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Kylotan

Thoughts on game complexity

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I was thinking recently about one way of making a game fun, and I think that one way is to make it so that it is possible to estimate the quality of a chosen strategy, but not with 100% accuracy. If it's always possible to reject the wrong strategies then it becomes quite boring (eg. tic-tac-toe), and if it's impossible to pick a better strategy (eg. rock-paper-scissors) then it's also not much fun. So there's a sweet spot in the middle - but how do you create it? Extra complexity seems to be one route, as taken by games like Civilization - so many choices and options that it's hard to predict what is the best one, though it's easy to see that some choices are better than others most of the time. Is there another way that doesn't just involve throwing so many choices at the player that mentally managing the decision tree becomes unwieldy?

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Randomness is always useful in adding that element of unpredicibility into the mix.

There's also the chess approach; have relatively simple options but involve planning to great depth.

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Randomness ultimately averages out though. It may double the decision tree if there are discrete successes or failures but it doesn't really add significantly more complexity into the equation.

As for chess, that's sort of what I was talking about, though I don't really agree that the options are simple given that you tend to have 20 to 30 different moves you can choose at any one point. Many computer games offer you fewer meaningful choices than that (eg. in which skills to choose, which items to wear, which buildings to construct).

And where does the requirement to plan to great depth come from? If that could be expressed clearly, perhaps it could hint at ways to add strategy to some games that is better than merely finding a new permutation of stat bonuses.

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Quote:
Original post by Kylotan
As for chess, that's sort of what I was talking about, though I don't really agree that the options are simple given that you tend to have 20 to 30 different moves you can choose at any one point. Many computer games offer you fewer meaningful choices than that (eg. in which skills to choose, which items to wear, which buildings to construct).

Well chess is very predictable, which is why you can think so many moves ahead. With a game things tend to be unpredictable (whats round the corner? Will I need to save this item for later?). I guess that this means that the complexity can be somewhat lower but still interesting.

Of course if you go too far with this then it ends up being impossible to make a good decision and becomes unrewarding. Eg. most RPGs which force the player to make long ranging decisions about the character with little or no knowledge of what will be useful or not (Eg. trying to pick between swimming or sneaking skills with no idea whether you might spend 90% of the game sneaking).

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Forgive me if I was missing the point; I've got a lot on my mind and this topic is extremely abstract [smile]. To be honest, I'm starting to get confused if we're talking about A.I. or just game theory; I'm assuming it's the latter.

Quote:
Original post by Kylotan
Randomness ultimately averages out though. It may double the decision tree if there are discrete successes or failures but it doesn't really add significantly more complexity into the equation.

Well, it depends a bit on exactly what the randomness is for, and the result of a success or fail. I tend to like randomness in games because it's a simple way to add a lot of implicit possibility; you need to factor in a lot of different options for every random element. It's also great because psychologically people aren't very good at dealing with averages with random elements; it's the reason the lottery is so successful.

Quote:
As for chess, that's sort of what I was talking about, though I don't really agree that the options are simple given that you tend to have 20 to 30 different moves you can choose at any one point. Many computer games offer you fewer meaningful choices than that (eg. in which skills to choose, which items to wear, which buildings to construct).

Yes; I was thinking of picking something like draughts (checkers) as my example, but chess is more canonical. Usually though a large proportion of those 20 moves can be dismissed for being irrelevant or stupid. I can somewhat agree that the number of options given to you is greater in chess than many games, but the comparison is hard to make in the general sense, particularly if we're comparing turn-based board games versus real time.

Quote:
And where does the requirement to plan to great depth come from? If that could be expressed clearly, perhaps it could hint at ways to add strategy to some games that is better than merely finding a new permutation of stat bonuses.

I wouldn't say the ability to plan to great depth is a requirement; I don't play chess that way because I'm not very good at the game. But I was thinking that to be really good at chess you need to go beyond the next couple of moves and understand the interaction between the pieces at a much deeper level.

