Monday, September 19, 2011

The Structure of Choices

Thinking a bit about the different kinds of choices, I just want to write down the best way to structure them. It's mostly a reminder for myself. This is an iteration of the calculation/incomplete information problem/incomparable distinction by Extra Credits.
Make sure to read the earlier posts on this topic to maximize your chances at understanding this one (1) (2) (3) :)
  1. the player thinks one of the possible decisions is the right one
    1. the right decision can realistically be calculated beforehand
      (e.g. tick-tack-toe, overall WoW boss strategies for the average player)
    2. the right decision can not be calculated beforehand
      1. because the player doesn't have sufficient tools/time
        (e.g. tournament chess against a computer, medium-term WoW boss fights)
      2. because the player does not have enough information
        (e.g. poker, chess against a human, WoW boss tactics)
      3. because of luck
        (e.g. gambling, RNGs, short-term WoW boss fights)
    3. but he is wrong
      (e.g. public quest rewards in early Warhammer Online)

    1. the player thinks there is no right decision
      1. the choice is an incomparable
        (e.g. looking good vs. being more effective, WoW boss fights)
      2. but he is wrong
        (I can't think of an example, can you?)

      (1)
      Please note that the inability to predict one's own success at execution turns many games into 1.2.2. You don't know whether your next kick will hit the goal in soccer. You have to make an educated guess concerning the probability and use this guess to determine your course of action.

      Please also note that many games become 1.2.2., because the opponent is not predictable. That's why chess against a human also has a lot to do with poker. At the end of the day the distinction between 1.2.1. and 1.2.2. blurs. A neuroscientist might be able to predict your opponent's next move, so it's not inherently unpredictable.

      Finally, 1.2.3. could be considered a special case of 1.2.2. The point really is what the player thinks is responsible for his inability to predict the right decision a priori. If he thinks luck is responsible, his reaction is usually completely different than compared to somebody outsmarting him. Some players like the one more than the other and vice versa.

       (2)
      Why is this structure superior to the one given by Extra Credits? First, because Extra Credits talks about what is, not about what the player thinks. This might not always be a big difference, but at the end of the day what the player thinks is what counts. Second, because whether the player can access the right answer before he acts is more important than whether there is incomplete information or not.

      Many choices fall into more than one category. WoW boss fights, obviously, also use random numbers, for example. And the player might even start to ponder whether it is more important to do the most dps (look good) or help the team. So WoW boss fights, among other things, also use incomparables. It doesn't surprise me at this point that WoW, despite all its failings, manages to keep your mind busy with so much stuff.

      10 comments:

      1. 1.3. it is comparable but the trade of is time vs. power

        There is a right answer for early gratification and a right one for late, but more powerful gratification. e.g. Mutagens in Witcher 2 which can't be replaced. Do you use a small mutagen for a small bonus starting now or wait for a greater one to drop which will give you a better bonus but at a later time and noting now?

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      2. Mmh, a very nice example for a choice, worth writing about. Thanks Kring ;)

        Is time vs. power comparable? Perhaps if you assume that the player intends to maximize his chances at survival. Of course, we have quick-load in The Witcher 2. Consequently, most players don't try to maximize the chance of survival, but rather try to build the best possible character. And in that case the choice becomes trivial: wait for the biggest mutagen.

        So, if you have the goal to build the best possible character, the choice falls into category 1.1. And the correct decision is trivial: "wait".

        But if you try to maximize your chances at survival (and/or play consistent with the simulation), it is a 1.2. - kind of choice. You have to make a really hard (almost impossible) decision while missing almost all the relevant information needed to make it.

        So, first you really need to make up your mind and in that it is an incomparable. Do you want to maximize chances of survival and/or play consistent with the simulation or build the best possible character? This is apples and oranges, really.

        Once you made up your mind, the incomparable generates a choice with one right answer and, depending on your goal, this one is either trivial or virtually impossible to find.

