Quote: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?

You are right, the S/P/R system is mainly good for direct confrontations. In a game of spells and weapons, this S/P/R system will mainly apply during the confrontation. However, indirect confrontations and also befit from S/P/R, but it is harder to apply and you have to approach it more abstractly.

A batter system for non confrontational choices might be through a Cost/Benefit system, where each choice has something that is good, and something that is bad. This way the player has to deal with the bad to ge the good, and if they can only choose one, then they have an interesting decision to make (that is what reward do they want and at what cost?).

Also (a bit off topic), here are a couple of wikipedia articles that might be of interest:

http://en.wikipedia.org/wiki/Game_theory
Game theory is always a good place to start.

http://en.wikipedia.org/wiki/Prisoner's_dilemma
A good place to start when trying to understand game theory

http://en.wikipedia.org/wiki/Diner%27s_dilemma
An interesting modification to the basic prisoners dilemma

http://en.wikipedia.org/wiki/Ultimatum_game
An interesting game that when performed in real life (using repetitions among people that communicate with each other) shows the origin of Altruism (that the cheats get punished).

http://en.wikipedia.org/wiki/Tragedy_of_the_commons
It would be interesting if this could be applied to an RTS game.

I think that the Ultimatum game and the Tragedy of the Commons might create a new and interesting way to give resources to players in an RTS game (imagine an RTS where the resources are split between you and your opponent through an ultimatum game mechanic, or one where you share a common resource that regenerates slowly, but if it is depleted it can't regenerate).

Or you could weave a prisoners dilemma into an RPG plot.

The advantage of understanding Game theory, although it is not always useful for actual games (it is better to economics and politics than games for fun), is that it gives you a tool to craft and test situations where players have to make choices, and it can lead to interesting applications of them in a game with a bit of imagination.

By using game theory to help craft a set of choices available to the player you can control the expected pay-offs and penalties associated with a set of choices and easily see and balance them.

Yeah, I'm quite familiar with economic game theory, and it's obvious that all this is underpinned by that, but it's hard to see how it applies usefully to designing games - after all, spotting the optimal strategy for those dilemmas is actually trivial once you see the 'trick', and there are typically only 2 choices, which is not good enough for most games. The complexity is too low to be fun. Perhaps the iterative nature of most games makes it more interesting, in the same way that iterative prisoner's dilemma is more interesting, but even that has a trivial best strategy too, apparently. To hide that from the player may well require more possible choices, making the payoff matrix far bigger.

My theory for creating challenging game-play dynamics is to give the user many choices of actions (some basic, some complex... but all of which have clear results), and then force the user to optimize not only their choices, but their sequence of choices through both experience as well as trial and error. Time constraints and lead times also help improve the experience.

Example 1 - Strength vs. Economy
A user is given 2 basic choices: Build up your Army, or Build up your city. This is a classic scenario of games like StarCraft, Civilization, etc. While it is of greater economical advantage to focus solely on ones city, it is unfeasible due to the threat of war. This creates a difficult, but understandable choice a user must make in order to optimize game play.

Example 2 - Ranged vs. Melee
A user is given a choice between 2 soldiers: One is weak, but ranged. The other is strong, but fights hand to hand. Again, this is not a complicated decision per say, but the results of the choice may make the difference between victory and defeat. Unfortunately, the effectiveness of this choice is a bit random because you can never accurately predict what your opponent will do. However, I find randomness of this nature better than computer generated chance.

Example 3 - Upgrades vs. Soldiers
A user can upgrade his weapons at a large cost. This creates a moment of weakness for the player upgrading, but can result in a large advantage. What do you do? Again, there is a good bit of chance involved with this decision, but it is not computer generated chance.

From here, we keep adding simple choices that we will present to the player. There are ultimately hundreds of 'vs' decisions (death chance vs. big payoff, high vs. low, numbers vs. size, etc). The key, which is not necessarily quantifiable, is to find a way to mix all of these decisions together without overwhelming the end user. How a game designer does that is a matter of artistic style. Note: Some styles are better than others.

Also: Challenge, as I have come to learn, does not mean difficult to figure out.... rather it means easy to figure out, extremely difficult to master.

