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Thinking Virtually

#60: Designing Strategy: Decision Sets

by Shannon Appelcline
Feb 07,2003

 

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To most players, strategy games exist as a balance of two core elements: decisions versus randomness. On the one hand you have a player controlling his own destiny, and on the other hand you have that destiny at the mercy of dice (or other randomizing elements). Most games are combinations of the two elements, running a spectrum from Candyland (entirely random) to Chess (entirely decisions).

This week I want to talk about the decision side of things. Next week I'm going to move on to randomness, and also will talk about how the two elements can be balanced.

Simple Decision Sets

At the simplest level a game designer needs to ask himself, "how many different decisions am I offering to my players at any time?" In other words, how many different options make up the decision set which a player is faced with at any one time? The answer to that question affects the complexity of its game and also its playability.

The Settlers of Catan is a good example of a fairly flat decision set, because the decisions are clearly defined. In that game you can build three different structures: settlements, cities, or roads, and you can buy development cards.

Looking at this in the most simplistic way possible, you can say that Catan has a 4-wide decision set: settlement, city, road, card. Technically, when you decide where an individual structure goes, you widen your decision set a bit, but that's really a sub-decision--part of a tree--which we'll get back to in a bit. But, for now, let's just go with the analysis of Settlers as a 4-wide decision set.

Monopoly is a good example of a game with two flat decision sets.

  • Whenever you land on an available property, you have the opportunity to buy it or not.
  • If you ever have a complete set of a property, you have the opportunity to improve that set of properties by buying houses (and later hotels).

Looking at this fairly simplistically, you can say that Monopoly has a 2-wide decision set (yes or no) for property purchase. In addition it has an n-wide decision set for property upgrade. That n can be as large as "8" since there are 8 different monopolies on the board, and if you owned them all, you'd have the opportunity to upgrade each of them each turn.

Chess is a good example of an extremely wide decision set. Your decision set is composed of all of your pieces multiplied by all of the spaces that they can end up on. At game start, when things are fairly simple, that means that your decision space is twenty wide. You can move each of the eight pawns one or two spaces and you can also move each of the two knights to two different spaces. As the game progresses, this decision set just gets wider and wider (for a while at least). If you thought Chess was too complex ... this is why.

Looking at these three examples we can come up with some pretty crude estimates of how many decisions each game requires. Settlers had a 4-wide decision set; Monopoly had a 2-wide decision set and a (potentially) 8-wide decision set; and Chess started off with a 20-wide decision set and got bigger. But, how wide should your decision set be?

The general answer to that is ... no more than 7.

The Rule of 7

Seven, or more correctly five to seven, is a good number to always keep in mind. It's generally what our human brains can hold together at one time. According to numerous studies the brain can intuitively grasp--without counting--between five and seven different possibilities.

Do you find some web sites easy to navigate and others a chore? It's probably because the good ones divide up each level of hierarchy into 7 or less possibilities. Are you able to easily memorize phone numbers but not social security numbers? That's because phone numbers are 7 digits and social security numbers are 9.

Personally, I tend to think of this rule the most often when I'm doing user interface work. But, it's also important when you're facing a player with choices in a game design. As a general rule of thumb, you shouldn't face them with more than 7 choices at a single time--unless you want to invoke very intense cognition.

With its 4 choices, Settlers of Catan clearly matches that criteria. Monopoly's 2-wide decision set is fine, but the 8-wide seems to skirt the edges (though, when we get to constraints, we'll see the real width of the set is much narrowed, and thus not an issue). Chess, on the other hand, clearly does not obey the rules of 7. The 20 initial possibilities are already three times what the human brain can intuitively grasp, and as I already said, that just gets worse.

However, saying that you should limit yourself to 7 choices isn't the same as saying you have to have a very simple game with only 7 different options. Rather, it's saying that if you want to design a more complex games, you should split up decision sets, or constraint them, which I'll be getting to in just a second.

Also, theoretically you don't have to follow the rule of 7. After all, Chess violates all of the rules I set forth here, and it's considered a classic. However, be aware that if you do decide to ignore the size of the decision set within your game, you'll be making a very complex, cerebral game, that will only be accessible to a small group of people, and definitely won't fit into the categories of "family games" or "beer & pretzels"--or really into the category of strategy games that the majority of people want to play.

It's your call based on what you're trying to do.

Constraining Decisions

Here's some of the top options used for constraining decisions in strategy games:

Constraining by Turn Phase: You give offer your players several different decision sets, but require them to be decided one after another. The card game Magic: The Gathering does this. There are separate phases for spell-casting and combat; you never have to decide what monsters are blocking when you're casting spells or vice-versa (though some "interrupt" and "instant" spells get around this ... and not surprisingly dramatically increase the complexity of the game).

Constraining by Game Phase: You can constraint not just by turn phase, as noted above, but also by broad, evolutionary game phases. At the extreme some games have different types of gameplay early in the game and late in the game. More often in a game certain actions early in the game help build toward other possibilities late in a game. This is one of the constraints that affects Monopoly. Landing on unowned properties tends to only happen early in the game, and building improvements on monopolies only tends to happen late in the game, thus the two decision sets remain almost totally separate.