        Consequently, I didn't have much fun with this choice. The simuilation was brought to life with insufficient gameplay that egged me to game it. I did end up building the best possible character. And my guess is 90% of the players ended up doing this.

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      3. > Is time vs. power comparable?

        Witcher 2 isn't a sandbox and has a maximum amount of time you can play it. If you've finished the story, you've finished the game. Every fight you've fought with an empty mutagen slot, waiting for the greater to drop, is one fight less with the mutagen bonus.

        > So, if you have the goal to build the best possible character

        It's possible (and probably likely, I haven't finished it yet) that you do not get enough greater mutagens of your choice by the time the story is done. Which means you won't be able to create the "mathematical" best character and the best "possible" character would have been the one using lesser mutagens. That would mean it's a 1.2.2?

        -----

        There was a similar, but different situation with T9 in WoW where you had to decide if you would like to buy T9.10 now or collect 25 badges more to buy T9.25 3 weeks later. The difference here is that you could recover by collecting an insane amount of badges. And the effect was that you would get T9.10 earlier but T9.25 later.

        But I think that's a 1.1 and an important input variable is the gear you already have in that slot.

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      4. Every fight you've fought with an empty mutagen slot, waiting for the greater to drop, is one fight less with the mutagen bonus.

        Very true. But why should maximizing the amount of encounters you can fight with mutagens be your goal? :)

        ---
        It's possible (and probably likely, I haven't finished it yet) that you do not get enough greater mutagens of your choice by the time the story is done. Which means you won't be able to create the "mathematical" best character and the best "possible" character would have been the one using lesser mutagens. That would mean it's a 1.2.2?

        I agree. When you get near to the end of the game (it is not actually obvious that you do ...), it becomes a 1.2.2.

        ---
        One more thing about the 1.2.1. and 1.2.2. distinction: This can change even if the goal changes only slightly. For example, if your goal in poker is to win a match, it's a 1.2.2. But if you want to maximize the probability to win a match, it's suddenly much more like a 1.2.1. The 1.2. sub-categories really require more thought.

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      5. Well if speaking about terms of choices in template, gear ,etc I always found MtG like approach almost infinitely interesting . You have a huge broad selection of approaches, the efficiency of your present choices is largely dependent on metagame (what skill bracket you playing , what decks other players are currently playing)

        In every game which allows to do this there is never optimal choice set in stone. Balance shifts and morphs constantly

        Deck building in MTG, team compositions in LoL, ship fittings in EvE.

        Every time you make a choice it is usually the "right" one for a given situation and time period, but it wont be the right one afterewards.

        Downside is that there is always steep learning curve. As vast as the field of "optimal" choices is the area of suboptimal, gimp ones is staggering.

        That whole things goes out of the window if you talk about skinner boxes (like wow). Whatever mechanics there are they are largely not there for gameplay reasons .

        They are there to provide illusion of power , illusion of intelligence (you win = therefore you are right, and you always "win").

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      6. I'll apologize beforehand if you've covered this already. Frankly, you had too many articles and comments on the topic for me to remember and I have not yet managed to listen to ExtraLife.

        I don't find your definition bad at all, but I tend to get hung up at the question of what constitutes the correct choice.

        In a game of hidden information, there are two types of "correct" choices which may or may not be opposites.

        For one, I can make the statistically correct choice - the one that has the highest likelihood of success given the information I have. For another I can make the choice with the actual best outcome.

        Most decisions in MtG come down to this. When presented with just one land in my opening hand for example, I get to choose whether I'll keep that hand or draw a new one of one less card.
        Because you know what cards are left in your deck but not the order in which they are in, you get to calculate the odds of drawing the required number of lands by the time you need them as well as your odds of winning if you do. You can then compare those odds to the odds of winning with one less card in hand and make your decision based on those.

        It is always correct in that situation to choose the option with the better odds of winning in the end - but that choice may turn out not to be correct at all and cost you the game.

        So, which of these two is the "right" decision you are talking about?

