Identity Relationship Linear Relationship An identity relationship - - PDF document

SLIDE 1

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Zach Laster University of Helsinki

 We talked previously on how values interrelate. Now we’ll

look at some concrete examples and forms of relationships.

 Numbers in games don’t mean anything alone. They need

some form of comparison points (context) to become meaningful.

 If an item costs 1000 gp, is it worth a lot?  What if a ship has 12 move a turn? Is it fast?  We only know whether something is good or bad based

• n its relationship to other things.

 If smelting a block of iron costs 200 smelt, and coal provides 1000, we know something about how smelting works.  If we frequently get bags of 10000 gp in a game, obviously the 1000 gp item isn’t really that valuable.  If the world is thousands of tiles in size, 12 move won’t feel very fast; but we still don’t know how it compares against other move speeds!

 Relationships between numbers can be either

two-way or one-way.

 Generally these relationships are in reference

to converting one resource to another

 We can convert 1000 gp into the item above, for

instance.

 We can get 10000 gp from running a dungeon.  We can spend 1000 gp for 10 HP  etc  When determining game balance, we often try

to tie all of the resources in a game back to a single resource. This helps us determine how various things compare.

Identity Relationship

 An identity relationship is where two numbers

move together in exactly the same way.

 As one increases, the other increases by an identical

amount.  They can start at different values, and other

things can act upon them

 Not quite the same as having a copy of the value  If you consider the example of food from

Ultima III: Exodus, we can get food from gold as a one-way identity relationship. Food then decreases over time.

Linear Relationship

 A linear relationship is like the identity

relationship, except it scales.

 We can have a 1-to-12 relationship, for

example.

 If I can get 10 HP for 1000 gp, that’s a 1-100

relationship.

○ This assumes there are no progressive deals,

like 20 HP for 1750 gp… That’s not a linear relationship at that point, obviously.

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Exponential Relationship

 Exponential numbers get big FAST  Basically, this relationship is when you want

something to scale very rapidly, like buying skill points or stats in a system where the next one is more valuable than the first.

 Stat points in D&D 3.5 are a great example (gp for

the magic items).

 Same for gp costs on a number of magic item properties,

actually  Often accomplished by doubling.  Typically, we don’t bother with anything more than

• doubling. Tripling makes things almost prohibitively

expensive, in practice, or far too powerful.

Triangular Relationship (Polygonal)

 When we want something like the exponential

relationship, just not as huge, we often go for triangle to stair relationships.

 For each step on the one side, we increase the other

by one more than it was increased last time.

 1, 3, 6, 10, 15, 21…  This probably looks really familiar  D&D 3.5 uses this as the XP requirement for leveling  Each level requires the previous level times 1000 XP

more than they had to get to that level

○ 0, 1000, 3000, 6000, 10000… etc

 We can actually use other shapes as well.

Formulaic Relationship

 There is no reason you can’t create more

customized relationships between numbers.

 Some numbers just might be lots more or less

valuable

 The difference between almost one-shotting

something and actually doing so is HUGE  If none of the standard relationships work

for your case, make one up. You can build it from the standard ones, as an aid.

 The only key is to understand how the

relationship will impact everything else!

Systems of Relationships

 Since we typically have more than two

numbers in a game which relate, we wind up with a network of numbers which interrelate.

 If we can convert 3 blue gems into a red

gem, and 4 red gems into a green one, we can obviously convert 12 blue gems into a green gem indirectly.

 If these relationships are two-way, then a

single green gem can get us 12 blue gems.

 Constructing this network can help tip us

• ff to issues in our relationships.

 I can get 100 gp from donating blood, and I lose

10 HP for doing this. (1HP→10gp)

 I can heal myself for 10 HP using 5 MP

(1MP→2HP)

 I can buy a MP potion (5MP) for 50gp

(10gp→5MP)

 1HP→10gp→5MP→10HP→100gp

○ Whoops

 Feedback loops aren’t inherently bad,

though, as we’ll see.

 We can also get an idea of what the

central resource in our game is.

 The above one was probably HP, given

there are probably other relationships I nthe game which affect HP directly (damage)

 Most of the time, the game’s win or loss

condition will be tied to this resource

 You lose if you run out of HP  If it isn’t perhaps you should move it, or

redirect some of the relationships

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 We’ve mentioned feedback loops, like the

blood donation one before.

