A Course About Game Balance
Summary
TLDR本视频是关于游戏设计课程的介绍,特别是游戏平衡方面的教学。讲师分享了他在2010年首次开设的10周游戏平衡课程的内容,并强调了数学工具在游戏设计中的重要性。课程内容包括基本定义、系统理论、正面与负面反馈循环、游戏的确定性与可解性等。讲师还讨论了游戏设计中的伦理问题,如概率的诚实性以及玩家心理。此外,课程还涉及了如何使用电子表格来解决游戏平衡问题,以及如何通过实际游戏来加深学生对理论的理解。
Takeaways
- 📚 游戏设计课程中,至少有一门课程提供游戏设计相关内容,许多学生对此有所了解。
- 🎮 在游戏设计中,专门话题如严肃游戏、叙事世界构建等有所涉及,但游戏平衡课程相对较少。
- 📈 游戏平衡不仅仅是数学问题,还涉及系统理解和心理学,旨在创造游戏中的公平感。
- 🔍 游戏平衡课程强调实践,通过分析现有游戏和创建原型来培养学生的直觉和测试技能。
- 📊 课程中使用技术树来帮助学生理解课程内容的构建和进阶。
- 🎲 游戏平衡课程中,学生通过玩《Cookie Clicker》等游戏来理解数字之间的关系。
- 🧮 数学建模和电子表格技能是游戏平衡课程的重点,帮助学生解决实际问题。
- 🎯 课程鼓励学生对游戏进行深入分析,如TCG(集换式卡牌游戏)的平衡性分析。
- 🎲 游戏设计中的伦理问题,如是否应该诚实地向玩家展示概率,也是课程讨论的一部分。
- 🔄 课程涵盖了概率、统计学、游戏理论等数学工具,以帮助学生理解和解决游戏设计问题。
- 📝 课程内容被整理成书籍初稿,未来可能成为游戏设计课程的教材。
- 🤔 课程强调数学思维和逻辑推理,帮助学生更好地理解和应用游戏设计中的数学概念。
Q & A
游戏设计课程中通常会包含哪些专业主题?
-游戏设计课程中通常会包含严肃游戏、说服性游戏、游戏写作(如叙事和世界构建)、游戏平衡等专业主题。
游戏平衡课程的目的是什么?
-游戏平衡课程的目的是教授学生如何创造游戏中的公平感,这涉及到玩家的感知以及游戏的数学、系统和心理学方面。
在游戏平衡课程中,学生如何学习数学工具?
-学生通过学习数学建模和建立电子表格技能来学习数学工具,以便解决游戏中的问题并提出解决方案。
游戏平衡课程中提到的“技术树”是什么?
-技术树是一种教学工具,用于展示学生在课程中所学内容的层次结构,帮助他们理解不同主题之间的联系和发展。
在游戏设计中,为什么概率和统计学很重要?
-概率和统计学在游戏设计中很重要,因为它们帮助设计师理解和预测游戏的随机性和玩家行为,从而实现更好的游戏平衡。
游戏平衡课程中如何处理游戏设计中的伦理问题?
-课程中会讨论游戏设计策略,如奖励系统和玩家心理操纵,以及这些策略可能对玩家产生的影响,引导学生思考作为游戏设计师应如何处理这些伦理问题。
为什么在游戏平衡课程中要强调电子表格的使用?
-电子表格是解决大多数游戏平衡问题的有效工具,课程强调电子表格的使用,以便学生能够熟练掌握并应用于游戏设计和平衡分析。
游戏平衡课程中如何结合理论与实践?
-课程通过分析现有游戏、设计新游戏以及进行数学建模等实践活动,结合理论教学,帮助学生更好地理解和应用游戏平衡的概念。
在游戏平衡课程中,如何处理游戏设计中的复杂性?
-课程通过分步骤介绍和实践,帮助学生逐步建立数学思维和直觉,从而能够理解和处理游戏设计中的复杂性。
游戏平衡课程对学生的数学基础有什么要求?