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      7. Scrusi, read my latest comment on this post. I touched that problem there ;). Now, I think this is a simple incomparable. You need to make up your mind about what you what.

        Do you want to win? In that case the stochastically correct option can be the wrong one. Or do you want to maximize the chances of winning. In that case you can never be wrong if you do this. But losing can now be consistent with your goal.

        Of course many games make it difficult to find the stochastically correct choice: if the opponent can predict that you are going to act rationally, he might use this predictability, and act "irrationally" himself. But this turns out to be actually rational!

        Game theory and e.g. the Doomsday device come to mind.

        But this is really beyond the scope of this post. If you have one goal, there is always exactly one correct course of action - xor the choice is meaningless. If you have conflicting goals, there can be more than one meaningful answer, but this situation is resolved as soon as you make up your mind about what you actually want.
        If you don't do this, and often players don't, the act of choosing often continues until the end of the game. But it's usually not a lot of fun.

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      8. My goal is (obviously) to win the game. I don't care about any probabilities as long as I will win. Obviously though, that is not the choice I get to make. While my choice will (may!) ultimately decide whether or not I will win the game, I don't actually get any say in that matter.

        I have to work with probabilities because they allow me to decide on the most likely path to lead me to victory. Maximizing my chances therefore is a sub-goal on the way to my actual goal but might lead me astray completely. Did I make the wrong choice then? (Assuming my math is correct, of course.)

        On a completely different note, my goal may be to simply enjoy the story of a game. I could then come up on a choice that will drastically change the further development of the story, with both branches being equally enjoyable. Does that make my choice meaningless?

        By your definition, it would. Yet it is a very important and central choice to how I experience the game.

        We could take this away from games and make it a choice of book to read - The Lord of The Rings or The Hitchhiker's Guide to the Galaxy. My goal would be to read a good book and be both entertained by it and have my thoughts stimulated. Is there a wrong choice here? Is it therefore meaningless which book I read?

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      9. Thanks for the detailed comment, Scrusi!

        ---
        "I have to work with probabilities because they allow me to decide on the most likely path to lead me to victory. Maximizing my chances therefore is a sub-goal on the way to my actual goal but might lead me astray completely. Did I make the wrong choice then? (Assuming my math is correct, of course.)"

        Yes, you did make the wrong choice. But there's a good chance you're frustrated now, because you lost due to bad luck. Probabilities are just a tool you employ to win. And this tool, by definition, isn't reliable. To give a player a goal and then a tool that doesn't work reliably is bad game design.

        ---
        "On a completely different note, my goal may be to simply enjoy the story of a game. I could then come up on a choice that will drastically change the further development of the story, with both branches being equally enjoyable. Does that make my choice meaningless?"

        Comments like these are why I have have comments enabled on the blog! Thanks a lot!

        The "maximize my own fun"-goal is a very, very special goal. I wouldn't even treat it like any other goal, because you get all kinds of infinite loops and recursions. Whenever a player starts to try to maximize his own fun, he is actually trying to figure out what he wants. Because fun is experienced while a player tries to achieve something - anything. Anything, but trying to figure out how to have fun himself!
        Those people who spend the most time trying to figure how to be happy is are usually the most unhappy.

        Once again for clarity: Solving problems is fun for humans. The problems need to have a few characteristics, like not too hard, not too easy, and stuff like that. But generally solving problems, the process itself, is where the fun is experienced.

        There is just one exception: Trying to figure out how to have fun oneself! It's perfectly fun trying to figure out how other people have fun (I like that! A lot!) But trying to figure out how I, myself, can have fun is deeply unfun. And it's easy to use evolutionary theory to explain, why.

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      10. Speaking of choices and predictions , Sirlin uses term "yomi". - It common in all games vs opponent. Poke and MTG are prime examples , but so is street fighter , wow arena and so on.

        One interesting analysis of algorithmically optimizing a yomi game (in form of rock-paper-scissors) is described here
        http://ofb.net/~egnor/iocaine.html

        There is always optimal strategy - its guessing correctly one your opponent :)

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