Constraining by Ability: Many games will constrain decision sets based upon your current abilities. You might need certain resources to make certain decisions: money, building materials, score, specific position on a board, etc. Or, your ability might be constrained by something fairly arbitrary, like a die roll at the start of your turn. In Magic: The Gathering the mana you have available acts as an ability constraint; very similarly in The Settlers of Catan resources limit which of the four items you can build. The Settlers of Catan also offers a further ability constraint on one of its building options: cities can only be built if you have a settlement to upgrade (and, for that matter, if you have a city token left). In Monopoly you're only allowed to upgrade properties where you have a monopoly, thus that n-wide decision set that I mentioned is actually limited to 2 or 3 decisions in a typical game, depending on what you own ("upgrade the purple monopoly or upgrade the yellow monopoly?"). Only Chess, of my examples, really doesn't constrain by ability (though I suppose you can say the individual abilities of different pieces act as a constraint, and keep the decision set from being even larger).

Constraining by Needs: The flipside to constraining by ability is constraining by need: some options will only be a part of your decision set if you need them. For example, if some of your tokens are in a bad state (wounded, imprisoned, lost, whatever), you might then, and only then, need to consider the decision that would rescue them. In Settlers of Catan, for example, you might have a card that can move the robber, but you'll usually only think about playing it if you need to--because the robber is sitting on one of your resource hexes.

Constraining by Attractiveness: At any point in a game some options will clearly be better than others, and that acts as a fairly de facto constraint. For example in Chess a move that lets you take a Queen might be more attractive than one that lets you take a Pawn; and in Settlers of Catan building a Settlement in a space surrounded by common resources is more attractive than building a Settlement in a space surrounded by rare resources.

Constraining by Results: Decision sets can be looked at in another way--based solely on results--and this too acts as a type of constraint. Based on the particular goals implicit in a decision set, only a few options might actually be even potentially desirable, with the rest of the options either disappearing for their unattractiveness or else compacting down to other possibilities. (In some ways, this is a shade of constraining by attractiveness, but looked at in a different manner.) For example, Formula De is a race car game, and based upon what you roll and where you are on the track you might be able to end up on a half-dozen or even a dozen different spaces on each turn, which offers the possibility of being a pretty dauntingly wide decision set. However, in truth only results matter, not the individual possibilities. At heart Formula De tends to have only two options in its where-to-end-up decision set: move as much as possible, or move as little as possible. Sometimes you might have a third option: block other cars. Thus, though there might be 6-12 total options, they're actually constrained down to 3 based upon the results which are actually desirable. Monopoly is somewhat interesting to approach when considering this type of constraint, because every result in Monopoly tends to be about the same: improving your ability to extort money from other players. Taken in this manner you could say that Monopoly effectively has decision sets with no width, and thus fails the complexity test in the opposite way that Chess does: by providing no options. (Perhaps there is some statistical analysis that might offer some decision set width in Monopoly based on, e.g., nearness of a property to the jail, but I wouldn't say that's regularly part of the game where you more frequently buy everything that you can.)

Decision Sets as Decision Trees

The last idea, of constraining by results, brings up an interesting alternative way to look at decision sets; instead of creating 1-dimensional sets we can outline decision trees. If you're writing a game where it's actually the results that are important, not the individual actions, then you can create a much more complex game by building up a trees of results.

The Settlers of Catan is a pretty good example of a decision tree. As already mentioned, there are four structures that you can build: roads, settlements, cities, and cards. Cards really don't produce any extra branches (though they provide you with an extra decision set down the road: to play a card or not). However, as soon as you make the choice to build a road, settlement, or city, additional branches of a decision tree appear.

When you decide to build a settlement, an n-wide decision set appears, where "n" is equal to the number of legal places for you to build settlements. (They must be built on your roads and no less than 2 spaces from any other settlement). In practice there tend to be somewhere between 1-5 legal places for a settlement. They're implicitly constrained by ability (there are only a few places you can legally build), and also tend to be constrained by attractiveness (some spaces are better than others) and need (some resources are more badly needed by you than others).

Deciding where to build a city ia an n-wide decision set, where "n" is equal to the number of settlements that you currently have (no more than 5), because you have to upgrade a settlement. Just like settlement building, this decision set is constrained by ability, attractiveness, and need.

Deciding where to build a road can be a fairly wide decision set, since you can theoretically build it anywhere adjacent to another road or one of your settlements or cities. By late game, this might be a dozen or more places on the board. However, it's constrained by results. You're either trying to extend your road's length or to build out to new locations to build cities or settlements--and there will be clear best ways to do this all.

Risk is another example of building a decision tree in a game. You don't think about what to do with every piece on the board, but rather look at a few major branches: what opponents to interact with, and what fronts to concentrate upon. You could see "opponents" as the first level of your tree and "fronts" as the second (or vice versa). Only once you've gotten that far do you start thinking about individual pieces. Because you worked through a tree, you get to consider a subset of the game. (And, as it happens, Risk also provides nice constraint by ability because only pieces toward the front can actually attack--the rest just provide defense or supply lines.)

