Tuesday, July 04, 2006

Elegance in Games

I'm trying to pin down an elusive quality of a game. It is the game play to game rules ratio (let's call it the PTR). It is not necessarily a predictor of what is good. It is a predictor of what is elegant.

What is game play? Some combination between the objective depth of the game in terms of strategy and tactics combined with your relative enjoyment of the game. Game rules refers to the extent of the core set of mechanics; clarifications about the rules don't count.

I'll just go through a few games to illustrate their PTR ratio.

Go is the poster child for a high PTR game. The number of rules is pitifully small: alternate turns, place stones, remove groups with no liberties, end after both players pass, count up controlled spaces. That's five rules. A few clarifications about the rules are also required, particularly with regards to scoring.

The amount of game play that results from these rules is very high. A human who spends his or her entire life studying the game will likely be only most of the way towards being an expert in it. Each game plays differently, and most games present unusual or interesting challenges.

Go is a very elegant game. Let's call the game rules of Go "5" and the game play "100". That gives Go a PTR of 20. Of course, if you can't stand Go, your PTR for Go will be lower.

Many other abstracts have this high PTR ratio, although many have more rules, and certainly most have much less game play possibility. Connect Four has elegant rules, even simpler than Go's. However, the game play is much more limited. Connect Four's rules are 2, but it's game play is something like 8, possibly even less. That gives it a PTR of 4. (Connect Four is actually solved, but most people don't know the practical method of implementing the solution).

As the game play shrinks, or as the game rules increase, the elegance decreases with its PTR.

Tigris and Euphrates's rules are more complex than Go's, for sure: how to set up the board, six action types (place leader, move leader, remove leader, place non-blue tile, place blue tile, place disaster, cycle tiles), possible monument placement, two possible conflicts with a few rules for each one, possible leader displacement, possible treasure acquisition and which one, point acquisition, two actions per turn, two game ending conditions, and scoring. We can call the rules of T&E something like 20. Assuming an average like for the game, the game play is about 75. PTR score: 3.5.

That doesn't mean that T&E is less fun than Connect Four. Only that it is marginally less elegant. Some might argue that elegance is not the game play divided by the game rules, but the game play minus the game rules. In that case T&E measures up more like we would expect. Let's call that equation PMR.

Go then has a PMR of 90, T&E has 55, and Connect Four has 6. That looks slightly better, but let's continue.

ASL has a tremendous amount of rules. Even though most of what look like rules are clarifications on the essential rules, there are still a lot of essential rules: initial setup, goals, terrain and atmosphere rules (many), turn order rules (many), weapon and unit rules, effects that occur after certain rounds, and game ending conditions. Remembering the specific effect of every weapon involved is also part of the game. That gives it a rules level of about 65 or more. YMMV, but I would put game play at about 90 or 95; I don't particularly like it, but there is no denying the depth of the strategy and tactics. PTR is about 1.2 to 1.5. PMR is about 20 to 25. Is that bad?

Not if you only care about game play. Is ASL elegant? Kind of. It is less elegant than Connect Four or Tigris and Euphrates, but it does provide higher game play.

ASL's has an ability to fold into the ruleset many different categories of weapons and vehicles and so on without having to alter the ruleset. That may be thought of more as comprehensive then elegant.

What games have a PTR lower than 1? How about Monopoly? Of course, this again depends on how you evaluate game play, but I would put the rules at around 12, and the game play (official rules, no house rules) at around 10. Is Monopoly less elegant than Tigris and Euphrates? The rules are simpler! Yes, but the resulting game you get out of those rules doesn't seem to me to be "worth" the amount of rules that are required to play the game.

For me, a high PTR is indicative of beauty and elegance in a game. There are objectively low PTR games that I like (Caylus), and high ones that I don't (Chess), but when I look at high PTR games I feel a certain satisfaction with the design that reminds me of art. That the design was waiting to be uncovered, and if this designer hadn't invented it, somebody else would have.



ekted said...

Interesting idea. I suspect a "proper" formula for what you are trying to objectify is more complex than A/B or A-B, but it is probably not worth trying to find.

I don't find the rules to Caylus inelegant at all. There are a lot of steps, but to me each is smooth. I would rate Go 100 for elegance, Caylus an 85, and Power Grid a 60. From an objective point of view, I would measure elegance not by the length of the "flow chart", but by the number of places where it branches (special cases).

Pawnstar said...

Very interesting; it seems a lot of games I would have classed as inelegant have a high PTR ratio, and vice-versa.

Personally, the highest PTR's I can think of belong to Liar's Dice and Fluxx; I have had a lot of mileage for both and neither has more than a few rules (although technically you could argue effectively Fluxx has many as dictated by special cases on the cards).

Yehuda Berlinger said...

I admit that something about this still feels elusive and over-simplified. Perhaps it's only a mechanic can be elegant, rather than an entire game.