Quote:Original post by Cygnus_X
Example 1 - Strength vs. Economy
A user is given 2 basic choices: Build up your Army, or Build up your city. This is a classic scenario of games like StarCraft, Civilization, etc. While it is of greater economical advantage to focus solely on ones city, it is unfeasible due to the threat of war. This creates a difficult, but understandable choice a user must make in order to optimize game play.

Imagine your game consisted solely of 2 statistics, City and Army, and every 10 seconds you could invest 1 point into just one of them. Would that make for a fun game? I don't think it would. You'd eventually work out the optimal balance and choose that all the time, until you got bored enough to try the other strategy.

Therefore, at the level I am talking about, the issue isn't really so much about whether you choose between building up your army or your city, but in the plethora of sub-options that let you build up both the city and the army in different ways, and to strike different compromises. Without those extra choices adding complexity, the choice seems to be uninteresting.

Quote:Example 3 - Upgrades vs. Soldiers
A user can upgrade his weapons at a large cost. This creates a moment of weakness for the player upgrading, but can result in a large advantage. What do you do? Again, there is a good bit of chance involved with this decision, but it is not computer generated chance.

Ultimately this comes down to information - if you can tell that you won't be attacked during the upgrade, you should always upgrade, and if you can tell that you will be attacked, you should never upgrade. If you don't know, you have to multiply the factors together and see which is best. So the gameplay here really comes from the management of information - can you get information about the other player or not, and if so, how much? There are potentially interesting choices there, of course, since gathering the information typically costs resources that could be deployed elsewhere.

Quote:Original post by Kylotan
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?

Yes throwing on him even more choices, and allow him to live with these choices, and have large possibility to change them without losing.

Actually there are not any problems with complexity, there are more problems with user interface, and problems with attention deficit of the player. If he could play just simple games, yet he becomes bored quickly... There is not help for him. People like that are often result of overdose by TV networks.

There is no sweet spot in the middle, the correct complexity results from game design. Even crazy games like Harvest moon, Lufia, Harpoon, Pokémon, or SEIV have theirs players.

Of course SEIV isn't completely reasonable example, because its complexity doesn't work well together and AI can't use it correctly, in addition there is complexity in one area, however unnecessary abstraction in other area.

On the other hand Pokémon actually hid its insane complexity under story. These Pokémons need to be trained, however what level of training would they get? It depends on theirs trainer, and what they experienced. If they had easy lives by avoiding challenges, they will have harsh time but they'd make it. If they had harsh live, however theirs trainer took care about them, they would curb stomp the opposition singlehandedly. The point is not every player even notice the complexity, it's somehow hidden under scenes, these players that do notice are the ones who are more likely to enjoy a complex game. (The others could stay ignorant as they are.)

From my experience it's more about what level of complexity the developer could stomach and if he would like to play that game with such level of complexity. If it's too simple for him... Why bother to make it?

[Edited by - Raghar on July 16, 2007 1:21:14 PM]

Quote:Original post by Kylotan

Quote:Original post by Cygnus_X

Example 3 - Upgrades vs. Soldiers
A user can upgrade his weapons at a large cost. This creates a moment of weakness for the player upgrading, but can result in a large advantage. What do you do? Again, there is a good bit of chance involved with this decision, but it is not computer generated chance.

Ultimately this comes down to information - if you can tell that you won't be attacked during the upgrade, you should always upgrade, and if you can tell that you will be attacked, you should never upgrade. If you don't know, you have to multiply the factors together and see which is best. So the gameplay here really comes from the management of information - can you get information about the other player or not, and if so, how much? There are potentially interesting choices there, of course, since gathering the information typically costs resources that could be deployed elsewhere.

First, I believe your response to the decision of weather or not to upgrade emphasizes my point that even small decision have vital and complicated roles in the overall game experience.

Second, I'd warn a developer about emphasizing making a game complex. I have found that players can get easily frustrated over game concepts that are difficult to understand or adjust to. Again, the idea should be to develop a game with a simple pattern, but a difficult solution (Sudoku and Chess are both good examples of this).

Finally, if we're not talking simple warrior or building selection, here are a few other ideas (just ideas, not well thought through concepts) that could be employed:

Stock Market for Resources - Ie, you can trade require resources on an open market, and the trade value of each resource changes based upon demand. I haven't seen this done well in many games.