I admit I'm not an expert at how the experts play chess, so I'm not sure if "planning at great depth" is the best way to describe how they function. I do have a mate who plays at international level; I should ask him because now I'm curious.

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I'd say, play more with risk versus reward. We all love low-risk, high-reward choices: cheap splash damage towers in those TD games, Overlord tanks with gattling guns in Generals, rapid fire snipers in CSS, and so on.

Rock-paper-scissors is pretty strong in that regard: everything is high-risk, high-reward. For experienced players, there's a lot of strategy involved: the way the opponent acts, reacts, how he played in previous games, and so on - all these factors play a role for them. There's a psychological game going on between them. That may just not be as visible to us, which is probably why we don't like it as much.

I also think dependencies between choices play an important role. In chess, units can cover each other, in TD games, slow towers can keep enemies within range of high-damage towers for a longer time (or distribute them more evenly across your towers, for better efficiency, etc.), in RTS games, different units can cover each others weaknesses, etc.


In other words, I think it's not so much the number of decisions that counts, but the depth of their effect. Different risks and dependencies will make it harder to foresee the consequences of your choices.

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I would recommend reading "Game Architecture and Design" (by Andrew Rollings and Dave Morris). Especially the first part as it deals with this issue.

Quote:
Extra complexity seems to be one route, as taken by games like Civilization - so many choices and options that it's hard to predict what is the best one, though it's easy to see that some choices are better than others most of the time.

There is Complexity and Complexity. One for of complexity is to dump a lot of choices on a player (like in civilization). However, another form of complexity is to have a lot if interactivity between the choices (like in Chess).

I am in favour of simple elegance, so I come down on the side of Chess. I like to have a few choices, but have those choices have a high level of interactivity with each other. The reason I like this form of complexity is that it more reliably leads to emergent gameplay, than just having a lot of strategically shallow choices. However, some people like having lots of choices, but I am not.

It is Depth vs Breadth.

Quote:
if it's impossible to pick a better strategy (eg. rock-paper-scissors) then it's also not much fun.

I agree. As it stands R/P/S is not a fun mechanic by its self. However, you can start to make it more interesting and fun by slightly breaking the symmetry of it (This is what "Game Architecture and Design" talks about).

So to start off with the RPS game has 3 choices and if you guess right, you win. Lets call winning a value of 1 and the cost of playing one of the options (Rock, Paper or Scissors) 2/3. The reason I call it 2/3 is that you have to choose 1 of 3 so the cost of playing 1 is not to play the other 2.

This is symmetrical. None of the choices have a higher cost or better score than the others. Now lets break the symmetry.

Lets say the costs for playing are Rock: 3/4, Scissors: 2/3 and Paper: 1/2 with victory remaining as being 1.

Now the whole game is different. Paper is the cheapest to play, but Scissors is only slightly more expensive and Rock being the most costly.

Because there is now different costs involved, it allows us to get a handle on what the other player might be thinking: "Kylotan doesn't have many points left, so he might try to play it safe and chose paper, but he still has enough points to play Rock. If he goes for the cheapest choice, then I can win by playing Scissors. I know that Kylotan is a sly player and would know that, so I think that he will choose to play Rock even though it is the most expensive because he thinks that I will choose scissors to counter the safe choice of scissors..." and so on.

If a player has a lot of points, then their choice can be more random, but if points are low, then their choice becomes dictated by the environment (the number of points) and the player's psychology (like in poker). It allows for bluffing and second guessing you opponent more than the perfectly symmetrical R/P/S mechanic.

If this was a Real Time strategy game, you might have Archers cost 6 Gold, Pikemen cost 8 Gold and Knights cost 9 gold. If 1 Knight can beat 12 Archers (before dying), 1 Pikeman can beat 12 Knights and 1 Archer can beat 12 Pikemen (then you have exactly the same system as I presented above - just multiply everything by 12, both costs and wins).

You can then further break the symmetry by adding in a few other units that don't directly effect the outcome of the contests (say a healer or a peasant that mines for gold) and further strategies and tactics will emerge (should you go after the peasants, or the healers, or will you have to have a pitched battle between the main 3 units, moving then to outflank the enemy).

