Luck, Randomness and Chaos: A Look at the Top 250 Games
Carl Anderson
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I've seen a decent amount of discussion on the site of late related to the amount of luck in games. From questions about which games have zero luck, to talk about what games have good strategies to mitigate the chaos, it's always enjoyable to see what's been bandied about.

To that end, I did a search for GeekLists that discussed something I wanted to investigate: What is the level of luck in the top N games on the site? I'm not sure how far I'll go; right now, I'll set a lofty goal of N=250.

I found rcarbone's list (http://www.boardgamegeek.com/geeklist/19782) that gave a rating to the amount of luck present in a game, but it's not quite what I had in mind. So, I'm creating my own GeekList.

For purposes of discussion, here are some definitions:

Chaos: Defined as the level of impact a player's actions can have to positively or negatively change the game, generally in wide-reaching ways. Games that have rigid rulesets or well-studied strategies likely (but may not always) have little chaos. As an example, Diplomacy has a lot of chaos, as do Bang! or Killer Bunnies (those two also have randomness; see below), while Chicago Express does not. Player order may be defined as chaos.

Randomness: Defined as outcomes that cannot be reasonably predicted. Dice are random; a shuffled deck of cards is random; player order is not random. For example, two players can negate white/black handicaps in Chess by playing one game as each--thus, there is no randomness, but there is chaos in the players' actions. Randomness and pseudo-randomness are defined as roughly equivalent for purposes of this list. (That is, a deck of cards, shuffled by a human being, likely can never be truly randomized; however, pseudo-randomness will work here.)

Luck: Defined as some combination of chaos and randomness. I separate this out for two reasons: first, I don't like the idea of saying that there is no luck in a game like Diplomacy, since there is chaos--the two are very different ideas; second, because I want some measure to say that Game X can be somewhat compared to Game Y, even if one is completely chaos-filled and the other is completely randomness-filled.

So with that, I'll begin adding games. I have not played all the games in the Top 250, so while I'll add the game, I'll rely on comments from fellow 'Geeks to make a judgment. So, add information on how you see each game fitting within the chaos/randomness/luck spectrum.

I'll periodically come back and revise the entries to take in information from comments.

(To keep myself sane, I plan on working on this list in piecemeal fashion. Thus, to start, I've added just the Top 10 games.)
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1. Board Game: Agricola [Average Rating:8.03 Overall Rank:16]
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Chaos: Somewhat high. A player can easily grab the last-available food space to screw you out of feeding your people in the Harvest round. Or he might grab the last Major Improvement, messing up your plans entirely. There's also some chaos coming from the play of minor improvements or occupations.

Randomness: Moderate to low. Depending on the version of the game you play (with cards or not), you either have randomness in the order that the "field" cards come out, or randomness in how your minor improvements or occupations are dealt, or both.

Luck: Even with a fairly high amount of chaos and a moderate amount of randomness, I'd say that the luck factor is moderate to low. From my plays of the game, it seems that good strategy can mitigate a lot of the chaos and randomness inherent in the game.
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2. Board Game: Puerto Rico [Average Rating:8.06 Overall Rank:15]
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Chaos: Fairly high. The impact on the game of the individual player actions (trade, build, etc.) is quite substantial. There's the oft-discussed issue of being to the left (or right, or across from, or...) of the newbie as well.

Randomness: Reasonably low. Almost non-existent. The only thing that comes to mind is the draw of the crop tiles. In my experience, this doesn't make a lot of difference in one's strategy, although it may dictate some early-game choices.

Luck: Reasonably low. From playing this a few dozen times online, and from reading others' experiences, it would seem that a skilled player will know how to roll with the punches and is going to almost always do far better than an unskilled player.
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3. Board Game: Power Grid [Average Rating:7.92 Overall Rank:28]
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Chaos: Somewhat group dependent. If you have someone who plays the part of the spoiler, buying up all the available coal just to screw over other players, the chaos can be high. If you have a group who tends to play with a mindset of buying just what they need, the chaos is fairly low. However, auctions by their very nature are somewhat chaotic as well, so take that into account.

Randomness: Very low. Aside from the order of the power plants in the shuffled deck, the game has no randomness.

Luck: Low. Chaos is what drives the luck factor here. If you have a player who intentionally cuts you off from the cheap connections, or if you have someone purchase the 8 nuke just to make you pay more, you're going to have to readjust your strategy to compensate.

(I have to admit some bias here--this is one of my absolute favorite games, so my judgment may be a bit clouded!)
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4. Board Game: Twilight Struggle [Average Rating:8.35 Overall Rank:4]
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Chaos: Moderate. Given that it's a two-player game, you're going to have a fair bit of chaos anyway, but at the same time--it's a two-player game! Thus, you don't have a large number of player styles to contend with. That said, a well-timed Headline play can certainly mess up your strategy, so there's still a fair bit of chaos going on.

Randomness: Moderate. The dice certainly add to the randomness of coup attempts and the like, and the card-driven nature of the game is inherently random. Mitigating this somewhat is the ability to play a card in several different ways (for the event, for the ops points, and so on).

Luck: Moderate. There isn't as much chaos as a game like Diplomacy, but the wide reach of the board, and all the things you have to keep your eye on, make for a chaotic situation. There's also plenty of randomness thanks to the dice and the cards themselves.
 
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5. Board Game: Tigris & Euphrates [Average Rating:7.71 Overall Rank:70]
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(I have not yet played this game, and so cannot comment on it.)