Team Contribution - You can set up a team structure such that it is 'best' for the team if each member contributes equally to a common goal, but it is 'better' for an individual to have all his team-mates contribute, and he keep his resources to himself. This would be a spin-off of the herder/pasture delimma.

Unity - This concept is employed by puzzle pirates. For those who haven't played, there are multiple stations on the ship that change difficulty based on the performance of your team-mates. If the crewman at the water ejector is doing poorly, it makes it tough on the captain (ie, more weight, less turns). If the captain is doing poorly (and is getting shot), it makes things difficult on the carpenter. If the carpenter is doing poorly, it makes things difficult on the water ejector. Thus, a player is only as good as his team-mates.

Conclusion: Good game complexity comes from unique permutations of these different concepts. Not all of them have to be included.

There are definitely lots of ideas like that which can be employed to make a game more interesting. But is it possible to describe them more abstractly, in terms of the decision tree, or in cost/payoff matrices as in game theory? And don't these things have to be more complex or they become too trivial? eg. Both the team contribute and unity ideas are easy to find the optimal strategy for.

You can, potentially, write down a game in a purely mathematical form, but as a completely abstract object it won't tell you much without further specifications. For instance, there is a massive fundmanetal difference between sequential (fully turn based) and simultaneous (both take turns at the same time) games, and different problems arise in either, requiring very different notation to solve. In a sequential game you have to watch out for "perfect strategies" (like in tic-tac-toe) whereas in simultaneous games these can be entirely avoided provided the game is symmetric (both players have the same choices, and the same rewards). As for whether there is a single definitive property that can detirmine how "good" a game is, I'm not too certain. The only thing I can think of is that a sufficiently superior AI (one with greater memory and processor time) can potentially beat an inferior one on the majority of occasions. This would be an intensely complicated property in an abstract mathematical setting though.

Probabilities can leave a game unchanged or drasticaly alter them depending on how they are implimented. If you had R/P/S where R beats S with 75% chance, P with 25% chance and R with 50% chance etc. then the core theory of the game is identical (in other words AIs in either game would be exactly matched*). On the other hand, in a game like Poker, the actual game is about modifying your returns for a particular round based on your estimated probability of winning. You could do a version of R/P/S using probabilities in a similar way to Poker as follows: Each player is assigned one of R, P or S randomly at the start of a round, then the players take it in turns to modify how much they want R, P and S to be worth for that round.

* - now that I think about it, this could be a good starting point. Given a game, take the set of all AIs as an abstract object S, and define a relation on S such that xRy if and only if x will beat y on average (the relation need not be transitive remember!). Then we can define an "isomophism" of games if the possible AIs from one can be mapped bijectively to the other in such a way that R is preserved.

Edit: Continuing on this idea, you could define a game as "fair" if for each x in S there exists a y in S such that yRx. In other words, for every strategy there is a strategy that beats it.

[Edited by - H4L on July 16, 2007 6:52:29 PM]

Quote:Edit: Continuing on this idea, you could define a game as "fair" if for each x in S there exists a y in S such that yRx. In other words, for every strategy there is a strategy that beats it.

Which is what the Rock Paper Scissors game (or an intransitive relationship) encompasses (although there are other game systems that also exhibit this formulation that aren't SPR derivatives).

Quote:Second, I'd warn a developer about emphasizing making a game complex. I have found that players can get easily frustrated over game concepts that are difficult to understand or adjust to.

I would say there is a difference between Complication and Complexity. Complication means that the game is more obscure, or there are more choices than a player can effectively consider. Complexity is that the components of the cam interact in many ways.

Chess is an example of a Complex game as it's components (the pieces, the board and the turn based structure) have a very high level of interactivity (any piece is capable of capturing any other piece if used correctly - that is placed on the board). Monopoly is a more Complicated game as there are many more components and there is less interactivity between them (on average).

Complexity and Complication, for their own sake, should not be advised (and should be advised against), but both can be used to improve a game.

