Strategic Freedom

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PingPangQui
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Strategic Freedom

Post by PingPangQui »

Is there a possibility to measure the strategic freedom of a game?

In order to answer this question one needs to know what I mean by "strategic freedom". I defined it for myself in the following way*: Strategic freedom is the number of different potentially successful strategies in order to win a game.

Alternativly: Strategic freedom is the number of different potentially successful strategies in order to not loose a game.

So what means potentially successful - a probablity of 1 to win or not to loose?

There are some games where this is relatively easy to measure, like this one (can't remeber the name in english)

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However for most other games, especially where randomness plays a role like in Battle for Wesnoth(BfW), this is not appropriate. Lets say then a potentially successful strategy is a strategy to win or not to loose a game with a probability > 0.5.

Measuring this directly seems rather incredibly complicated or rather impossible for games like wesnoth. However it might be possible to measure it indirectly by using some game parameters, talking about BfW, the average maximum number of move points(mp) of units, for instance. Ofcourse such a method would permit the comparison between different games but it would allow the comparison between different game settings within BfW. That said, does a reduction of average mp redcue or increase the strategic freedom? Does Battle for Wesnoth have a higher degree of strategic freedom with the concept of zone of control compared to BfW without such a concept? Does reducing the size of a map reduce or increase strategic freedom? Does reducing the number of villages on a map reduce or increase the strategic freedom? ...


*Strategic Freedom is a term used in buisiness related topics. However I couldn't find anything regarding to games.

Note: I posted this here, and not in off-topic, since this might be interesting for game development in general.
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suiraCLAW
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Post by suiraCLAW »

First of all, one bad move should never make you loose or win the game alone. You should always win because you made more consuctive good moves than your opponent.

In my opinion, strategic freedom divided by the game complexity and skill required are often inversely proportional: how less ways you can move while winning the game, how higher the chance that you picked that right way by tactic and insight instead of just having an lucky guess. Compare it to the shooter genre: how smaller the hit box (the places where you can hit your target), the more aiming is required. In the strategy genre, making less good moves possible (and making more bad moves possible), will result in making the players job to choose the right option harder.

However, going for the highest game complexity and lowest strategic freedom isn't really an option either, since that will often reduce the fun.
In the strategy genre, having a small strategic freedom would decrease the variety of the actions extremely much. For example, if there's only 1 succesful option to take at turn 1 if you don't want to loose, turn 2 will always start the same. While if you could take say 50 different good moves available at turn 1 for both players, the second turn may start in 2^50 ways.

This also means that the smaller the strategic freedom, the more experience (remembering how you solved the problem the previous time) becomes important.
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Post by CarpeGuitarrem »

suiraCLAW wrote:First of all, one bad move should never make you loose or win the game alone. You should always win because you made more consuctive good moves than your opponent.
Depends on the game. Take Tic-Tac-Toe (Noughts and Crosses), for example. (PingPangQui, that's the English name of the game you showed) If you make one wrong move, you're toast, and so it's a very intense game. You have to weigh every move carefully. (Kinda like sometimes in real life, like when you're in a duel with somebody. You can't slip up.) The more complex the game is, the more moves it takes for you to mess it up.
In my opinion, strategic freedom divided by the game complexity and skill required are often inversely proportional: how less ways you can move while winning the game, how higher the chance that you picked that right way by tactic and insight instead of just having an lucky guess. Compare it to the shooter genre: how smaller the hit box (the places where you can hit your target), the more aiming is required. In the strategy genre, making less good moves possible (and making more bad moves possible), will result in making the players job to choose the right option harder.
Exactly. And a good way to look at it.
However, going for the highest game complexity and lowest strategic freedom isn't really an option either, since that will often reduce the fun.
In the strategy genre, having a small strategic freedom would decrease the variety of the actions extremely much. For example, if there's only 1 succesful option to take at turn 1 if you don't want to loose, turn 2 will always start the same. While if you could take say 50 different good moves available at turn 1 for both players, the second turn may start in 2^50 ways.
Agreed. Yay for stats.
This also means that the smaller the strategic freedom, the more experience (remembering how you solved the problem the previous time) becomes important.
Yep, I like this way of putting it. A good game is all about balancing strategic freedom and complexity. The interesting thing is, it's not the same for all audiences. Seasoned wargamers, for example, can deal with a high level of strategic freedom and complexity. But a casual gamer wants less complexity, and less strategic freedom.