-学生需要具备基本的代数知识,能够解决方程式,这样教师就可以在此基础上构建更高级的数学概念。
游戏平衡课程的时长是多少?
-在当前的课程设置中,这是一个15周的三学分课程。
Outlines
📚 游戏设计课程介绍
讲师介绍了游戏设计课程的内容,包括游戏平衡、叙事构建、游戏写作等。强调了游戏平衡的重要性,并分享了个人在2010年首次开设的10周游戏平衡课程的经验。提到了课程大纲中的技术树,以及如何通过游戏设计课程来提升学生的数学技能和游戏设计理解。
🎮 数值关系与游戏平衡
讲师详细讲解了游戏中的数值关系,如线性、指数和对数关系,以及资源流图和游戏经济系统。通过《Cookie Clicker》等游戏实例,展示了数值如何在游戏设计中发挥作用。同时,讨论了游戏设计中的经济概念,如供需、通货膨胀和交易策略。
🎲 概率与游戏设计
讲师探讨了概率在游戏设计中的应用,包括独立概率和依赖概率的计算。通过分析《Magic: The Gathering》等集换式卡牌游戏(TCGs),展示了如何通过数学模型来平衡游戏元素。同时,强调了概率直觉的重要性,并讨论了玩家对概率的直觉理解可能出错的情况。
🔢 数学工具与游戏平衡
讲师介绍了多种数学工具在游戏平衡中的应用,包括蒙特卡洛模拟、马尔可夫链和线性代数。通过分析《Monopoly》等游戏,展示了如何使用这些工具来解决特定的游戏设计问题。同时,讨论了游戏设计中的伦理问题,如是否应该诚实地呈现游戏概率。
🏆 游戏设计中的奖励系统
讲师讨论了游戏中的奖励系统和进度设计,包括随机战利品掉落和角色升级系统。强调了玩家心理学在设计奖励时的重要性,以及如何通过数据分析来评估游戏平衡。同时,探讨了游戏设计中的伦理问题,尤其是在社交和移动游戏中使用奖励系统来操纵玩家行为。
📈 统计学与游戏分析
讲师介绍了统计学在游戏分析中的应用,包括基本的统计工具和如何使用数据来评估游戏平衡。通过分析《Dota 2》等游戏,展示了如何收集和解读数据来优化游戏设计。同时,讨论了在游戏设计中使用数据驱动方法的伦理问题。
🤹♂️ 游戏设计课程的实践与应用
讲师分享了游戏设计课程的实践经验,包括使用电子表格解决游戏平衡问题,以及如何通过游戏设计项目来提升学生的技能。强调了游戏设计中的PvP机制和多部分项目的重要性,以及如何通过这些项目来提高学生的参与度和理解。
📖 游戏设计课程的未来规划
讲师讨论了游戏设计课程的未来,包括出版教材的计划和如何将课程内容适应不同年龄段的学生。分享了在教学过程中遇到的挑战,以及如何通过游戏设计来培养学生的数学思维和直觉。
Mindmap
Keywords
💡游戏设计
💡游戏平衡
💡概率
💡数学建模
💡游戏理论
💡认知偏差
💡伦理
💡游戏分析
💡电子表格
💡游戏开发
💡游戏测试
Highlights
游戏设计课程中,至少有一门课程提供游戏设计内容。
专门话题如严肃游戏、说服性游戏或具有特定目的的游戏在课程中有所涉及。
游戏写作、叙事和世界构建在课程中占有一席之地。
游戏平衡课程的开设相对较少。
游戏平衡不仅仅是数学问题,还涉及系统和心理学。
通过设计直觉、游戏测试、分析和数学建模等多种方法来实现游戏平衡。
游戏平衡课程强调数学技能是可以学习的,打破“数学好坏”的固有观念。
课程内容包括数值关系、资源流图、游戏经济系统等。
通过实际游戏分析和平衡练习来培养学生的直觉和测试技能。
课程中使用《Cookie Clicker》等游戏来展示数值关系和游戏机制。
探讨了概率计算在游戏设计中的应用和局限性。
课程讨论了认知偏差和玩家对概率的直觉理解。
介绍了蒙特卡洛模拟和马尔可夫链等概率工具。
课程强调了游戏设计中的伦理问题,如玩家心理操纵。
课程内容还包括了非随机的传递机制和概率的结合。
通过游戏平衡项目,学生学习如何分析和改进游戏。
课程鼓励学生使用电子表格来解决游戏平衡问题。
课程内容涵盖了游戏设计中的逻辑和数学推理。
课程提供了一个完整的游戏平衡概念书籍的初稿。
课程通过实际游戏案例分析,帮助学生理解游戏设计的复杂性。
课程强调了游戏设计中的专业伦理,如玩家体验与收益之间的关系。
Transcripts
all right so I would like to start off
with a question how many of you your
school has at least one course offering
in game design okay pretty much everyone
or at least a lot of you now let's talk
about specialized topics within game
design how many of you have an offering
in serious games or persuasive games or
games with the purpose or something fair
number of you how many of you have
something related to game writing like
narrative world-building fair number of
you how many of you have an offering in
game balance so lot smaller so in some
of you are like a sort of like an actual
class dedicated to that now I'll just
point out I mean every game project not
every game project is a serious game but
we have a lot of those not every game
needs a serious amount of game writing
you know but we have a lot of those
pretty much every game needs to be
balanced in some form arouser at some
point and we don't have a lot of those
so maybe at least for those of us with
game design programs that go beyond 101
maybe we should all think about doing
this that's what this is about
so case study in how I teach it so this
was my first iteration on a full 10-week
game balance course back in 2010 it's
still up there online it's released
under Creative Commons license anyone
who wants to mind it for anything useful
can feel free to do that without having
to ask permission this is from the first
page of the syllabus of my most recent
iteration on the course I think all
courses where the topics build on each
other should probably have a tech tree
in it so students can see all the things
that they learn and how they level and I
also think every games rigging game
degree curriculum with prerequisites or
tracks or course sequences should
probably be laid out like this I don't
know if anyone's doing it like that but
you might want to think about it so I'll
just put that over there on the left
side in one piece and let's unpack this
a bit and walk through kind of what I
put in this course so we start off with
some critical vocabulary just laying out
basic definitions like what do I mean
when I say game balance how is that
different from pacing or tuning
reminding everyone what a system is and
what positive and negative feedback
loops are what we mean when we say that
a game is deterministic or solvable
especially since that starts getting
weird when we get into solving games of
chance and rule symmetry and asymmetry
this is where we set the boundaries of
the course for
or what exactly the scope is when we
talk about balance and by the way I just
