems with a very small variance are vulnerable to being reduced to a simple formula – “I do move X, then two Ys to kill this type of enemy.” Games with a deep combat system can minimize this tendency, but doing so effectively is a very difficult achievement. Most games are best-suited for the middle ground which avoids the problems found at the extremes.

Critical hits are another way combat in games use luck to spice things up. It can be exciting to do a bunch of extra damage when you only have a 1-10% chance of doing so. However, if this likelihood creeps much above that range players will come to expect a critical hit and be disappointed when it doesn’t happen. Something else for designers to keep in mind is that while landing a critical hit on an enemy is awesome, being at the receiving end of one is not nearly as gratifying. A game can strive to be completely ‘fair’ and subject human and AI to the same rules, but developers less dedicated to that noble pursuit might consider ‘fudging’ things a bit. The only place “fun” really exists is in the player’s head, after all.

The final application of luck I’ll talk about is the player’s access to resources. A “resource” in this sense can be anything from an actual source of iron on a map to the amount of mana in your opening hand of Magic. It’s simply the stuff players must obtain in order to unlock certain actions. Luck of this type is most often confined to the strategy genre – the environments in other types of games like shooters and RPGs tend to be mostly static. The purpose of applying luck with resources is usually either to force players to adapt (“hmmm, no iron… I suppose I should play for science instead”), to marginalize ‘perfect’ strategies that can unhinge a game (just imagine what Magic would be like if you could order the deck in any way you like!), or simply to provide variety. Randomized maps fill this role superbly and there’s a lot more to discuss with them, but I’ll save that for another article!

Luck can make a game beloved or reviled. Designers should ponder not only “how much luck is there in my game?” but also “how is luck used in my game?” Luck is a major force in shaping players’ experiences, and we have to ensure we’re using it, instead of letting luck take the wheel and send our games to places we don’t want to go. As with everything in design, we must maintain a clear focus on the goals we’ve laid down and ensure the systems we craft don’t betray our intentions.

- Jon

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13 Comments

  1. My experience is that there’s a subtle distinction between luck and randomness, and I think it depends on whether or not the mechanics are transparent/flexible enough to allow players to make choices about it. Yes, some amount of risk is fun, but only when the player is willing to accept the consequences of a bad outcome.

    Personally, I do not like situations where luck overrides skill. Even Magic allows for a mulligan if you don’t like your initial hand. And of course, with competitive multiplayer, one player’s good luck is necessarily another player’s bad luck. Inexperienced players might win occasionally because of it, but seasoned players hate to lose because of factors entirely beyond their control.

    Reply
  2. Total determinism is the design philosophy behind Starcraft because its multiplayer mode is aimed at hardcore tournament players, but personally I prefer some degree of randomness. The art is creating randomness so that players can have unexpected success or disaster but not so much that the entire game is won or lost because of it.

    The old randomized damage in combat is a basic mechanic that works very well for that because it evens out over lots of units produced in a game. The fewer repetitions of a random choice, the greater the danger that it turns the whole game into a die roll. Example: starting positions in Civilization, which had to be increasingly de-randomized to avoid completely screwing over players who start in a poor location.

    Reply
    • Kitaru

       /  July 10, 2012

      StarCraft is not exactly deterministic; although direct melee attacks have a 100% hit chance, ranged attacks can miss. If the attacking unit is at a lower elevation than the target, or the target is obscured by certain map elements (trees, signs, etc.), there is a 53.125% chance of a given shot hitting. Even under normal conditions (same elevation, no obstructions), there is a 1/256 chance of an “air shot” that misses the target anyhow.

      Reply
      • quanticle

         /  July 11, 2012

        In original Starcraft and Starcraft: Brood Wars, yes, that was how the system worked, but in Starcraft 2, it’s been replaced with much simpler system whereby units on a higher elevation are simply untargetable by virtue of being out of sight.

        Frankly, I prefer Starcraft 2’s system. In my eyes, one of the (few) flaws in Brood Wars was that terrain never seemed to matter all that much. Yes, maps could have ramps and choke points where the defender could potentially make a stand and hold off a superior aggressor. Their effectiveness, however, was undermined by the fact that the attacker could just spread out along the low ground and still hit your clumped up units on the high ground well enough to nullify the existence of the choke point.

