On Game Theory: Part II

In the previous installment (https://willowrants.wordpress.com/2006/09/16/on-game-theory-part-i/) I wrote about how Game Theory applies to players (specifically in chargen and minmaxing.)  Now let’s move up to the next level: that of game design.

Game Theory says that there’s two types of games: Known Games and Unknown Games.  A Known Game is one that has been sufficiently studied that the dominant strategies are known to the participants.  An Unknown Game is one where that is the case.

A classic example of a Known Game is the Prisoner’s Dilemmia.  You’re probably familiar with it: two players have two options: cooperation, or betrayal.  They choose in secret, without any communication.  If both players choose to cooperate, they get a prize.  (Say, one point.)  If both players betray one another, they both get hosec (say, they get no points.)  If one player betrays, and one tries to cooperate, the traitor gets a big prize, and the cooperative one gets hosed big time.  (The traitor gets two points, the cooperative player actually loses a point.)

The best total outcome is mutual cooperation: a total of two points are gained.  What’s the most likely outcome?  The worst one: mutual betrayal.

Let’s say I know you’re going to cooperate with me.  If I cooperate, I get a point.  If I betray, I increase my winnings by a point.  If I know you’re going to betray me, and I cooperate, I lose a point.  If I betray, I cut my losses to no points.  No matter what you do, I’m better off if I betray you.  Of course, you know this too, so we’re likely to just betray each other.

The game gets more complicated if communication and repetition are involved, but its as Known as a game can get.  There’s some interesting analysis in the process of going from Unknown to Known, but once you Know the game, its boring as hell to play.

I find it helpful to think of Unknown and Known not as absolutes, but as a spectrum.  Chess is far too known of a game for my tastes: there’s too much rote memorization of openings and gambits, and the player with more Chess knowledge is likely to win.  I do enjoy playing with people who (like me) haven’t done any chess research: it turns a Knownish game into a Unknown one.

For a game to be enjoyable on a Gamist level it MUST be an Unknown game!  Unknown games require intuition, estimation, tactical thinking, and a bit of luck to win the day.

(One way to make Known Games Unknown is to limit analysis time.  However, this is not always possible, especially that discussion of general case analysis is easier than ever with the internet.)

As Game Designers, how do we make our games Unknown?

For character generation, it means making no one character building option definitively better than all others.  I think many games handle this very well; there are different strategies that can be pursued, group builds with combined arms, aims of focus vs. general, etc.  Some types of options may are better than other types of options, but this is not problematic as long as there is variety within types. (for example, in D&D, warrior types are more effective than spellcasting types at lower levels, while at higher levels the balance of power reverses.)  There aren’t too many examples of Known Chargen Games, and the ones that are are completely broken.  (Do a search on EN World for Pun Pun, a D&D build that should not exist.)

(Of course, if you’re writing a Sim game where everyone is supposed to be a plate-mail clad knight or a Nar game where you’re mopey teenagers, you’re well withing your rights to make knights and mopers the most effective character types.)

Tactical, session to session, moment to moment play is more difficult.  I think that many RPGs, D&D included, are Known Games.  Figure out the best strategy for your group, and do it every turn.  Got a cool feat combo?  Maneuver into position so you can use it.  You’re a Rogue?  After you get Magic Items that help you Sneak Attack all the time (Hint: Ring of Blinking), just move into position and full attack until they’re dead.  As far as a tactical minis game goes, I’ve seen better.  The trick is variety of situations.  Different wierd monsters help, but once you’ve played D&D as much as I have, you figure out the ‘correct’ moves.

Burning Wheel is much more Unknown.  There’s an element of player psychology to the scripting, and more tactics.  What do you think the opponent’s going to do?  How can you counter it?  When do you take your actions?

At its basic level, HERO plays like D&D.  However, there’s options for the players that make it more Unknown, and the variety of possible situations is higher than for D&D.

Enough half-hearted case studies.  How do we make a game Unknown?

*Uncertainty of Resource Management: One of the biggest questions in D&D is ‘how fast should I cast my spells?’  Make people doubt how much safety they have.  Don’t let them know how many encounters until they can rest.  Vary your encounter strengths and numbers.  Give the players resources, and give the GM tools to make the players have to make hard choices about how fast they spend them. 

*Unrecoverable Resources:  Hit points, spell slots, and the like are all recoverable resources.  At some point in the future of the game, they’ll come back.  Players can agonize over those, but they’ll agonize even more about the ones they can’t get back.  (This includes stuff like certain D&D Magic Items, and Artha Points in Burning Wheel.)  Presence of Unrecoverable Resources as a backup to Recoverable Resources is also good thing in the sense that it gives conservative players a reward when they save their stuff (they didn’t have to spend the big stuff), but it gives the heavy spenders something to fall back on.  (The reward for the heavy spenders is that they get to do more stuff, and are less likely to die in opening encounters.)  The less recoverable your resources are, the more potent you need to make them!

