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:

Unit	Size	Hit E.V. per Die	Avg. Dice Needed
Infantry	4	50%	8
Armor	3	33%	9
Artillery	2	16%	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.