I find Caylus to be pretty inelegant. That doesn't mean that there is not good game play, but elegance? No. You've just gotten used to it.

And Fluxx may have simple rules, but the game play is so low that it also isn't elegant as far as I can see. If you like Fluxx a lot, your game play score is higher, I suppose.

Which all basically means that maybe elegance is relative.


Fraser said...

Is there an inherent assumption that you will actually like an elegant game and thus would give it a high game play score?

Admittedly I can't think of any examples off the top of my head but conceptually I have no problem with the possibility that there may be an extremely elegant game with beautifully written rules and excellent mechanics that I just have no interest in playing.

Yehuda Berlinger said...

I'm not sure. I began thinking about it after playing Santiago, which is a perfect example of a high PTR game. It's also very elegant.

One of the reasons that I love it is due to its elegance. If the same game play had many more rules, it would feel awkward.

A small amount of game play for very clean rules is good, like No Thanks! A larger amount of rules must result in much more game play. A game like No Thanks! with a lot more rules would be a chore. A large amount of rules for a medium amount of game play bothers me.


Gerald McD said...

Another thought about elegance -- If a ruleset is highly intuitive and memorable, I consider it more elegant than one that requires me to "look up" something while playing the game, even after several played games. Of course, that's related to the complexity of the rules, but some game rulesets just seem very logical and natural, while others seem contrived. Elegance is in the mind of the evaluator, of course.

Paul Kidd said...

How would you measure the elegance of a game like the Faidutti games Citadels and Fist of Dragonstones?

In these games the basic rules are quite simple, but the interesting part of the game is in the special abilities of the various characters, so each card adds its own rules, in a sense.

Coldfoot said...

I really enjoyed reading this but it seems to miss something. It doesn't seem to be this simplistic, though it's close, so I've been thinking about it.

I think Gerald made a good point regarding the logic and intuitiveness of the rules. I agree that Caylus (only played once) is inelegant, in the same way that Reef Encounter is and to me they both bog down in too many stair steps.

In many games you have choices of how to make points but they're
simply A, B, C, etc., like radiating lines. But in Reef Encounter,
and to a lesser degree, Caylus, the choice is more of a straight line
with stair steps in it. Before you can get to the points, you have to
have maneuvered through the steps above it. In my one play of RE
online, I kept backtracking from the points I wanted to get trying to
figure out what I had to control, what I needed to acquire for that
control, how to acquire *that*, etc., until the fun was sucked out of the game and I couldn't wait for it to end.

I don't know whether this makes sense to anyone else but me as it's
hard to explain but I felt I had to give it a try. :)

Anyway, this stair step progression, to me, is the height of

Yehuda Berlinger said...

fraser - I mentioned Chess as a game with high PTR that I don't like. I suspect that that is an abberation, however, and generally I like high PTR games.

That's just my scale for what I like, however. As I noted, some people like high PMR, some simply like high game play, some like low game rules, and I'm sure that there are other combinations.

I'm proposing a correlation between PTR and elegance. But I could be wrong.

Gerald, Oz - does that include the rules on the cards? What about San Juan or Citadels where every card has a different rule?

I guess I need to add another rules division: a) "core" game rules, b) specific card, token or tiles rules, c) game clarification rules.

Is the game more elegant by having the specific exceptional rules on the cards, within reach , than in the game rules book?

If so, then elegance has to include not only "play" and "rules" within its equation, but "presentation" as well. And while we are at it, if the theme of the game helps you remember the rules, we will have to include "theme" too.

If so, we lose the simple, raw, gut measurement I was looking to discover. It may be that there is no gut rule. But my gut is telling otherwise.

For Citadels, each card represents two entire new rules, so I would have to add them to the game rules numbers.

For San Juan, about half of the cards represent new rules, while others seamlessly modify existing rules; for me, these cards are halfway elegant.

For ASL, each weapon doesn't change any core rules, but only because the core rules are so bloated to begin with.

Magic: the Gathering is the same. Only 20-30% of the cards really add new rules, but there are a whole lot of rules.

These additional rules, in the case of good games, also up the game play, so that doesn't mean that they are bad. But they do lose elegance. So long as the game rules number is less than the game play number, the ratio of game play to game rules is always going to get smaller if both numbers increase at the same constant rate.

sodak - ladder progresion games tend to have a lot of rules, I believe.


Anonymous said...

Well... this is a late reply.
I got here by searching stuff on the discussed subject.

What I mainly wanted to say was "Chess has a high PTR??!"
even if you put it at 120 for game play (though I don't think it really surpasses Go) it still has tons of rules (placement of pieces, movements of different pieces, and quite a few special cases) so it can't possibly get a PTR close to Go's PTR.

Elegance is a complicated philosophical subject. I thought that since the term is used so much in Math and Computer Science there would be some formalization of it, but I have yet to find one and I guess it doesn't really exist...