 Actually, most games use these loops. They

aren’t really bad.

 The one given was bad because donating blood

probably isn’t something we wanted to incentivize like that. If it was, though, we’ve done it.

 Usually the loop looks more like:

○ Kill monster (HP→gp) buy more stuff

(gp→damage) kill more monsters (less HP→gp)

○ So feedback loops can also produce a

progression, if they are controlled properly.

 Usually, these loops are controlled in the manner of

diminishing returns.

 Killing Monsters results in XP (HP→XP)  XP produces level ups (XP→Level)  Levels increase damage and such (Level→damage)  Which makes us better at killing stuff  We’d be stuck in a loop (we are, actually, but…)

except killing that monster tends to become less effective after a while.

 We need more XP to get that next level  The monster stops providing as much XP as it did before.  The combination is brutal. We need more, and we get less

than before. It’s like a drug addition. (Actually, a lot like, but that’s another story.)



Progression can also be tied to the resources, such as buying maps or keys using gold to allow us to access new areas, or buying item blueprints or better items.

 Often, gold is a related resource to HP, so really we are kind of spending HP 

In some cases, we can’t actually use all of the resource we have

 Once you’ve bought all the stuff you want with gold, what’s it good for aside from healing? 

We can also bias costs to make certain things more or less cost effective, making them more valuable in terms of HP than other things of a similar price.

 Incentivize particular items or spells.  Make higher tier things less effective by cost, but still more effective, slowing progression 

When looking at these relationships, we should also consider how time is affected (it’s almost always a resource).

 Now that we can compare things fairly well, what do we

do with it?

 The previous set dealt mostly in resources. Now we’ll look

at things from the perspective of costs and benefits.

 A cost is anything which can be considered a drawback or

limitation.

 Spending gold, using an action, expending a charge, unit caps, etc.  The item has a limited number of uses, only works under certain conditions, etc.  A benefit, then, is anything which improves out position  Increases our health/damage/power  Makes the other guy more squishy  Cool powers

 When balancing things, we generally want our

costs and benefits on an element to balance

• ut

 Of course there might be a general bias towards

benefits, but that’s a design decision  We can still tie these back to the resources

fairly well, most of the time, but the only important part be that they compare to each

• ther.

 Note that some benefits come with costs.  A weapon that deals double damage to orcs is really cool against orcs, but the benefit doesn’t apply most

• f the time (unless you are mostly fighting orcs)

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 Remember our definitions for overpowered,

underpowered, overcosted, and undercosted.

 If a sword has some kind of special ability on it, it needs to

have more costs attached to it than normal.

 We could make the sword more expensive  Or we could make it have a limited number of uses  Or we could make it so the sword does something annoying/negative under certain circumstances  It could also be made to take more time to swing  However we choose to counteract the benefit, it only

matters that the costs and the benefits balance correctly

 In some games, any of those would work. In others, some of them would be too much, or not enough.  The trick is to determine the value of the costs and

benefits relative to each other.

Cost curves

 Once more, we go back to comparing

everything to resources.

 Once more, ideally a single resource.  If we determine a sword’s value in terms of

how much HP you save using it, we have a value for its benefit.

 We can do the same thing for abilities on the

weapon  If we have an attack stat, which has a

relationship of 1:12 to gp, we can easily determine that a sword with +5 attack should cost us 60 gp.

 The catch, of course, is that we don’t

always have such simple relationships

 Things may grow triangularly or exponentially.  We might also want to change the

relationship between costs and benefits

 We can build some artificial resources “cost”

and “benefit” and relate those back to the central resource(s)

 Once we have their values, we may wish for 1

benefit to require 2 cost on an item

 More likely, we’ll have a triangular relationship  It’s also possible for the cost/benefit

relationship to be a diminishing relationship

 Requiring fewer cost to get each benefit  This could be to encourage resource hoarding,

where it would otherwise be punished by the game  A curve (more complex relationship) can

also be defined, such as in Magic

 Lots of lands gets powerful fast, but only after a

certain point.  In addition to the cost/benefit

relationship, we need to define how much each effect produces in terms of cost or benefit

 Some effects won’t necessarily tie back

to the resources conveniently

 In these cases, you’ll basically have to

compare them to other effects you know

 This largely comes down to getting a feel for

how things fit together in your game

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 Inventory is just a way of referencing the player’s

resources

 Economy, resources, units, player inventory, health, ammo, etc.  All the things the player has, even if you wouldn’t normally consider this an “inventory” system.  We’ve talked about relating resources and numbers to

each other, and tying them all back to central resource, but what are resources?