love that a word cloud is the first
thing that comes up when I Google the
word vocabulary it's just so meta so how
I define game balance for this class is
creating game balance is creating the
appearance of fairness in a game and
appearance is really important here it's
about player perception as much as
reality because as game designers we are
crafting an experience and it's that
experience that matters so balance is
part math part systems and part
psychology we do this for several
methods one is designer intuition or
experience the game designer chooses to
make certain things a certain way
because it feels right to them another
is playtesting you create a rapid
prototype play on your own or with
friends observe and make changes based
on any rules exploits or weaknesses that
you find play testing is another thing
that everyone has to do and there's few
very few courses offered in that's a
different presentation in the summit a
third method is analytics
taking actual data from games and using
statistical analysis to draw conclusions
about how it's actually played and a
fourth method is mathematical modeling
using math to understand the
relationships between all the numbers in
the game in order to choose the most
appropriate ones most of the focus in
this course is on learning mathematical
tools to do this modeling and also
building spreadsheet proficiency so
students can use these to solve problems
in present solutions we also spend a lot
of time well we spent some time on
analytics because that's widely used
it's very useful now I want them to
encounter that as for building their own
intuition and building their own clay
testing skills we do that through
practical exercises where they analyze
the balance of an existing game or do
balance on a game of their own I also
point out to my students that on the
very first day that math is a skill it
can be learned like any other and the
whole concept of a person being good at
math or bad at math is just an American
cultural myth there's been a ton of
research showing that so therefore this
will not be a valid excuse in this class
to say oh I'm bad at math therefore I
suck at this every student can get this
if they apply themselves and so far that
has turned out to be the case problem so
once everyone's clear on the scope of
the class and everyone's been given the
chance to drop if this isn't what they
thought it was then we start off looking
at numeric relationships because just
saying I have 5 hit points left is
meaningless unless you know
there are other things do zero damage or
occasionally one or if things are doing
one to five damage or things are doing a
thousand damage it's all about how
numbers in the game relate to each other
so we examine linear and identity
relationships triangular and polynomial
relationships and exponential and
logarithmic relationships and also
change up relationships like how if a
player is getting stronger in an RPG
through polynomial growth and monsters
are also scaling polynomially than the
relationship with the monster path
between the player power and the monster
power will be linear not polynomial
things like that we also examine
resource flow diagrams like your storm
ends wonderful machinations tool just
because it's a great way to visually
show relationships between numbers and I
also have the class play cookie clicker
and mechanically it's just a very pure
implementation of the relationship
between numbers you have cookies that
are increasing at a rate of cookies per
second and then you use your cookies to
increase your cookies per second but at
less efficient rates of exchange over
time that's pretty much all the engine
of the game is it's also important
historically as the game that really
popularized the idol game genre and this
is controversial among my students they
generally hate me for introducing them
to this game if they haven't played it
before because once it's totally
addicting and yet it's really stupid and
you're fully aware of how stupid it is
that you're clicking on cookies and
that's all you're doing
just to increment it counter and it's
stupid but you get addicted to it and
continue to do it anyway so really it's
a game about self-loathing and which is
one of the prerequisites to being a game