Now if only there was a way to have high strategic freedom and low complexity...
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cool evil
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Post by cool evil »

Tic-Tac_Toe is probably the most simple strategic game ever, with 9 squares, its like placing three soldiers to form a line which means you have won. To make a game with low complexity and high strategic freedom is quite hard, wesnoth is somewhat complex, but offers extreme strategic freedom, the move of an unit can be only limited by it's movement points and the available tiles. And every user input easily multiply the amount of possibilities in a match. I think it's safe to say there's at least over an million possible outcomes(as in any event such as units recruited, unit dies, how long it takes to win/lose)

On a site note: How to win Tic Tac Toe (only one possible way unless your opponent decides to not block you when you have 2 tiles placed already and are only one away from winning)

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X |   | 
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Velensk
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Post by Velensk »

The defender needs to place his first O in a corner. No, tic tac toe between two people who know what they are doing is impossible to win.
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Derekkk
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Post by Derekkk »

The first thing I wanted to say is that in a perfectly balanced 2-player game, there should be no strategy that can guarantee a person >50% chance of winning. And wesnoth was made with this in mind.

But as humans (or even computers), we cannot ensure that every step we took is the best one, especially if there are very few right "steps" among many many bad "steps". So perhaps if a strategy can limit the opponent's choice of steps, so that he has a high tendency to pick the bad steps, then the strategy is a "Good" strategy.

Suppose strategic freedom is defined as the number of Good strategies.
And strategy is defined to be a set of rules regarding a set of situations. For example, in tic-tac-toe, the first rule might be to put a cross in the center square when you start the game. This rule is part of your strategy. Let's also take [for each turn, >50% of the steps are bad steps] as a requirement for a Good strategy.

For this definition of strategy, we can clearly see that a 3x3 tic-tac-toe allows a larger strategic freedom than a 2x2 one since, taking symmetry into account, there is only 1 starting rule which gives the opponent >50% bad steps in a 2x2 but 2 for 3x3.

(2x2: take any one square; 3x3: take any 1 corner or take the center)

Generally, the higher the game complexity, the larger the strategic freedom. This is purely because a higher complexity allows a much higher number of strategies, but this doesn't mean that the proportion of Good strategy increases.

My feeling is that, under changes in the game complexity, the proportion of Good strategy remains constant, and is inversely proportional to the % chosen as the requirement. Assuming that the game is balanced, this proportion of Good strategy should be the same for both players too.

As for finding the exact strategic freedom a person gets in a non-deterministic game like wesnoth, I don't think anyone can give you an easy answer.
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Post by PingPangQui »

Velensk wrote:The defender needs to place his first O in a corner. No, tic tac toe between two people who know what they are doing is impossible to win.
Correct. That's also why I gave two alternative definitions for strategic freedom. They don't mean neccessarily the same. An example would be BfW multiplayer games in case a turn limit has been set.

Furthermore, I think I have to clearify what I mean by strategy. To me it is not a walk through line or tree showing every single step one has to do. It is rather an overall guide of a few lines explaining how to play. For tic tac toe a "not to loose strategy" is the following:
  • Place your piece in a way that results in the highest amount of possibilities to form a line later. In case your oponent has the possibility to form a straight line in his/her next turn put a piece on the respective location to prevent the oponent of doing so. (If you are the first player, then you may place the first piece anywhere.)
A native speaker may be able to describe that even shorter. So my question is how many different potentially successful strategies exist for a certain game? For tic tac toe there is only one I can think of (see above). Please correct me in case I'm mistaken. Since I can't think of an appropriate way how to measure that easily for many other games lets start with one we all know - Battle for Wesnoth ;).

Maybe we'll find a way to approximate strategic freedom for certain settings or can at least approximate the change of strategic freedom in case certain paramters are changed (see also questions in my first post). Since every unique setup of a BfW multiplayer game is actually a different game, the best way to start with is probably to constrain the discussion to a certain setup.

Lets say, the map is Weldyn Channel (Blitz) with default settings and default era. If you post a strategy, please make it as short as possible. Furthermore name the factions, name their leaders (hero), name the faction and the side for which the strategy applies and don't forget to mention the version of BfW.

Example:

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BfW Version: 1.3.11
Factions(side 1 - side 2): Loyelists - Rebels
Heros(side 1 - side 2): Lieutenant - Elvish Captain

Strategy for Rebels: bla bla
If the strategy given doesn't depend on the hero, side position, etc. please say so explicitly.

P.S.: Thanks for all your posts and the healthy discussion so far which will hopefully continue this way.

P.P.S.: Derekkk, the answer will most likly not be easy. I do not expect to gain a formula to measure strategic freedom (sf) exactly, but to get an answer how to approximate it or at least an idea about how to do it.
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Incompetent
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Re: Strategic Freedom

Post by Incompetent »

Go is interesting in this respect. On the one hand it's very freeform early on; on the other, when a fight gets going in a particular region, making just one move that doesn't contribute to that fight will often automatically cause you to lose a cluster of stones in the first region unless your move threatens to kill even more stones elsewhere. Go strategy is immensely complicated to write down precisely, but for some reason, humans have a knack for knowing roughly what to do, and this works rather well.