Quote:

Quote:Original post by Cygnus_X
Example 1 - Strength vs. Economy
A user is given 2 basic choices: Build up your Army, or Build up your city. This is a classic scenario of games like StarCraft, Civilization, etc. While it is of greater economical advantage to focus solely on ones city, it is unfeasible due to the threat of war. This creates a difficult, but understandable choice a user must make in order to optimize game play.

Imagine your game consisted solely of 2 statistics, City and Army, and every 10 seconds you could invest 1 point into just one of them. Would that make for a fun game? I don't think it would. You'd eventually work out the optimal balance and choose that all the time, until you got bored enough to try the other strategy.

Actually, the reason this dose not make an interesting game is that there is no real interactivity between the components. If we add in one: That the higher the level of your city the faster you produce Armies. Then it does create an interesting choice.

Now you have an advantage to upgrading your city instead of increasing your army. And because of that interactivity different strategies can present them selves.

First there is the Rush: Only build armies. In the initial scenario this was the only viable strategy as upgrading the city would not effect your army sizes (except to reduce the number of armies you have).

Second is the Counter Rush: Build enough armies to hold off the enemy armies (althoug not win), but then upgrade the city to the point where you can pump out armies fast enough to overwhelm the enemy when the do finally attack. As the Rushers won't have the ability to pump out armies as quickly, you can hold them off and then swarm then under. The difficulty here is in gauging how many armies you will need to hold off the rush long enough to give you time to build up your swarm.

The last main strategy is the Economic win: In this, if they don't rush (if they are doing the Counter Rush), and you spend all your efforts on just upgrading your cities, eventually, you will have the ability to out produce your enemy and then do a late rush and swarm them under.

Actually, unintentionally, this creates a Scissors Paper Rock relationship between the Different strategies. Rush beats Economic, Economic beats Counter Rush and Counter Rush beats Rush.

The main difference between this type of game and a pure SPR is that SPR is an all or nothing game. You have to choose one and can't easily change it later. In the cities and armies game, there exists a continuum between each of the different strategies and you can "hedge your bets". You could go for the Rush, but also upgrade your cities a little which give you a better chance to beat a Counter Rusher in that they will have misjudged the number of Armies needed to finally swarm you under.

However, you might think this would lead to the dominant strategy being to find the middle ground of all three strategies and following that. However, any one of the three extreme strategies should be able to beat this Middle Ground Strategy. But, it also pays to be flexible, so following one of the extremes make it a gamble.

How is that for complexity? Just by creating an interaction between the city upgrades and the armies, you create a complex game that has no optimal solution.

On a final note: http://www.gamasutra.com/features/20070123/chelaru_01.shtml
Have a look at this gamasutra article, especially the bit about signals and fake signals.). These can also be used to make a game have more complexity.

Quote:Original post by Edtharan
Actually, the reason this dose not make an interesting game is that there is no real interactivity between the components. If we add in one: That the higher the level of your city the faster you produce Armies. Then it does create an interesting choice.

Now you have an advantage to upgrading your city instead of increasing your army. And because of that interactivity different strategies can present them selves.

Well, I was assuming that there was a benefit from having a powerful city too. The point I was making is that if you just have 2 variables, even if both feed into each other and both can be used in resolving whether the game is won or lost, there is an optimal strategy and it's likely to be trivial to find. If you don't know what your opponent will do, then there is likely to be one and only one choice that gives you the highest chance of victory. If you do know what your opponent will do, then you have probably been told exactly which will give you the highest chance of victory. Even adding asymmetry to the mix, while making it more interesting, ultimately can show you which choice is most likely to win, given a rational opponent and not a random one.

A lot of these methodologies rely on an opponent who is slightly random - either a human who will sometimes choose a suboptimal strategy to try and trick you (or because they're bored), or a computer that will randomly choose one, or an opponent of either type who will try to predict what you will do based on previous actions. And I think that's sidestepping the essence of game complexity that I was hoping to single out in this thread. With games like Chess, or Civilization, the optimal strategy is hidden by the level of complexity, which is a large part of what makes it fun. A lot of what people are proposing here are instead games where the optimal strategy is apparent, but where how to beat it is also apparent, leading to a bluffing war. This is certainly a valid way to design a game but it's not what I'm interested in at this stage. I'm interested in how to design enough complexity to hide the optimal strategy, without just throwing more and more features at it until it seems to work.