designer which is why I keep it in here
from there we look at a special case of
numeric relationships which is resource
systems and economic systems because
those come up a lot in games we cover
the bits of an economics 101 course that
are directly relevant to games things
like how supply and demand would affect
prices in an MMO auction house how
inflation affects those prices and
different straddle strategies for
handling inflation in a game economy and
interplay our trading and the
differences in how that works between
closed and open game economies and also
various auction and interplay or trading
systems which are a lot more common in
Euro games than in video games and I
encourage them to play euro games that
have strong trading or auction mechanics
here like Settlers of Catan or modern
art after that we have enough tools to
get into our first reel in the frenches
game balance
project where we talk about games where
better stuff cost more
i giggle ii refer to this as transitive
relationships between the various game
elements and one of the purest examples
and the one that i examine a lot just
because of my personal experience in the
industry is TCG's like magic the
gathering or hearthstone you have a cost
to put a card into play and then the
card has an effect and more expensive
cards are more powerful and what you're
doing is putting all of the cost
limitations and drawbacks and also the
powers abilities and benefits in terms
of numbers scale so that the card is
balanced if the value of its cost equals
the value of its benefits and you can
put this into a spreadsheet where each
mechanic has its own column each row has
each row is its own card and there's one
column that just contains some math
function that incorporates all the other
columns and spits out a number that
tells you if the card is balanced or not
and if not how far off it is in which
direction very powerful technique I
actually just talked about this in the
map for programmers tutorial an hour and
a half ago if you want to look that up
on the vault later so one of the
projects here is for students to take an
existing game with transitive mechanics
and analyze it to find the game objects
like the cards or whatever that are the
most powerful the weakest and the most
balanced and then compare that in their
math with the generally accepted wisdom
of the games community so at this point
now we've taken things as far as we can
balancing games based on skill but we
haven't done anything involving
mechanics of chance yet so now we dive
into basic probability specifically how
to calculate independent probabilities
like die rolls where each roll doesn't
affect the odds of future rolls and
dependent probabilities like drawing a
card from a deck where each card draw
does affect the probability of future
card draws if you know what was removed
so this is basically taking a
probability 101 class extracting the
parts that we use in games and ignoring
the rest although I do make sure they
encounter things like the Monty Hall
problem just so they understand that
probability isn't always intuitive I
also go over ways to do sanity checks
like probabilities are always between 0
& 1
adding up all the non-overlapping
non-overlapping outcomes should always
get you one exactly because probability
is very easy to screw up if you don't
know what you're doing and you're not
careful but most of the time if
something goes wrong it goes wrong
enough to fail a sanity check so it kind
of has its built-in debugger which is
nice this stuff actually doesn't take
that long to cover just a week or so but
I throw
another week up playing some dice and
card games in class and analyzing them
like the strategy between behind bluff
and Liars dice or which side has the
natural advantage in one night ultimate
werewolf or any other relevant games
that I've acquired recently now at this
point my students know how to calculate
exactly how fast they'll go broke in
Vegas and then I deliver some bad news
which is probability doesn't actually
solve everything for two reasons the
first is that humans socket probability
we generally find it unintuitive even if
you do your odds calculations correctly
as the game designer a lot of times they
will feel wrong to players the great Sid
Meier even talked about some of his