 This is basically the same concepts, from a different perspective.  Resources help drive the game forward.  What are the costs of things and what are the limits on things?  Where do these things come from and where do they go?  How do the resources relate to each other? Do they? Can you convert one to another? What's the conversion rate?

 Resources allow us to limit what the

player can and cannot do, generally through limiting the availability and utility

• f resources. If you need the red key to

go through a door, then we can prevent the player from accessing part of the game world by hiding or limiting the red key in some way.

 Resources commonly have sources and

• utlets.

 The resource comes from somewhere, such as

being generated or traded for

 It is then expended in some way  This limits the amount of a resource, and gives it

a value  From the perspective of economics, this is

a scarcity system

 We can control how valuable a resource is

by limiting where it comes from and where it goes, and in what quantities

 The scarcity or availability of resources

also affects game balance.

 If a player is constantly given ample supplies of

ammo in a shooter, then they will not value that ammo highly.

 This will enable and encourage more casual

weapon use, such as spray-and-pray tactics.

 However, if the ammo supply in a game is more

conservative then the player will generally value the ammo more.

 The important question is: How should the game

be played?

 If we wish for the player to have an easy time

running through game levels, blasting enemies left and right without a care in the world an a maniacal smile on their faces, then we can provide them with generous supplies of ammo and health packs.

 However, if the intent is to make the player

carefully open every door, weigh every decision, and always feel like they just barely survived each level, then we should make these packs scarce.

 Similar concepts apply to economies and other

resources.

Sinks and Sources



As said, resource come from somewhere (sources), and go away elsewhere (sinks)

 Since most games are a closed system, we can control the amount of any given resource by manipulating these. 

If we need more of something, we can make sources more numerous or plentiful



If something is currently in abundance and we wish to make it more scarce, we can increase the rate of drain by increasing the number of requirement of sinks.



If metal is mined from regenerating deposits, then that’s an infinite source.

 Unless we want that metal to effectively infinitely accrue within our system, we need an outlet for it.  One example sink could be armor (made from metal) wearing out. 

Most MMOs have implicit sinks which are difficult to control

 Players stop playing. When they do, the resources they have are lost to the rest of the world.

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 One thing we can do is to build a network of all

the sinks and sources for a resource to analyze how it moves around.

 If the paths along the network have

information attached, we can also consider the cost of moving along it, such as how hard it is to convert iron into armor.

 We can actually do this for all the resources in

the game, in order to fully assess how everything moves and interrelates.

 This might take some time on large systems, such

as highly complex economy systems or MMOs with lots of items and/or base resources  Such a network is fairly similar to the numbers

system from before.

 Combining the two concepts, we can readily

determine the value of anything in the game, and how it moves around.

 We can more easily make these two things correlate.  We can control the availability of things  While the number relationship network tells us

a gold to HP ratio, the sinks and sources network shows us how these things move around and where most of our “HP” goes. And where it comes from!

 The two combined can be extremely powerful!

 We’ve already looked at two kinds of

networks (graphs) we can build to analyze our game.

 Number relationships  Resource sinks and sources  Are there other kinds we can build that

show different information?

 What information can we pull from what

we have?

 As it turns out, we’ve covered pretty much

everything with the two kinds we have.

 Either one already covers most things, though from

different perspectives  The relationship graph tells us about global

information, such as the relationship between gold and HP.

 The resource graph has a more spatial taste to

• it. It tells us more about our game world itself.

 This can be more useful for handling an economy

system, where the relationship graph would actually kind of fall flat!

 Since our resource graph tells us how hard it is to

move things around, we can use it to detect particular kinds of cycles.

 While our relationship graph can tell us about

positive or negative cycles overall, we can attach more information to the resource graph to find locally powerful cycles, such as trade routes which are ridiculously short.

 For instance, say we’ve intentionally made trading in

energy valuable in a space trading game

○ If there is a sector which sells energy from one area, and

buys it from another nearby such that the player can turn a profit, that trade route will become too valuable.

