Thursday, November 17, 2005

The Problem with Luck

I am sick to death of people complaining about luck in their board games.

OK, fine, if you can't stand luck at all, and you spend your life playing Chess in a hermetically sealed bubble, I won't complain. That's your call.

But this article is for the rest of you, who happily draw cards, pick tiles, and maybe even (heaven forbid) roll dice in your favorite games--who do all these things, but then complain about the newest Beowulf, Settlers, or Louis XIV, because it's trendy to do so, and all the cool kids are. I'm sick to death of people complaining about luck in their board games because, simply enough, most people don't understand how randomness actually works and don't understand how moderating luck is an important game skill.

The Truly Lucky Game

Yes, there is such a thing as a truly lucky game. Candyland is one of the most simple and obvious example. You draw a card and you move forward to the appropriately colored space.

What's notable about Candyland, however, isn't the fact that there's a random draw of the cards. Instead it's that there is no option for choice. You can't do a darned thing to make your next draw of the cards more or less useful.

That's a truly lucky game.

Controlling Luck

Let's move on to These Games of Ours, which aren't truly lucky in nearly the same way. I think many people would admit that one of the "luckiest" games around is The Settlers of Catan. Don't roll your numbers and you don't produce goods, period. This is lucky, but probably not as much as most people think.

Part of the feeling of luck in The Settlers of Catan is human psychology. We always remember the unusual, not the usual, so that string of no "8"s for half the game stands out, while the other three games where "8" came up an average amount of time aren't remembered. That's Fortune Telling 101.

However another reason that people feel that Settlers of Catan is luckier than it actually is is that they do a bad job of controlling their luck in the game.

Consider the following situation: you have a wheat production on an "8" and you're given an opportunity to build a second wheat production either on an "8" or a "10". Which do you do? Statistically "8" is a better choice, because you're 5.5% more likely to produce there (13.8% v. 8.3%). However that presumes that an arbitrarily large number of rolls will be made, sufficient that all numbers produce according to their probabilities, and that's just not the case in The Settlers of Catan, particularly not as the game goes on. Instead the "10" can often be a better choice because it insures you against a slightly (but not very) unlikely event where "8" doesn't get rolled enough in a single game.

If you complain about the luck in Settlers, but you greedily grabbed up only the most likely production numbers, even if it meant clustering on the same numbers, then it's your own fault that you did poorly, because you didn't attempt to control the randomness of the game.

Risk v. Reward

Another way to look at how to control luck is by measuring risk vs. reward. This is actually a central basis of many games that people call "lucky". In my Settlers example you took a bigger risk (clustering on fewer production numbers) in the hope of a bigger reward (more production). That's fine. It's a meaningful choice, but step up and admit your own culpability in your loss.

Be a man. (Or woman. Or meeple.)

Beowulf is the game that really got me started on this article, and it has the exact same structure. If you take more risks, you're likely to earn more rewards, but you're also likely to be punished more if you fail at the risk. Figuring out when your level of risk is greater than the potential reward and when your level of reward is greater than the potential risk is the heart of those games, and if you're not able to do that well, 3 games out of 4, that's why you lost, not because Joe or Fred got particularly lucky.

Risk/reward's less probabilistic cousin, which you might be more familiar with, is the cost/benefit analysis.

Consider Age of Steam where you might say, "If I defer a move action to upgrade my locomotive from 4 to 5, instead of doing two 3-value moves, I can instead do one 5-value move. Therefore I have a cost of 1 point, plus the cost of using a better cube, all paying for the benefit of upgrading my locomotive." And then you figure out if the cost or the benefit is greater. If the cost is greater you don't take the considered action, if the benefit is, you do.

You can make a similar analysis in Beowulf where you say "I have a 25% chance of failing this risk, which results in my gaining a second scratch and having to defer a draw of two cards down the line to heal myself, but I have a 50% chance of getting one card from the risk and a 25% chance of getting two." And then you figure out if the risk or reward is greater. In this case I can even thumbnail that caculation: the risk = 25% * 2 cards, or a loss of half a card, while the reward = 25% * 2 cards + 50% * 1 card, of a gain of a full card. I take the risk because it has a sum half-a-card benefit.

If you're doing these types of thumbnail calculations, and when you're familiar enough with a game they'll come naturally, then you're playing a risk/reward game right, and if you're just taking chances as they strike you, that's why you're losing.

Perceiving Luck

The thing that really drives me crazy about complaints about luck in games is that it's all about perception. First off, if someone does well in a "lucky" game, more often than not it's attributed to luck. If someone played brilliantly, but was also a little more lucky than average, we see the luck but not the skill.