        Contrast this with Starcraft 2. In Starcraft 2, there are no randomized misses (outside of a few abilities, like the Seeker Missile). Instead, units on the low ground simply cannot see (and, therefore, target) units on the high ground. This seeming restriction, in fact, actually expands the number of options that players and map designers have. Players have to show more depth and skill because victory at a ramp or a chokepoint is no longer guaranteed to the one who brings the most firepower. Mapmakers, too, have a larger number of options in map design, because it is easier to use the terrain to restrict the things that the player can do at any given time. In short, I think that move away from a luck-based combat system to a strictly deterministic combat system has added strategic depth to Starcraft and made it a more enjoyable game to play and watch.

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  3. LORD-ORION

     /  July 9, 2012

    Catan and people’s warped sense of probability…

    I actually played my 1st game of Catan a week ago and it’s funny compared to your example. (Can you remember all your starting settlement tile numbers? I am interested in that)

    In a 4 player game that lasted 60 turns, 8 did not come up once.

    This was problematic for the veteran player who started with 2 settlements, one each next to the two “8” tiles.

    Bad luck, cursed dice? Or failed gamble and basic failure to grasp probability within the game’s framework?

    Before we start: Remdial Dice Probability for everyone

    There are 6 ways to get a “7” when tossing 2x 6 sided dice. 1+6, 2+5, 3+4, 4+3, 5+2, 6+1.

    As such, the chance of rolling a number with 2 six sided dice.
    7 = 6/36
    6 or 8 = 5/36
    5 or 9 = 4/36
    4 or 10 = 3/36
    3 or 11 = 2/ 36
    2 or 12 = 1/ 36

    Here is the problem with going with both settlements on 8. (or 6, but this is not the example I am using)

    1) You cannot convert resources into “things” unless it is your turn, so if you are hoping for a double pay day to power build something, statistically speaking it isn’t going to happen on your turn, and you’re more likely to have the same amount of resources to spend when your turn comes up anyways.
    2) What if an 8 is not rolled? Although 8 and 6 have the same probability on any dice toss, if an 8 is not rolled, 6 is the next number that is more likely to be rolled before any of the others.
    3) You might not think it, but a 5/36 chance not coming up in 60 tries is not a statistical aberration. You can expect something similar to happen roughly one in every 7 games you play.
    4) There are not enough turns in a typical Catan game for uniform probability. Maybe if 8 didn’t come up after 361 turns you might banish the dice… but that is not a concern you are going to ever face in 1 game of Catan.

    Of course Catan is more complicated then just dice tossing… but I see people having this ongoing problem with probability and applying it strategically to the rules of a game all the time.

    Reply
  4. AndyM

     /  July 10, 2012

    When I did the math on a 5/36 chance not coming up in 60 trials, I came up with a bit higher than a 0.0125% chance of that happening. I suppose it depends on how you define “statistically aberrant”, but I would consider a 1-in-8000 chance to be pretty unusual. What calculations did you use to come up with your numbers?

    Reply
    • Daniel

       /  July 11, 2012

      Andy: that’s an application of the gambler’s fallacy. The correct math is 60 * (5/36) as the odds of rolling an 8 (or 6, independently) in a given game of 60 turns, so 8.33… : 1, or a little worse than a 1 in 9 chance of NOT rolling an 8 (or 6, independently) in a given 60 turn game. I suspect the 1 in 7 was thrown out as an off the top of the head guess, it’s not a bad estimate.