Strategic depth and freedom are very important to a game, I think, and a big part of game design is about thinking how players could use a 'gamey' strategy to simplify the game too much. I came up with a board game on the following principle: players write their orders simultaneously, but individual pieces take turns: the longer an order a piece has been given, the later it will act. The result is a game with fairly fluid strategy; in fact, predictable strategies are disastrous, because there is always a counter - you would need overwhelming superiority in unit power, at least 2:1, to beat an opponent who knows how you're going to move. But I was worried about two annoying strategies: the random strategy and the dreadnought strategy. The random strategy is to just be as unpredictable as possible, and pick moves for your units randomly out of a collection of vaguely sensible moves, but with no overall plan. It turns out that random looks surprisingly sound in the short run, but not in the long run: if player A is playing randomly and player B is playing strategically, player A will initially suffer few casualties. But they'll inflict even fewer on B, and B will gradually take strategic control of the battlefield and pin A down, at which point A starts getting massacred. So that works out OK. The dreadnought strategy is to build a single super-unit, which makes the game boil down to the outcome of a single dreadnought fight if both players do it. Now in this game high-level units don't have any extra hitpoints or firepower, so if used stupidly they will die very easily, but they move faster, which it turns out is a *massive* advantage if used well, so that a single super-unit can be a match for 3 or more moderately priced units. I still haven't come up with an answer to this, but maybe more play-testing will reveal some good counters to it.

Hmm, maybe I should put the rules of this game somewhere on the Internet for people to read. I'm generally happy with it, but there are a few rough edges to polish. Incidentally, it's played on a square grid with no diagonal moves, and I don't see any problem with this in terms of fluidity.
PingPangQui
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Re: Strategic Freedom

Post by PingPangQui »

Incompetent wrote:Hmm, maybe I should put the rules of this game somewhere on the Internet for people to read.
Please do so, this sounds very interesting.
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Re: Strategic Freedom

Post by markm »

Wesnoth's campaigns seem, to me, an interesting case study in strategic freedom. The freedom comes in bursts, with a limited spacetime-locus. It seems like a selective set of worlds from a multiple worlds hypothesis type of universe.

Take Heir to the Throne for example. You have lots of freedom as to how exactly the young lad grows up to marry the Princess and have two sons and one daughter, but all those possible routes to that nexus are surrounded by ignored worlds/possibilities.

I have also been exploring The Rise of Wesnoth and Under the Burning Suns. In the latter, who knows or cares whether it was the dwarves or the trolls that were allies? In the long run, does it matter? Either way, you reach the same end-scenario. Different people(s) might have totally different 'histories' and 'legends' about what really happened, but the campain asserts bubbles around or between nexi where timelines are considered by someone or other not to necessarily matter in much detail provided the intended/desired/forced end-result is achieved.

The playback ability in Wesnoth whereby it is not just savegames of static states (state at start of turn / end of turn) but also a blow-by-blow through the turn makes it potentially useful for very fine granularity. Any individual attack of one unit upon another unit could in principle be blown up into a whole more-detailed game, becoming a scenario. Or one entire turn could be made into a campaign, with each move in the turn being a move from one scenario to another. Each hex being potentially a scenario.

Supposedly when electrons tunnel they somehow seem to consider all the possible routes they each could take, and cancel out the choices that cancel out, ending up with 'what really happens' being the end result of working out all possible happenings and having them all take each other into account.

We can get something similar to that in Wesnoth. Umpteen people try umpteen strategies, and as the strategies are refined the scenarios themselves could even end up being 'adjusted'.

Presently the normal adjustment made in mainline is to adjust for balance. But in principle there could be factions trying to influence adjustment processes in their own favour. Development itself could become a kind of campaign. Presently the mainline seems to assume that some kind of 'powers that be', or 'necessity', or 'providence', or some such thing, is acting to ensure that that kid does marry that princess and they do have two sons and one daughter.

But huge numbers of savegames could be generated demonstrating that that is not the only route history could have taken. We already see a whole lot of variant histories that all fit within the criteria of the mainline campaigns, and a number of people seem quite content that no timelines violating those constraints shall be taken as valid real timelines by mainstream inhabitants of the mainline.

Imagine, though, being able to track down the Lich or Wizard or whoever that used his or her 'magick' to cause the mainline to be main, and kill him or her, or take on their forces with opposed forces.

I am not fond of investing umpteen hours into developing my forces throughout a campain only to have all that 'work' be for 'nothing'. So I am trying to work on ways to add more continuity. One possibility is to have a means of increasing the number of 'must not die' units. One thing that could allow history to become more and more tightly pinned down would be to be concerned about more units or bloodlines. For example if we surveyed huge numbers of savegames of a campaign, as played by more and more players, maybe we could discover some unit-name that occurs over and over again, enough that it could be braided into the campaigns. This could be a 'hard' difficulty level, or 'chronodynamics institute difficulty levels'.