Lastly, you can add in choices that mess with the dominance of the choices (so sometimes scissors might just be able to beat Rock and paper can manage an uprising against those oppressive scissors). In the case of the medieval units, sometimes the archer might not be effective against pikemen (by placing the pikemen on top of a hill, etc).

So, 3 techniqies that can help:

1) Break the symmetry slightly (with costs and rewards) between your choices.

2) Add in options that don't directly (but indirectly) effect the outcomes of the contests between your choices.

3) Add in options that allow you to change the dominance of the choices.

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Let me try and elucidate a bit - this is necessarily an abstract topic, as I'm looking at the fundamentals that underpin all games to a lesser or greater extent. But I'll be as clear as possible.

Firstly, I'm trying to ignore randomness because it can be 'rolled into' the mathematics. Compare one chess piece taking another, with a battle in Civilization - say, a militia attacking a phalanx, who will win just one time in three. The random factor only adds 1 extra outcome. In chess, you can choose to take the piece or not. In Civilization, you can choose to attack and success, choose to attack and fail, or choose not to attack. Now, the relative importance of those decisions does rest on the random factor, but the same would apply in Chess since you don't know what the opponent will do. So the difference it makes to the decision tree and hence the planning is not all that great.

Trapper Zoid - when you say "Usually though a large proportion of those 20 moves can be dismissed for being irrelevant or stupid." you're totally right, but a new player might not be able to dismiss more than one or two, and even for an expert player, the top 5 or 6 are hard to rank accurately. And that's exactly the middle ground I think is 'right'... a decent player has an idea of what is good and what is bad, at least in a given context, but is unable to know the theoretical perfect strategy that would make playing trivial.

I think great chess players see overall patterns that substitute for needing to look at each potential move exhaustively. It's a heuristic they've developed to judge move quality without needing to explicitly plan. Is there a way to design a game such that players need to develop that sort of holistic understanding, and if so, does it require that you set up such a large branching factor to the decision tree?

Captain P - the dependencies between choices is a large part of the puzzle, I think. But how can that be explicitly engineered in a game, beyond something trivial like "wear the complete matching suit of armour and get an extra +10"? It's easy to recognise in existing games but I'm not sure how to implement it without it being a crude tool. Depth is easy to recognise, but how is it created?

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My previous post was done before I saw this, so I'll answer separately.

Quote:
Original post by Edtharan
I would recommend reading "Game Architecture and Design" (by Andrew Rollings and Dave Morris). Especially the first part as it deals with this issue.


Aargh, I've got that book in my 'to read' pile. I may just promote it to the top of said pile now. I was hoping I'd find some books or papers on this sort of topic, so thanks.

Quote:
I like to have a few choices, but have those choices have a high level of interactivity with each other. The reason I like this form of complexity is that it more reliably leads to emergent gameplay, than just having a lot of strategically shallow choices.


The problem with 'emergent' properties is that it's hard to create something that manifests them in the first place. :) How would you go about creating something that gives as much depth as chess, without merely taking chess and altering a few rules?

Quote:
if it's impossible to pick a better strategy (eg. rock-paper-scissors) then it's also not much fun.

I agree. As it stands R/P/S is not a fun mechanic by its self. However, you can start to make it more interesting and fun by slightly breaking the symmetry of it (This is what "Game Architecture and Design" talks about).[/quote]

I will read more on that for myself. I agree that asymmetry can make things interesting, although I'm having a bit of trouble imagining how it would apply outside of scenarios where you're pitting your resources directly against someone else's. An example I keep thinking of is choice of equipment or spells/skills in an RPG-like game - how do you make such a choice interesting, and make it so that - given the same resources available to all - good players will be able to pick better combinations, but not necessarily be able to know which is mathematically the best?

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theres the "fog of war approach"

in that you have a fairly predictable system but you hide some of the information from the player and force them to build a strategy on what they know while considering everything they don't know

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