      Reply
      • Chris

         /  July 11, 2012

        Daniel:
        I believe you’re misapplying the label of “gambler’s fallacy,” and AndyM was the one who got it right. By multiplying the odds of one “8” roll by 60, you’re essentially adding the results of all of the rolls together. See here for an explanation of how that’s not correct: http://mathforum.org/library/drmath/view/56503.html

        Reply
      • Kolmogorov

         /  July 11, 2012

        Daniel, what are you talking about? 60*(5/36) is the expected number of times an 8 comes up; that is, across many, many 60-turn games of Catan, the average number of times an 8 gets rolled will tend towards 25/3 = 8.33… . The probability that an 8 does not come up in 60 consecutive rolls of a pair of fair dice is (1 – 5/36)^60 = .00012692…, i.e. the 0.0125% or 1-in-8000 chance that AndyM quoted. Rather, the 1-in-7 event turns out to be getting five 8’s or fewer in a 60-turn game, or a given 13 rolls not having an 8 come up during them.

        There’s certainly room in games like Catan for reducing the variance of your yield versus increasing its expected value, but it’s absurd to think that players wouldn’t get upset when they’re screwed over by a 1-in-8000 chance event occurring. If you try to control for an event like that in a game like Catan, you’ll just lose the other 7999 times out of 8000.

        Reply
  5. Takezo

     /  July 10, 2012

    Well designed randomness can help capture that in reality there tend to be far too many variables to allow for perfect strategies. Having your plan thrown to the wind and being forced to adjust can be a different and equally enjoyable kind of fun! But of course I can understand that some people don’t find that fun at all…

    Reply
  6. Maarten Edgar

     /  July 12, 2012

    Luck, the chance of something extreme (good, bad or different) happening, ties directly into the infrequent reward itch: mice, apes and humans, when faced with a lever which always, or on a set amount of pulls, gives a reward will pull it only when they want that reward. If however the chance of getting the reward is de-coupled from the amount of lever-pulls (sometimes it takes five pulls, sometimes the next pull rewards), all animals will pull the lever with much greater frequency. Hence the effectiveness of grinding and slotmachines.

    Luck/chance, however is the anti-thesis of ‘fair'; you can’t have a game which is fair and involves luck … . Of course, two players in a game have the exact same chance (one could say: luck distribution) of something happening, and in that a game could be called fair by an outsider, but tell that to the unlucky player.

    The real question is not a question, but a debate: when is it ok to apply luck and when isn’t it? And to what degree do you allow it to happen.

    I think of it as a Gauss curve, with good outcomes to one side and bad ones to the left. If a game mechanism is decided to be determined/influenced by luck/randomness, the debate should be what frequency good/bad luck should occur and what amplitude/effect it has (respectively the area under the curve and the length of the outliers).

    That’s all nothing new, but it occurs to me that you could extend this plot into 3d, plotting luck against time (extruding the Gauss curve, if you will). The shape/thickness of this “Gauss tube” can be played with, determining and influencing the feelings a player has over the course of playing the game.
    Come to think of it, this representation could be applied to a lot of systems in a game, all influencing the player, nudging him into certain directions of play and/or emotional state!

    Reply
  7. Stephen

     /  July 12, 2012

    One of the modifications for luck I find really interesting is pre-determining when a player will be lucky. Valve does this with hat drops in TF2, where they calculate once when the next hat will drop, rather than rolling every single time you do something. Doing this makes REALLY bad luck impossible, because you can set upper limits on success and failure rates, and effectively reduces randomness in the short term, all while preserving the appearance of a random system.

    Reply
  8. Matt Swanson

     /  July 12, 2012

    There is a lot a good designer can do to fudge randomness to make it work for them and reinforce fun. The elegantly simple iOS game Jetpack Joyride is a great example of this. The level layouts are randomly generated, but only within a strict set of guidelines – there is always a safe path to follow, picking up a vehicle item or losing one clears the region and gives you two “coin sets” worth of safe area to reacquaint yourself with the new control scheme, the lasers always clear out other hazards before and after spawning to give you a chance to regain control, and so on. A number of other “random” factors in the game fudge themselves toward fun – if you have a mission that requires a specific vehicle to complete, it makes the likelihood of getting that vehicle much more likely, and increases over time the more you get a vehicle that isn’t the one you need.

    Examining how the luck systems work in your game and doing some behind the scenes work to help push it closer to fun without making it entirely transparent or obvious makes your players feel more lucky, reduces frustration and can make your games more fun as a result.

    Reply

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