If you find the campaigns too easy, would adding more 'must not die' units make them harder? Suppose we went to the extreme of making every unit you recruit be a must not die unit? Too hard? How about a 'compromise' then: any unit you recall must not die? Still too hard? Lets start easy then: fight or argue or bargain or in some other way decide on one unit a bunch of people's best-timeline-so-far features, and make it a must not die unit, so that even though 'mainline' might not insist that unit must not have died nonetheless the Chronodynamics Institute's 'tightline', a more 'tight' constraining of 'mainline', insists that it must not.

I am working on a way of making this a game or campaign of a kind itself, such as using 'golden apples' to give your 'loyal' units the ability to live long enough to move with you from campaign to campaign. To get these 'golden apples' would be a quest itself. Multiplayer would be an option for determining which players get how many 'golden apples', but I am thinking of a less synchronous approach to accomodating multiple players. No need to wait for the other players to move, you can go ahead and play all possible moves if you want, pin down more and more precisely exactly what happened not simply by having a multiplayer match or duel but by fighting for each alternate action or strategy so it becomes more and more obvious what 'must' happen or what the 'key nexi' are, the key choices that can end up being the defining criteria of 'scenarios'.

Your elf killed his troll? Fine, if that is the one and only result that counts, there is a 'scenario' right there. It is a 'kill that troll to win' scenario. Does it matter whether the elf that killed the troll survived or not? Maybe not. But if it does, then that is also a 'this elf must not die' scenario.

A lot of roleplaying games include 'spells' or 'abilities' to look into the future. In some you supposedly actually walk through time, being able to jump back if you encounter something you don't like. The players, by using the savegame feature, already have that ability. The challenge is to incorporate that ability into the game itself, so that ultimately you could work a wizard up to a level where he could legitimately, within the game, rollback to a savegame...

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Re: Strategic Freedom

Post by Dave »

I think that this concept is the reason why many computer games become boring at very high levels of play.

In many computer strategy games -- especially 4X style games -- there are numerous ways you can play. Passively, aggressively, and so forth. This works well on intermediate levels of play, when players are playing fairly casually.

However, if you want to play the game at a high level -- becoming very skilled at it -- winning on the very hardest levels often start removing strategic freedom. It is often possible to win the game on very hard levels, but only using very very specific strategies, with little variation.

I think that Wesnoth allows a reasonably large amount of strategic freedom, even at higher levels of play. It's far from perfect, but relatively to many other games, I think it's quite good. Additionally, and importantly, playing Wesnoth at a high level is still all about fundamentals. It's not about using some obscure strategy to win, it's about the core game features of risk analysis, careful planning, strategy, and so forth.

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Re: Strategic Freedom

Post by markm »

Luckily Lord Linus's objective isn't, as far as I am aware, to eliminate fun but, merely, to take over the world.

We Linicists are quite willing to allow as much strategic freedom as remains consistent with taking over the world, and, in addition, as much fun. :)

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Re: Strategic Freedom

Post by CarpeGuitarrem »

Oooh...time warp...sorry, that just got my mind flowing a bit. Intriguing scenario idea.
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Re: Strategic Freedom

Post by meriton »

In many computer strategy games -- especially 4X style games -- there are numerous ways you can play. Passively, aggressively, and so forth. This works well on intermediate levels of play, when players are playing fairly casually.

However, if you want to play the game at a high level -- becoming very skilled at it -- winning on the very hardest levels often start removing strategic freedom. It is often possible to win the game on very hard levels, but only using very very specific strategies, with little variation.
Yes, many games work that way. But there are exceptions, even in the 4X genre. In Master of Orion, to implement any strategy matching technology is needed, but the technology actually available to the player is restricted by events outside his control. (Briefly, each player can only research a random subset of the technologies. Players can complement these technologies by aquiring (through conquest, espionage or diplomancy) techs known to other players). Therefore, a strategy working in one game does not necessarily work in the next, allowing - even forcing - variation in strategies from game to game. Variety need not necessarily arise from players' choices.
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Re: Strategic Freedom

Post by Max »

you could easily do this with wesnoth too. just design a scenario to e.g. randomly spread some units on the map (perhaps in clusters).
it's a bit harder in bfw to do this also during a scenario and still keep up balance, but would it change the strategic freedom?

whatever happens, you are still facing a certain situation. imo such things just introduce a few twists where you have to adept your plans.

i think Dave is right - if i play campaigns in easy mode i have much more options. i can choose to maximize gold, or maybe xp's, number of leveled units or just being lazy and make sure i don't loose any high level units (and usually there are more ways to reach these goals). in hard things change. it's often just a matter of surviving and reaching your goal on time.
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