More importantly, though, people seem to have major knee-jerk reactions to "luck" in a game if it's easier to see. Take Louis XIV an analytical gamer's game released this year. Everyone and their brother complains and complains about the fact that some points are distributed at the end of the game based upon which shields players (randomly) collected.

The thing is, it's just a few percent swing on the points. A player is very unlikely to get more than 1 or 2 points other than his expected value. And, I've never seen those one or two points actually make a difference in a game. I'm sure if I played enough I would, but I consider that a pretty minor cost to the benefit of the game not breaking down with end-game paralysis and king-making.

What really bugs me is the fact I don't think the shields are even the largest random element in Louis XIV. That would be the mission card draw, where randomly drawing particularly good or bad cards can give you very quick swings of +5 points (or alternatively the loss of the tokens that you need to turn in for those same points).

But because the shield lottery happens at the end of the game, everyone kvetches much more than is warranted, and because the card lottery happens on a turn-by-turn basis, everyone forgets about it.

And before I close out, let me offer an additional note about Louis XIV. As with any good game, there's an opportunity to control your luck, to balance risk versus reward. If you lose a game because you tried to take a medium mission, when you might have been able to complete an easy one, that's your fault, and if you won a game because you against all odds completed a hard mission with a lucky draw, that was a reward for the risk that you took.

Probability as Meta-Game

Perhaps people could deal with luck better if they understood it was a sort of meta-game. Yes, I might win an individual game of Settlers/Louis XIV/Beowulf due to a particularly lucky opportunity, which usually means a long risk that I took. You can similarly sometimes win Poker, Bridge, or almost any classic game due to a risk.

However if you keep taking those long risks, you're going to lose a lot more than you win, and that's the meta-game that you have to keep in mind in any game with any random element in it. Poker makes it easy, because those chips mark how someone is doing, long-term. Similarly Bridge has a clever invention called "points" to mark the same. These Games of Ours are longer, and so we usually can't play multiple rounds of a game to even out the luck, but if it really bugs you, figure out how to do so.

In your secret little game notebook you can keep track of how often you beat Crazy Harvey, and then that one time his long risk comes through will be more obviously the fluke that it actually is.

Understanding Luck

I suspect that a lot of players would be a lot happier with the luck in games if they understood the odds. I mean, you don't hear a lot of whining about how you can win a hand of Poker if you happen to draw a Royal Flush, because the average player understands that a Royal Flush is pretty unlikely, and that the idiot player drawing for the same will lose the other 649,739 times.

So, before you condemn the "luck" in a game, try to at least understand it, and to help with that I offer two simple thumbnails for probability calculation.

First, the odds of an event occurring are the numbers of ways it can occur divided by the total number of possible events. So, take Memoir '44 as an example, where you attack with a die with 6 faces: infantry, infantry, tank, grenade, star, retreat. The odds of hitting an infantry with a die are thus 3/6 (infantry, infantry, grenade), the odds of hitting a tank with a die are thus 2/6 (tank, grenade), and the odds of hitting an artillery with a die are thus 1/6 (grenade)--50%, 33%, and 16%.

Second, the expected value (E.V.) of something occurring is the probability of it occurring, times the number of times you take that chance. So, if you're throwing two dice at infantry in Memoir'44, your expected value of kills = 2 * 50%, or 1. If you hit 0 or 2 times, that was slightly unlikely. I'm amazed how often someone has the expected value for something happen in a game, then curses their luck. ("How could I only get one infantry!?")

Finally, with these two simple statistical ideas, you can even start making some good strategic plans. Take Memoir '44 again. By looking at the expected value of a single die roll and the number of hits required to destroy a unit, we can then quickly calculate how many dice we want to throw to have an average chance of destroying a unit:

UnitSizeHit E.V.
per Die
Avg. Dice
Needed
Infantry450%8
Armor333%9
Artillery216%12

And that's one the clearest examples I can offer of how actually understanding the probability of a game, instead of just complaining about it, can improve not just your game experience, but your gameplay too.

15 comments:

Dwayne "aka okiedokie" said...

I've heard "it's a poor athelete that blames his equipment" and I feel that it's a poor gamer that blames the dice. It's a GAME and part of the GAME is being able to CHANGE your behavior when something UNEXPECTED happens (like CHANCE or LUCK).

If I get a string of bad (perceived) rolls, how I respond to them is how I guage how well I play. I may not finish first, but if I finish better than some monkey handed the exact same situation, then I consider it a win.

ekted said...

100% information abstracts have their place, but luck can make even the deepest game fun, not to mention provide a changing "landscape" every game.