Finally, I tried to lay out Chess as a decision tree, but it was ultimately unconvincing. Moving individual pieces doesn't really form branches in a tree, because you're really working toward two results: taking enemy pieces and controlling territory. And, you don't have fronts like you do in Risk, because so pieces can move across the entire board.

If you want to put together a very complex game, and you can't constrain it via any other method, you should definitely try and form your decision sets into a tree--but be warned, it has hidden gotchas that can't be predicted. Decisions might interweave with each other in ways that start to make your whole tree feel strangled.

For example, going back to Settlers, building a city requires a settlement, and building a settlement requires roads. Despite this, it tends to work well, but once you reach a certain level of interwoveness, the distinct branches of your tree can get confused, and your decision set widths will grow in a way that's not necessarily easy to define.

Decision Multipliers: Results

Just as it's possible to constrain a decision set, and make it more manageable, it's also possible to increase the width of decision sets in various ways. The first way to do that is by allowing a singular decision to have multiple consequences.

As an example ...

Reiner Knizia wrote a game called Grand National Derby. In it players bet on horses, and also played cards on those horses to ensure that some won and others lost. There were two different decision sets, constrained by turn phase: bet on one of the 8 horses, and play one of your 8 cards. Ability and need constraints tended to limit who you bet on and what cards you played, so the decision set actually tended to be less than 7; there might be 4 or 5 cards which were really playable at any one time.

Then the design was expanded upon in a game called Titan: The Arena. This time around, each horse (now monster) had a special power which the person with the most bets got to use if he played a card on that monster. He still had his set of 8 cards to play, but now some fraction of those cards (perhaps 25% in a 4-player game) had an additional power. Effectively, 1 out of 4 of his cards had an additional result, and so his decision set for playing cards was really 25% wider. The 4-5 options I noted in GND became 5-6 in T:tA. But, that was still within the Rule of 7.

Then the design was expanded upon in a game called Galaxy: The Dark Ages. This time around, each card had a special power too. In my opinion the game was too complex and much less fun to play than its predecessors. By looking at the width of the decision sets mathematically, it's pretty easy to see why. We started out with a set of 8 options that was constrained down to 4 or 5 by needs and abilities. That was multiplied up by 25% by the monster (now alien) powers, and then multiplied up by 100% by the card powers. Or, to put it another way, each card had, on average, 2.25 results. Multiplying that through, we see that the total size of the decision set had risen to somewhere between 9 and 11 wide.

The simple point here is this: if you overload multiply results on a single decision, take that into account when looking at the width of your decision set.

Decision Multipliers: Look Aheads

One other possibility can effectively multiply the size of a decision set, though this one's a bit harder to quantify.

If your game has a lot of look ahead ("If I do 'A', then my opponent will do 'B', then I should do 'C' ...") that's a multiplier on the decision complexity. The more levels of look ahead you can iterate through, the more the complexity increases, primarily because every time you have to consider a number of different options that your opponent might decide upon, then account for your own responses to each.

Look ahead is usually a big consequence of a lack of randomness in a game. Chess is the prime example; not only do you have to keep that 20+ wide decision set in mind, but you also need to look ahead several turns, which multiplies it many fold.

My prime suggestion here is: make sure you have sufficient randomness to limit look ahead and protect the playability of your game. But, that's a topic I'll get into more next week.

Another option is to make sure that other players have a sufficiently varied decision set that you never know what they're going to do, which effectively introduces the same chaotic future state into your game.

Some Final Words on Options

Throughout this article I've been talking about the general idea of decision sets filled with options.

What I haven't really said yet is that having decision sets empowers players. Though you do need to be concerned about the width of a decision set, you also have to have decisions, or your game is just going to be a boring exercise of rolling dice.

And, beyond that decisions have to be significant and have real impact. If your games' options only affect pedantic, unimportant parts of the game, that counts not. If your options don't really allow results that change the course of the game, that counts not.

Finally decisions have to be long-lasting. If the decisions in the latter part of a game totally overwhelm those in the early part, then you might as well not have those early decisions at all.

Conclusion

My simple point this week is that you should carefully examine the decision sets that are implicit within your game. Unless you're planning to create a very cerebral game, try to keep them within 7 different choices either naturally or by using different constraints. Be aware of the multiplying affect of overloaded results and look ahead. And, if all else fails, at least try and design a decision tree that'll make sense to your players.

Decisions are one of the most important hearts of strategy games, and thus we'll come back to them again and again. Upcoming topics that will look back at decisions include:

  • Randomness. We'll consider its role as a counter to decisions, and how decisions can be a part of randomness.
  • Phases. We'll investigate the role of decisions at various points in a game, and particularly how they interact with the end game.
  • Expansions & Supplements. We'll investigate how expansions and supplements for games tend to be built, and see how that affects decision sets.

Randomness is the first of those topics I'll be discussing, and we'll be back for it in 7.

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