○ In an MMO, this would result in a lot of players in the area,

which can be bad.

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 One solution to such a cycle is to move the

buying station further away. The cost of using the route goes up.

 Alternatively, we could implement a supply and

demand system, such that the station will buy energy at a price set by how much it currently has

 Nothing actually says we HAVE to solve this,

• r that it’s technically a problem.

 If we don’t mind the cheap route, or that players will

gravitate here, it’s actually fine.

 In a single player game, it’d actually be fairly

reasonable, if a little imbalanced.

Constraints

 Using the resource information we have, we

can establish basic concepts for what a balanced area is.

 If we want a level to flow a particular way, we

can devise a set of rules that describe how

• ften and where resources should appear.

 We’ll call these constraints  If we are playing a first person shooter, such

as Half Life, we have two primary resources: health and ammo

 If we wish to scale the difficulty of a level a

particular way, we can obviously adjust how much ammo and health is in the level

 One of the key elements here is we wish to

control how much ammo and health the player has at any given time.

 We don’t want to give the player all the

resources up front, we want to space them out

• ver the level so they always have just the right

amount  If we want the player to conserve ammo,

we given them just enough to kill the coming enemies.

 We can also use this to encourage the player

follow a certain path.

 We can actually use our constraints to do a

number of very interesting things.

 We can use them to build randomly generated

levels which are properly balanced.

 We can use them to adjust the difficulty of a

game as it is played.

 This gets into adaptive difficulty which I think might

be a little too advanced for this course. We might discuss it on day 5.

○ For anyone interested, look up Half Life 2 Hamlet ○ “AI for Dynamic Difficulty Adjustment in Games”

Hunicke  At a more normal level, we can use these

constraints to evaluate the balance of areas

 Is there enough ammo, too little? Too much?  We can also use constraints to determine how much

is needed to accomplish the level

○ If we need two yellow keys in the level, and there’s only

• ne, we have a problem.

○ If the second yellow key is behind one of the yellow

doors, and both are available to be unlocked with the first, we might have a problem.  Largely I use these to devise automated

systems, but the concepts stand for use in an “offline” context.

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What is Content Progression

 As the player goes through a game,

more content should become unlocked

 Better stuff  More world  More story  Harder gameplay  etc.  Why’s this matter?  What’s the value to it as a game mechanic?

Ending the game

 Particularly for shorter games, we want to

move the game towards its end

 We also want to control the timeframe that

• ccurs within

 We don’t want the player completing our big

blockbuster title in an hour!

 We also don’t want a boardgame to last for 10

hours…  We therefore control the timing and pacing

• f the game through content unlock

Ending the game when it doesn’t

 Some games simply don’t end. They go

• n and on.

 MMOs, many tabletop RPGs, the Sims  However, there does come a point

where you’ve exhausted (most of) the content.

 “I’m a level 300 warmage with a celestial

skybear and my own undersea house”

 In these games, you enter the elder

game

 The elder game is the point where the

game changes

 In the Sims, you switch to playing story time  In MMOs you switch to high-level game content,

like PvP, raids, or crafting or social aspects such as being guild leaders or region controllers  In Tabletop RPGs, the elder game is a

quest to end the game

 “I want my character to build a thing and retire

there”

 “I want my character to die in some ridiculous

battle”  Not everyone enjoys the elder game of

games they otherwise enjoyed

 Some people get bored  Some people don’t like raiding  Some people just don’t think building another

fancy house in the Sims will really do it.  Balancing these elder games and

managing the transition to them is a bit of an art and has to be considered.

 On the flip side, some people who would

love the elder game of a game never make it there.

Ending on a good note

 Games which do end actually have a

different problem, they end.

 I just built up to supreme power of the world.

Game over.   In many cases you’ll end right at the peak

• f your power.

 Games like Civ tend to let you keep playing, but

what’s the point (half the time)?  Other games you’ll steadily lose power, like

in chess.

 At this point you end having just been ground

down constantly. Not exactly a high point.

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 Peter Molyneux’s intent with Fable 3

was to have the player reach most of their power early on and then spend the rest of the game paying back for that power.

 This was pretty clever, actually, and worked

• ut pretty well.

 However, it means that the game needed to

provide a strong elder game in order to be successful

Balancing Progression

 We need to consider how this content is

unlocked and when, and make sure that it works in a balanced manner.

