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Donald X.

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Complexity in Rules on Cards
« on: June 20, 2011, 04:03:01 pm »
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[This is an essay I wrote for the Alchemy preview, then decided to save for a later set. Now that BGN is part of BGG I've talked myself out of doing that kind of preview, so here it is.]

Somehow I have fallen into the trap of writing essays about random Dominion-related topics and including them in these previews. And this preview was especially short, what with the set being a small one. Here then is a lengthy bunch of thoughts on the topic of card complexity.

Alchemy's cards are more complex than those in Dominion's main set. Dominion has six "vanilla" cards - just combinations of pluses. Alchemy has zero. Alchemy does have a couple fairly simple cards - Vineyard is a straightforward victory card; Familiar is a very simple attack; University is pretty simple. But it also has a couple very wordy cards - Scrying Pool and Possession are both thick with text. And then, the cards in-between are more involved than Dominion's non-vanilla cards. As you can see from the images!

So how did that happen? Weren't there more simple cards left that were worth doing?

The short answer is, not really! There were only so many simple cards worth making. I spread them out among the main set and six expansions that I had before the game was published. The main set got the lion's share, because simplicity was its theme. Some expansions managed to get new simple cards from their themes, such as the simpler Duration cards in Seaside. Alchemy didn't have anything like that; I could have had a card with "+1 potion symbol," but it would have been a dud when there were no other Alchemy cards out.

So, what's the deal? Why are there only so many simple cards worth doing? In fact there are several factors pushing cards to be more complex.

1. The Card Complexity Axiom

At the root of it all is this:

The number of cards you can make for a game is proportional to the product of the complexity of the game and the amount of space you allow yourself for card text.

That's pretty basic and obvious but still seems worth going on about for a paragraph. There are only so many possibilities within a certain amount of space. To get more possibilities you have to add more space. You can add that space in the rulebook, or on the cards themselves, but it has to be somewhere. Dominion has very few rules, so by default the burden is on the cards.

2. Little Computer Programs

Cards are little computer programs. They refer to data, and have operations and "program flow." There are only so many elements to combine, and getting more cards at some point requires combining more elements (or creating new elements).

Each game has its "atoms." These are the simplest ways that data in the game can change. In Dominion you can move cards between the places that they hang out, and can muck with the amount of actions/buys/coins/vp you have. Those are the atoms. There are also a few more exotic things, i.e. the turn sequence. I am probably never making "The turn order switches direction," but it would be simple.

The simplest cards just do the atomic things. +3 Cards! Simple. Courtyard from Intrigue is "+3 Cards, put a card from your hand on top of your deck." That's just two atoms, even though the second one doesn't have a shorthand for it.

You can spice these up with qualifiers. University doesn't just gain you cards; it only gains you Action cards, and only ones costing $5 or less. Adding qualifiers like that is a good next step towards getting fairly simple cards.

Then there are formulas. In general you can only do the simplest things. We can access data directly, with no math beyond counting; how many cards are in play? I also let myself divide by N; Philosopher's Stone and Vineyard both make you divide. Multiplication, I don't know if I will ever go that far. I don't know why division seems simpler. Anyway this can never account for very many cards.

Finally there's "program flow." This is the stuff in computer programs that determines what happens next. "If X then Y else Z." "Repeat X until Y." And also simple stuff like "Do X, then do Y." This is stuff you can do on cards to get more variety, and it's the bulk of what there is to do. There are only so many ways to use qualifiers on a basic concept that will be interesting enough. You can't do very many things with formulas at once. And there are only so many atoms.

So in the end it's all about using program flow to combine atoms involving qualified data. There are only so many atoms, so once you've made all of those cards, you're going to have to make more complex cards.

For Dominion specifically, we can go further. Some of the atoms have parameters, but not all simple combinations of atoms with parameters are worth doing. Most of them are either utter duds ("+1 Card"), too strong to cost low enough to get to buy them before the game's over ("+6 Cards"), or too close to an existing card ("+2 Actions +2 Buys +$2" is too close to Festival). A bunch are randomly different in a really uninteresting way ("+2 Cards +$1"). At one point I made a chart of all of the combinations of pluses to possibly consider, and figured out which ones I thought were good enough to actually do. There weren't many.

3. The Vanilla Card Problem

In some games, one card can just be better than another one. Medici has a 3 of spices and a 4 of spices and no-one is like "omg the 4 of spices is broken." You bid on those cards, that's what makes them fair. In other games, including Dominion, there's a cost system balancing the cards, and at a given cost the cards are expected to be about as good. Obviously there will always be cards better than other cards. Each game the cards vary in value based on what other cards are out, so hopefully every card gets its day in the sun. But still. In general, one card will be better than another at the same cost. And that's fine, and anyway unavoidable.

It's a problem though if two cards are very similar and one is clearly better. In particular, if one card does everything another card does plus a little more, for the same cost, that's bad. It makes some people unhappy. If both are in the same game, we don't buy the one until the other sells out. That's still not a complete loss, but it's not as good as having some other card there.

With only so many atoms, like I was saying above, there are inevitably going to be similar cards - a new Village, a new Remodel. And these cards help make the game work - you need some Villages here and there. I just need to try to keep them enough different that this issue doesn't come up.