experiences with this at a keynote here
in GDC back in 2010 so you also have to
learn about not just how to calculate
odds and probabilities but also
cognitive biases to explain why people
get intuitive probability wrong and when
they do and we talk about game design
strategies to compensate for your
players being buggy and this is also a
great time to revisit games like liars
dice and poker to learn the difference
between just doing the math and actually
using psychological mechanics like
bluffing and interestingly another thing
that we mentioned here for the first
time is ethics because whether we should
be honest with our you know should we be
honest with our players and do the
probabilities of the way they we say
we're going to or should we you know
fudge our die roles to conform to and
reinforce our players flawed
understandings of probability basically
is it okay to lie to our players or not
that's something worth thinking about
and I mentioned this here because we
normally don't see matters of
professional ethics emerging as a key
topic in a math class second thing that
goes wrong with probability is that even
if we're honest and our rent our random
number generators are not physical dice
and cards are generally imperfect and
not fully random any pseudo-random
numbers generated on a computer of
course can't be random at all and it's
worth understanding a little bit about
how these things work so you can predict
how players could exploit these random
systems to gain an unfair advantage
whether it be through cheating at Vegas
or at a high-stakes eSport or just
coming the save files of a single-player
RPG to gain an unfair advantage now I
could switch this next topic with the
previous but I like making sure that
students don't come to rely too much on
probability before realizing its
limitations but after I do that I cycle
back to a couple of other useful
probably
the tools specifically Monte Carlo
simulations and Markov chains now Monte
Carlo is just repeating a random trial a
few thousand or a million times and
seeing what happens and then through the
law of averages your results should be
pretty close to an exact mathematical
solution if there is one and Monte Carlo
solutions are useful because they're
easy there's no math required you just
make a spreadsheet or sometimes do some
light scripting they can be used in
situations where calculating calculating
the exact solution is impossible or too
unwieldy and slow or if the student just
doesn't know how to do it
Monte Carlo solutions also work as a
useful sanity check if you do have an
exact solution if you solve a
probability question both ways and with
Monte Carlo and with math and get the
same answer then it gives you a lot of
extra certainty that you didn't make a
mistake Markov chains on the other hand
are useful for solving some very
specific types of game design problems
that involve repeating something where
the results of one thing affects the
results of the next recursively as an
example consider a board game Monopoly
and if you're trying to figure out which
properties are the most or least likely
to be landed on in order to compute the
ROI for the purchase price of the
properties you could do that with a
Monte Carlo simulation just start at go
and roll to d6 a bunch of times go to
jail when you roll three doubles in the
roads of stuff like that but you can
also treat this as a set of states where
each state is a combination of what
space you're on and how many times
you've rolled doubles in a row and you
could build this transition matrix of
probabilities between states take a
column vector of probabilities of being
in any given state at a time and
multiply that by the matrix a bunch of
times and you'll know after every single
turn in the game what the possibility
space is in terms of which spaces you
might be on with what probabilities it's
a bit complicated compared to most of
the other topics in the course and it's
limited to some very specific situations
but it's very powerful for getting exact
mathematical solutions for things that
you couldn't do any other way if you
haven't encountered this before there's
a blog on a website called data genetics
com that has an analysis of games like
Candyland and chutes and ladders and
things they're very helpful primers on