 We prefer to keep the player’s power level in

check, for example

 Again, the difficulty of the game overall

depends on our target (audience).

 Technically, we can define whatever and we’ll

attract the appropriate audience. We just need a target something.

 Remember the flowchannel!  As the player progress, they will get better

at the game

 Either in person skill, through unlocked content,

• r both

 We want to keep this within the flowchannel,

too!

○ In fact, this is primarily what the flowchannel is for!

Types of Progression

 When playing against other players

(PvP), the progression is obviously in comparison to them

 Your power is only important in relation to

your enemies’ power

 In a PvE or singleplayer game, the

progression compares against the world, so it’s a bit more absolute

 The combination of the two is obviously

more complex

PvE Progression

 We ultimately want the player to feel

challenged, but the player isn’t really aware of the myriad causes of that, only that they are or are not

 “it’s like if the dashboard of your car took the

gas, current speed, and engine RPMs and multiplied them all together to get a single “happiness” rating, and you only had this

• ne number to look at to try to figure out

what was causing it to go up or down.” - Ian Schreiber

Perceived Difficulty

 Components  Player Skill  Player Power  Skill-based challenge  Power-based challenge  Skill and power can be interchanged,

especially on the challenge side

 Halo AI used this, for example, to produce the

illusion of better enemies  (Perceived)Difficulty = (SChallenge +

PChallenge) - (PlayerS + PlayerP)

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Controlling Player Skill

 Obviously, one of the most defining factors

in perceived difficulty is how skilled the player is.

 One might think we have no control over

this, but we can actually do soemthings about it

 We can control the rate and limits for player

improvement

 We can provide areas to boost their skill

(tutorials, safe zones)

 “skill gating”

Measuring

 We’ll talk more about this on Day 4  One of the best things we can do is try to

track how often a player fails or falls

 We can then adjust difficulty elements

accordingly  Comparing player power and power

challenge is easy, as we control both

 Basically, we can build our expected curves for

this and adjust the challenge as we see fit, probably even including some additional increase to compensate for player skill increases

PvE Rewards

 Content as a reward  One of the main methods we can use to control progression is as a reward to the player  Really, this is part of the innate content unlock

system

 We just want the player to feel like they earned it  If they don’t think of it as a reward, it doesn’t seem

as valuable

 Rewards are fun!  There are two important notes to this:  The player needs to recognize when they are being

rewarded

 The rewards need to be appropriately distributed  We don’t want to give too few rewards, lest the

player feel they aren’t progressing

 Or they might get bored, which is probably worse  Conversely, too many rewards reduces their

perceived value

 “I’m sorry you are bored, have a ring of three

wishes”

 Spacing out rewards helps too. Rather than giving a

big reward at the end, split it into parts so the player feels rewarded the whole way through  A slightly random reward schedule is also

highly effective, but must be tied to player action and intent

 A good example of such a random schedule is loot

drops

 Sometimes you get pretty cool stuff (and you can bias

that, as well talk about tomorrow)  On the other hand, a slightly irregular schedule

works similarly

 A cut-scene when arriving somewhere or something works

well

 Basically, unpredicable is the key  However, this can be done wrong  Freebie achievements  Hidden Achievements  Arbitrary Achievements  Rewards for something the player wasn’t even going for

Power through Toys!

 Obviously, part of this rewards progression is

an increase in power

 Also in toys, though, like the gravity gun  However, if at some point you run out of toys

to give, you need to keep the player entertained by other means

 Increased complexity in the application of they toy  Increase the rate of other rewards  Toy upgrades (similar to new toys, but not quite as

cool)

 Shorten the game (what’s the extra stuff at the end if

you gave out all the toys?)

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Levels as Rewards

 Obviously game progress is a reward of

sorts

 The player probably wants to progress along

this, assuming you did your job at all correctly  Story progression (which is everywhere

these days, which is awesome!) is also a reward

 It’s probably worth trying to keep the game

difficulty in-line with the story tension, too

○ This is easier to do via numbers changes than

story changes, by the way

PvP Progression

 Since PvP progression is relative to your

• pponents, we obviously wish to have

gains in power against them

 This results in a tug of war  Power here means more options,

generally, such as more ammo, health, weapons, cards, spells, etc.

 It’s also possible to make players lose

power over time, but then they just want to make the enemies lose more than they do.