Enter vanilla cards. Vanilla cards in Dominion are ones that just have pluses. More broadly it's all of the simplest versions of concepts; the vanilla card problem applies to some cards that aren't strictly vanilla. But it especially applies to vanilla cards. Whatever it is.

Okay the vanilla card problem is this: vanilla cards limit what other cards you can make, without having two similar cards such that one is too obviously better than the other.

For example, Dominion has Village: "+1 Card +2 Actions." It costs $3. Village means I can never make a card that's Village-with-a-bonus, without charging $4 or more for it. I make Village-with-a-bonus sometimes - Mining Village in Intrigue is one. And when I do it has to cost $4.

It's not so bad charging $4 for Village-with-a-bonus. In Dominion, $3 is secretly pretty close to $4. By putting Village at $3, I gave myself some room to make variations on it at $4.

I can do Village-with-a-bonus cards at $4 forever. As long as each bonus is different, the cards don't end up too close. Sure they're both Villages, but is the one bonus always better than the other?

Now consider Throne Room. It's not a vanilla card, but it's the simplest version of its concept. Suppose I wanted to make Throne Room with a bonus. That would have to cost $5. At $4 it would just be better than Throne Room. But in Dominion, $5 is a lot more than $4. That bonus would have to be pretty significant in order for that card to be worth buying. And in fact that came up. Originally Throne Room cost $3, and I had a variation for $4 in an expansion that was "Choose one: +1 Card +1 Action, or Throne Room." Once Throne Room went to $4, the variation had to go to $5, and it wasn't worth $5. So it died.

The solution to the vanilla card problem is not to do vanilla cards. If your basic version of a concept includes a bonus, you can vary the bonus and keep the cost the same. Only when you do the bonus-less version are you stuck with increasing the cost. But you can't just not do vanilla cards. You need them for how simple they are. So in the end you pick and choose. For example Dominion does not have a card that just says "+1 Card +1 Action +$1." If I made that card, it would limit what other cards I could make. So instead I just do variations on it.

I should note that the vanilla card problem only exists in games with a lot of granularity to their costs. Generally you want to keep numbers in games as low as possible. Dominion has small cost numbers and that's good. But it means that a difference of +$1 is sometimes very significant. With larger costs, you would have more room to tweak costs for similar cards.

4. Complexity: The Panacea

You've just playtested a card. It's too weak / too strong. How do you fix it? By making it more complex. If it's too weak, you add a bonus; if it's too strong, you add a penalty. Or, if it's too strong, you weaken it too much, then add a bonus, and if it's too weak, you power it up, then add a penalty. In fact normally you add bonuses, not penalties, one way or another. Bonuses are more fun.

Adding complexity isn't the only option. But there is a lot of pull in that direction. The granularity of the system is again the issue.

Let's say Militia is too weak. It's "+$2. Each other player discards down to 3 cards in hand." It's not too weak. But let's say it is.

I can't just change it to +$3 - that's vastly more powerful. I can't just make it "discards down to 2 cards in hand" - that's crippling. I can't just lower it to costing $3 - that's not going to make the difference, and then maybe it's too good at $2. I could try a mix of things - up it to costing $6, make it +$3. In general though, the granularity of the system is fighting me. There may simply be no fair version of the card that just tweaks the numbers.

But I can always tack on another ability. And if that other ability is too weak or strong, I can replace it with a different one. I can also just replace Militia, but that's not nearly as good of an option. Militia may be doing something I need, and may be the best version of it in some other way. It may be totally worth doing except for power level. It may be a card people adore.

So the normal progression is, a card starts out simple, and if it isn't perfect, it desperately tries to get more complex, as I struggle to rein it in.

This also happens when power level is fine. A card is filling an important role but is too boring. What could spice it up? How about another line of text?

5. Ideas vs. Text

In these many paragraphs on this exciting card complexity topic, I have really been talking about complexity of ideas. A card can also just have a lot of words. But that's not as bad.

Suppose the rulebook defined "dig" appropriately. Then Golem could have read, "Dig for two Action cards other than Golems. Play them in either order."

That's pretty simple. Golem doesn't do anything complex really. Once you have that definition of "dig." And digging is straightforward too. But there aren't enough cards that dig, so digging is always spelled out on the cards, and well it takes a bunch of words.

Contrast this with Scrying Pool. Scrying Pool does two things: first it lets you toss or keep each player's top card, and then it draws you all of the actions from the top of your deck, plus a card. That's how many words it took me to tell you what it does, as a non-precise summary. It's not just wordy, it's complex idea-wise.

In general it's the multiple-idea complexity that's really complex. And sometimes even those cards can be simplified by having a strong connection of some kind between the ideas. Having a bunch of words can be intimidating when you first see a card, but you learn it quickly if those words just add up to one idea.

6. Complexity Solved

So there it is. Rules end up in the rulebook or on the cards, but they're somewhere. There are only so many game elements to combine, so you end up combining multiple elements to get more cards. You can't even do all of the vanilla cards that are possible. And in any case you're pushed towards complexity just by trying to make the game work.
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