GROGnads said...

heh heh heh, I could say the same thing concerning "Battle Cry", as I've 'seen' where I was about to WIN with just '1' more lousy "Flag" to grab, and THEN have my 'opponent' come from behind(needing at least '3' himself!) and 'steal' MY "thunder", while they GET the WIN! But, that's the "fortune of WAR!", or what I'd attribute this to, and it does actually occur in some instances. Now, I've 'mellowed' considerably in my temperament, ever since my younger gaming "daze", as I tend to let others make 'mistakes' that I will point out to them when it's MY 'Turn'! "Play and LEARN from the 'Master' !" is my credo, but, they never do...

Coldfoot said...

My head hurts.

Fellonmyhead said...

It's all about perception, this "luck" (I hate using that word, for reasons I may divulge elsewhere).

The coat-of-arms draw concerned me when I bought a copy of Louis XIV (solely from hearsay). Our first game was decided on them which wasn't encouraging; however the player who took victory had gone after them in the final round with the aim of tipping the balance in his favour. Everything else was roughly equal between three of us. I would call that a well calculated risk.

This hasn't got back to the table, however; I think this is because of two reasons. The players found the flow of play rather stagnant and it only seats four (an awkward number when we're usually five).

Shannon Appelcline said...

We played Louis XIV again last night, and one of our players called the shield lottery a "tie breaker". That's pretty insightful, and I think accurate.

The end score was 44-43-39-37.

The winner, who had played for shields, had probably one shield less than he should have, and I, in second place, probably had one more. As usual the distribution of the shields didn't actually make a difference in winning.

DWTripp said...

One thing I have noticed is how many people don't easily observe that they do "average" out over the course of a game involving dice.

You are correct in that some tend to perceive only the things that don't work out and "forget" those that do.

If you have a specific number or result you need you WILL most certainly get that result. You may just not get it when you need it. Your M'44 example is a perfect one. I have played perhaps 100 games of M'44 and on many occasions I have rolled three infantry sides out of three dice. The fact that I sometimes happened to be attacking tanks made that "lucky" roll less useful.

Sometimes reducing the random factor improves a game mechanic. The recent release of Railroad Tycoon (a derivative of Age of Steam) actually has less luck in it than Age of Steam. All the product locations are known upfront. The starting cards are known up front. So it comes down to your willingness to bid for starting player in each turn so as to take advantage of what's known.

Behind almost every die roll, card shuffle or tile draw there is a decision or series of decisions that either enhance or degrade the usefullness of the random factor. Bitching about it is a sign that the player has a less than comprehensive grasp of the game mechanics and the odds.

Nice article... one of my favorite subjects.

huzonfirst said...

Shannon, I'm sure there's plenty of gamers who don't understand basic probability or risk mitigation, but I assure you that I and many other gamers I know who prefer less luck in games grasp the concepts quite well. We just like more control in the games we play.

I've talked quite a bit about the difference between Situation luck (where you can react to the randomness) and Resolution luck (where you can't), so I won't beat that dead horse again. You'll just have to believe me when I say that there's a huge difference (to me, at least) between figuring out how to best use the cards I draw in Louis XIV (that's Situation luck) and the total crapshoot of the shields at the end of the game (which is the ultimate in Resolution luck, since the game is now over!). (Louis isn't the best example in this regard, but it's the game you brought up.)

By the way, a couple of my games of Louis have been decided because of unusual shield distributions. It's not the worst thing in the world, but it does tend to take something away from the win (and annoys the second place player). I wish the mechanic wasn't there, but it's not enough to stop me from playing what is otherwise a great game.

Sorry to read about your sickness, but it doesn't alter the fact that many people who contend that Game X has too much luck for their tastes aren't trying to emulate the cool kids. They're just stating their preference in games. Different strokes, and all that.

MMM said...

Well written and well said. Half of getting lucky is putting yourself in position to benefit from that dice roll in the first place. As DW said, too much emphasis tends to be put on the final determining element - ie the random event that swings one way or another - and not enough on the myriad of decisions that lead to that point in the first place.

ChristopherA said...

I think that one of the issues for the more serious gamer is that they have so many games to play that they seldom play a single game very often. When randomness is a significant factor in a game they'd have to play it too many times to determine that it truely is their skill and not luck that is causing them to win or loose.

ChristopherA said...

I liked in some of your TT&T articles the discussion of "random" vs. "arbitrary". I rarely see in discussions of luck in games the distinction.

Shannon Appelcline said...

Huzon: Thanks, I appreciate all the thoughts, and I definitely understand & appreciate that there are folks who just don't want luck (or certain types of luck) in their game.