*Knowledge of Opposition:  Unless the players know something of their enemies’s strengths and weaknesses, they cannot determine a successful strategy.  All options are shots in the dark.  (Classic example: two doors.  To the left is certain death.  To the right is massive treasure.  There isn’t any meaningful choice here.)

*Uncertainty of Opposition:  There always needs to be an unknown variable.  This should not come out of nowhere; hints are your friends; when the villian pulls the ace out of his sleeve, the players should say, “I should have known!”  (One of my favorite instances of this was when the players in my game found out that a new villain on the scene was actually an old villain they had killed, reincarnated as a member of a different race.)  This unknown variable doesn’t have to be about the opposition’s capabilities; it can be the opposition’s actions (like in Burning Wheel).

I recommend against opposition with unknown vulnerabilities; this tends to become “guess the one random stupid thing we need to kill him with.”

*Risk Management:  Some options are riskier than others.  Allowing players to control their degree of risk is a good thing.  Risk Adverisity is a fascinating quality and outside the scope of this post, however in certain cases (mostly survival), its preferable to make the riskier option have the better expected return (this is the principle insurance sales are based on; people are willing to pay, and settle for a lower average wealth in return for a more stable expectation.  Risky options should payoff big, but fail terribly.)  In other cases (mostly killing others), the safe, expected strike that does low damage should usually be better than the crazy off the wall strike; people are more willing to take risks when it comes to gaining things.  Here the designs should take advantage of people’s natural stances towards risk and make decisions harder.

*The Role of Chance:  Chance is a must, but if everything depends solely on the dice, the game is not worth playing.  Dice systems that skew the results towards the mean (such as GURPS/HERO’s 3d6, most die pool systems, or Fudge/TSOY) give an easily eyeballed expected result, but there’s all sorts of room for risk-hedging and unexpected results.

*Wealth of Options:  The most important thing is for the players to have meaningful choices.  If a choice isn’t hard, it isn’t meaningful!  How can a game designer push the envelope and make every choice hard?  This is the question we must ask ourselves.

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7 thoughts on “On Game Theory: Part II

  1. […] On Game Theory: Part II […]

  2. Rahvin says:

    So many things here deserve commenting on. Maybe you should break the ideas into individual posts…?

    There are three points I’d like to comment on briefly:

    1) Uncertain or unreplenishable resources: Most of my players don’t spend unreplenishable resources. Ever. Some of my players don’t even bother to earn them. I don’t understand this myself, but that’s just a comment from my own game group. They will always favor replenishable options if they exist, and ignore unreplenishable options if they don’t.

    2) It seems to go against Forge theory as I understand it to take away knowledge from the PCs in order to encourage them to make decisions. Meaningful decisions come from the players knowing exact consequences. Isn’t that one of your own blogs?

    3) Known and Unknown games sounds much the same as your post on Strategic vs Tactical game play and has the same problems I pointed out in that post.

    4) In the case of unknown opposition, an emphasis should be based on the seeking of knowledge and finding out of knowledge, rather than relying on GM hints which is basically fiat.

  3. Willow says:

    “It seems to go against Forge theory as I understand it to take away knowledge from the PCs in order to encourage them to make decisions. Meaningful decisions come from the players knowing exact consequences. Isn’t that one of your own blogs?”

    Indeed, however that sentiment is largely (but not completely) skewed towards Narrativistic principles. If we get into stakes for example, we have known possible consequences (and this can be key) unknown means. There’s a thread over on http://www.story-games.com that I consider to be largely inconsequential to me and filled with heavy jargon, that relates directly to this. Check it out, if you dare.
    http://www.story-games.com/forums/comments.php?DiscussionID=1199&page=1

    I’m of the opinion that a mental risk calculus is no fun without some sort of ‘X Factor.’ And you’re right: if the players make it a priority to uncover knowledge they don’t know, then you have the option of making *that* the exciting conflict.

  4. Rahvin says:

    This is of key interest to me. If you think of any more ideas on the line of identifying or creating more “X factors,” please let me know.

  5. Rahvin says:

    I read the thread you suggested, but I have no idea what it pertains to in this thread/post. I thought I had agreed with you that this was all mostly crap in the “Setting Stakes” post.

    The linked thread has nothing to do with Unknown vs Known Games, Tactical vs Strategy, the distribution of information to players, uncertainty of resources, unrecoverable resources, knowledge of opposition, uncertainty of opposition, or having a wealth of options.

    It is only marginally related to risk management and the role of chance.

    P.S. My comment about sharing information with players for meaningful decisions was primarily a response to the “Uncertainty of Resources Management” principle.

    P.S.S. My reference to your previous blog shared the same irrelevance as this thread. That is, your blog that I am referencing was about setting stakes, which has litle or nothing to do with this blog. However, although the reasons and circumstance are different, I feel the same principle that apply in setting “meaningful” decisions to stakes, also apply to setting “meaningful” decisions in the acquisition and expenditure of resources, strategic and tactical options.

    I hope that clarified things. I can get kind of wordy sometimes.

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