Chaos:

Randomness:

Luck:
 
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6. Board Game: Through the Ages: A Story of Civilization [Average Rating:8.03 Overall Rank:26]
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(I have played only one abbreviated game of this, so I do not feel qualified to comment yet.)

Chaos:

Randomness:

Luck:
 
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7. Board Game: Dominion [Average Rating:7.67 Overall Rank:72] [Average Rating:7.67 Unranked]
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Chaos: Low to moderate. Depending on the selection of cards available to you, you might end up with a situation of little to no attacks, or lots and lots of Witches being tossed about. Overall, though, since you're building your own deck, the chaos is kept to a minimum.

Randomness: Low to moderate. I'd argue that any game in which you shuffle cards and draw a set has a fair bit of randomness, but because you can tune the makeup of your deck, you in essence are controlling the probabilities. That helps to keep the randomness at an acceptable level.

Luck: Low to moderate. Again, given that you're shuffling a deck and given that you may or may not end up with a hand of coins that get you that crucial final province, or a Moat to protect you from the Militia of an attack-happy player, you're definitely going to see luck at play. But it's luck that, I think, is well balanced against a good strategy and a skilled player.
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8. Board Game: El Grande [Average Rating:7.79 Overall Rank:54]
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Chaos: Moderate to high. Think you've got that province all buttoned up? Ah, wait until Miguel comes in there and plops down his yellow caballeros and you'll think twice. This game also seems to have a bash-the-leader issue to it, although I hesitate to call it a "problem." Also, there's the tendency to forget all about the Castillo... Don't forget too about the bidding for turn order.

Randomness: Low. Sure, there are cards that come out each round from shuffled decks, but in general you're balancing the randomness here with card play in the auction.

Luck: Low to moderate. The chaos is what's driving things here, more so than in something like Power Grid. Also, like Twilight Struggle, you have to keep tabs on potentially a large number of provinces at once, so it can be difficult to adequately know the situation at any one time--allowing the possibility of a player swooping in and taking first place from you quickly.
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9. Board Game: Caylus [Average Rating:7.83 Overall Rank:45]
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(It's been a while since I've played this, so some of my comments may be off.)

Chaos: Moderate. The nature of the provost makes this something of a chaotic game. ("Sure, place that building right on the edge of the path...I promise I won't move the provost!") Turn order can also be an issue, especially when it comes to donating goods to the castle.

Randomness: Negligible. The starting buildings are placed in a random order, but as the comments indicate below, this doesn't affect the game terribly much.

Luck: Low. The chaos is there, but it's not tremendous, so on the whole this is not a very luck-filled game. That can be seen as one of its benefits, I'm sure.
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10. Board Game: Race for the Galaxy [Average Rating:7.77 Overall Rank:49]
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Chaos: Moderate to high. Like Puerto Rico, the role selection mechanic gives a good dose of chaos to the game. Second-guessing other players is common here--trying to figure out if a person is going to help you out by choosing Develop while you choose Settle is part of the meta-game. Plus, you never know when you might be forced to Consume some of your goods that you might otherwise have wanted to save.

Randomness: Moderate. As with all card-based games, this Race for the Galaxy has its share of randomness. I've seen this handled well, though, in many games. As an example, if I'm handed a lot of military cards from the get-go, I'll adjust my strategy to be military-heavy. The randomness is here, for sure, but it simply makes a player choose a strategy--it doesn't seem to derail it.

Luck: Moderate. The role selection cards, coupled with the random nature of card draws, makes this a fairly luck-driven game. All the same, its luck is easily (and frequently) drowned out by skillful play.
 
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11. Board Game: The Princes of Florence [Average Rating:7.57 Overall Rank:116]
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(I have played only one abbreviated game of this, so I do not feel qualified to comment yet.)

Chaos:

Randomness:

Luck:
 
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12. Board Game: Age of Steam [Average Rating:7.69 Overall Rank:114]
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(I have not yet played this game, but my copy--and several expansion maps!--is in the mail.)

Chaos:

Randomness:

Luck:
 
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13. Board Game: Commands & Colors: Ancients [Average Rating:7.78 Overall Rank:98]
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Chaos: Low. As with Twilight Struggle, there's not a whole lot of worry about multiple opponents to mess with your head. All the information is out there in the open for you to see (at least, the units on the map, their strength, and the number of cards your opponent has). There also isn't a lot of chance for a completely off-the-wall unexpected event to happen either.

Randomness: Fairly high. Sure, you've got those Warriors with their charged-up energy ready to roll 27 dice against the Auxilia. There's still a 1 in 1.02349037 × 10^21 chance that you roll all red squares! Plus, the cards don't help a whole lot. You might end up with a whole handful of right-flank cards when all you have are units in the center and left flank.

Luck: Moderate to high. The randomness from the cards and dice is the deciding factor here. Some days you're the dice, and some days you're the dice tower...
 
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14. Board Game: War of the Ring (First Edition) [Average Rating:7.79 Overall Rank:82]
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(I have not played this game and so cannot judge it.)

Chaos:

Randomness:

Luck:
 
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15. Board Game: Brass: Lancashire [Average Rating:8.01 Overall Rank:34]
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(I have not played this game and so cannot judge it.)

Chaos:

Randomness:

Luck:
 
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16. Board Game: Hannibal: Rome vs. Carthage [Average Rating:7.82 Overall Rank:135]
 
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(I have not played this game and so cannot judge it.)

Chaos:

Randomness:

Luck:
 
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17. Board Game: Paths of Glory [Average Rating:8.00 Overall Rank:100]
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(I have not played this game and so cannot judge it.)

Chaos:

Randomness:

Luck:
 
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