 Either way, the goal is advantage

Game Theory!

 And you thought there wouldn’t be any more math.  When looking at games power progressions,

particularly for PvP, it helps to look at the game’s

• verall outcome tendencies (for utility)

 A positive-sum game is one where the total power is

increasing over time

 Monopoly  The total power in the game is increasing  A zero-sum action is one where the total power in the

game stays the same

 A negative-sum game is one where the power in the

game steadily drains

Feedback loops

 We’ve already mentioned feedback loops

to some extent

 A positive feedback loop tends to result in

players’ power increasing

 A negative feedback loop either decreases the

player’s power or reduces the gain  What are they good for, though? Should we

remove them?

 Actually, we can use feedback loops to

encourage preferred play or make strategies viable

 Positive feedback loops can help push the game

towards an end

 We actually want power increase to accelerate towards

the end, no point dragging out a forgone conclusion.

 We actually put all the players on such a curve, of course.

Balance and all that.

○ We don’t care who ends up ahead

 Negative feedback allows weaker players to catch up  Leveling curves sort of accomplish this  XP diminishing returns does a better job  In this case, we actually only wish to apply the negative feedback to players who are ahead, not all players

○ When they catch up, they shouldn’t be slowed down like

the other player was, or else they didn’t really catch up

Power curves

 The power curve of a player is the graph of the

player’s power over time

 Positive-sum games have a constantly increasing

curve

 Positive feedback makes he rate of increase increase  Negative feedback will slow the curve based on the curve

• f other players

 Zero-sum games have a fixed sum for all power

curves, and the power moves around between the players

 Positive feedback here can result in advantages; those

with power can take more more easily

 Negative feedback makes taking power harder the less

• thers have

○ Often brings the leader back to the center

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 Negative-sum games the power slowly

degrades, meaning that players are trying to avoid losing power

 Positive feedback causes players who are

losing to lose faster if the positive feedback is applied to everyone

 Negative feedback tends to make people

losing lose slower, reducing the rate which the lose power

Measuring Power

 The hard part is actually formally defining the

power curve in some unit of power

 If the game has some kind of unit of power,

such as overall wealth, score, unit points, etc, this is easier

 Generally, summing the primary or important

resources can give a good estimation

 I’d suggest using multiple power metrics,

weighted together

 Something like a potential power curve might also be

reasonable, like resources which are convertible to power right now

 Once you have a power function

defined, you can plot the player’s power

• ver time to make sure it is within

expected/reasonable bounds

 At the very least, this will produce

interesting patterns which can be analyzed

Game Phases

 Within a game we can often see definite

phases

 Here we mean things like moving between early

game to late game, rather than the phases in a turn  Often these are a simple as early-game, late-

game, and end-game

 Once aware of these phases (or having

designed them), we need to consider the power curves of the players within them

 It’s possible that the thing which defines moving from

• ne phase to another is actually that the power

curves align a particular way

Game Length

 Once of the things we can control using these

phases is the length of the game overall

 We can control the length and relative length of the

phases to push the game towards it’s conclusion within a rough timeframe

 We can also extend the length of the game by

extending some of the phases

 The elder game is often an infinite length phase  One thing we often want (though not nearly always)

is to move to the mid-game quickly

 Facilitating the player’s entry to mid-game means they

spend less time at a low power state

○ This is often a more fun stage of the game ○ Can be accomplished in some cases just by helping the

player get a good grip on the game

Asymmetric Phases

 Some games actually have phases of

the game that mean different things to different players

 For example, Netrunner  In cases like this balancing is harder, of

course, but possible

 For example, in Netrunner the rate of

progression can be pushed forward or held back by player action

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Ideal Game Length

 How long the game lasts is ultimately up to

how you design it, and you can choose to make the game shorter or longer

 But what should we target?  You are always free to choose whatever length feels best, but it will alter the interested audience some  Younger audiences will tend towards preferring short games  Casual players want games they can play in short sessions (this also applies to bigger games)  Longer games require more skill

Don’t drag it out

 Stop when the player feels they’ve won

Homework

 Consider the desired length of your

game.

 Also consider how long a single session is, if

that’s applicable.

 Are there ways to determine how long it

actually plays for?

 What are the game phases?  Is it positive, negative, or zero-sum?

Are there feedback loops?