However to your two types of luck, 'resolution' and 'situation' I'd add another axis. You also have controllable and uncontrollable luck, the first of which you can set yourself up for and the second of which you can't.

So, using a combination of terms, I'd call that LXIV shield lottery 'controllable resolution luck'. Yes, you can't react to it afterward, but you did have some control of the situation beforehand, based on how heavily you went for shields.

Chris: It can indeed be hard to see what's luck and what isn't. Heck, you surely remember my long string of losses on _For Sale_ until this GenCon. It would have been easy to mark that up as luck if, perhaps, my losing wasn't *so* consistent.

And, yeah, the arbitrary/random/chaos distinction is a good one. I considered talking about it here too, but really every type can be offset in some of the same ways. I was considering reprinting my Skotos/RPGnet article on the topic next week, but eventually decided to save it until I revamp all those articles. I've learned a lot about games in the last two years.

But:
http://www.skotos.net/articles/TTnT_106.shtml

For anyone interested in looking at it now. It's my discussion of types of randomness in games and why you want them.

huzonfirst said...

Shannon, I think I'll have to disagree with your definition of "controllable" and "uncontrollable" luck, at least with respect to the shield mechanic in Louis XIV. Obviously, you have some control of how many shields you accumulate over the course of the game. But once that number is set, you have NO control of how many bonus shields the end-game lottery grants you. I have 12 shields, you have 10. You wind up with 4 bonus shields, I get 2 (I've seen this happen). In a close game, I could easily lose to you in a tiebreaker, when I "should" have had a rather comfortable three or four point victory. I did everything in my power to control the shield totals and achieved an advantage, only to see it frittered away through blind luck. That, my friend, is not controllable luck.

The usual response at this point is, "you could have picked up a 13th shield and won despite the bad break". This assumes that acquiring an extra shield has no opportunity cost. Assuming that I've played well, the cost of getting that extra shield was probably one fewer mission accomplished, obviously a bad bargain. The point is, I could have played optimally and still lost due to bad luck.

The truly annoying thing about this is that it's so unnecessary. Having a pure luck conclusion to a high-skill game like Louis sticks out like the proverbial sore thumb. It would be like finishing up a game of Puerto Rico by having everyone roll a D6 and add that many VPs to their total. Something like that may work fine in a game like Killer Bunnies, but not PR. And even if you allow the possession of certain buildings modify that roll, the fact remains that the game could be decided by a random process at its conclusion, for no apparent design reason.

Shannon Appelcline said...

Well, the thing about randomness is that it's *never* entirely controllable. *That's* why it's randomness. You can set yourself up to try and take the best use of probabilities, but that's as far as you can go, and then it's a literal crapshoop.

I'd agree with you about the shield draw being "unnecessary", except I don't believe it'd be in the game if it were. My long-held presumption is that it's there to keep people from breaking the game in the last phase by counting up VPs and making king-maker moves. I'm generally willing to trust good developers & designers on this sort of thing, and LXIV has both.

However, it's also easy enough to avoid. Just give people 1 extra shield per 5 shields, or something like that. And then you can see if knowing the precise scores causes king-making in your group of not.

Mario T. Lanza said...

Your post is provocative and largely accurate. I agree with it.

However, not all luck can be mitigated. In Setters, the design itself mitigates the luck in that the dice are rolled dozens of times allowing for the bell curve of expected results to equalize. Still other designs that use die rolls to determine outcomes may not require very many rolls, thus the bell curve could be totally "off" even by the end of the game. It might take many other playings to follow (as noted by christophera) before the curve equalizes. The results in each game ; however, may appear and, in fact, be more chaotic, creating a luckier environment for some.

Take Louis, a game without die rolls. I may evaluate everything as well as my best competitor matching him mission for mission and shield for shield. Still, if his shields put him in the lead more often, he wins. It was luck.

I'm not at all against luck. I like hedging my bets and applying other tactical choices just as you've described them. I'm okay with losing even when I played spot on, due to a luck. That doesn't mean, however, that I won't chose to mostly play games where luck can be better mitigated. In my mind, better designs allow for better luck mitigation. As noted, Candyland allows for zero mitigation of luck.

One other factor that comes to mind is timing. In development games early bad luck may stunt my growth more severly than others and I may never be able to recover. Again, the design of the game affords for the mitigation of luck. The best designs offer ways to mitigate luck so that every player can expect the hope of victory to be based "somewhat" on the quality of his decisions.

All in all, mitigating luck is a tremendous element of Eurogames. It makes them more enjoyable than chess.