that kind of thing so now we've covered
non-random transitive mechanics and also
probability the next thing we do is
smash those two things together to learn
how to balance
transitive mechanics that have a random
or situational element to them this is
something that most students will have
run into already in their earlier design
analysis of a TCG or similar game what
do you do when a card
with a card when it says you only get
some benefit in a particular situation
like only if you're fully healed or only
if the opponent has more than four cards
in play or something and the short
answer is that you come up with some
kind of reasonable estimate for how
often that benefit would trigger and you
treat it as a probability no different
from saying fifty percent of the time
you get this benefit or whatever so
probably the purest instance of
situational balance I've seen is in
tower defense games and I like to have
the students play and analyze desktop
tower defense 1.5 specifically it's old
enough that many of them haven't played
it before it's historically important as
one of the games that popularized the
genre and almost everything in that game
is situational you have some towers to
do area effect damage which were great
when enemies are clustered together but
not when they're spread out towers that
only hit flying or non flying enemies or
other towers that can hit both but are
less powerful towers that do no damage
at all and just boost the power of the
towers next to them so it all depends on
where you put it and so on the value of
everything depends on the board state
and what kinds of enemies are in the
next wave and what kinds of towers you
make and if you really want students to
go all-in for this you could even have a
tournament see who can use their
analysis to build the best tower load
out and give your excess GDC swag to the
winners then we take the stuff that we
learned about numeric relationships and
transitive systems and put that together
with probability again to examine reward
systems and advancement in progression
and pacing this includes things like
random loot drop tables and RPGs so that
you can make sure the player doesn't get
the ultimate sort of awesomeness +5 as a
random drop in the first dungeon we also
look at progression systems like
leveling curves how many enemies you
have to kill to gain a level on average
how long is that expected to take in
playtime so you're trading off danger
for time for advancement and also
looking at advancement into story which
is a reward in and of itself and then
bringing in human psychology and how a
lot of little rewards spread out provide
more impact than a single big reward and
how rewards on a random reinforcement
schedule are more powerful than a fixed
schedule stuff like that if you want to
place more emphasis on this you could
easily make this a semester-long project
where you take a game like an old-school
day RPG and go through all the encounter
and loot and level charts and tables and
use math to predict how long it will
take a player to grind through each area
when they level up and how often and
generally winners the player receiving
some kind of reward and then
cross-referencing that reward schedule
with the most and least memorable events
in areas in the game
in order to understand from a
mathematical perspective where the
enjoyment of the game is coming from
this is also another place where
professional ethics comes up because
reward schedules come up a lot in social
and mobile games and also in the
gambling industry as ways to
psychologically manipulate players to
pay money or continue playing and
there's the question of whether that is
okay and if so where do we cross the
line into unethical behavior and what
ads do we as game designers do about it
next up we take a look at the reverse of
probability which is statistics and
probability you know the nature of the
randomness and you use it to predict the
what the actual data will look like like
the results of a die roll in statistics
you see the results and you use those to
try and derive the nature of the
randomness that they arose from
statistics is a bit harder than
probability because it's just as
unintuitive just as easy to get wrong
and there's fewer sanity checks to alert
you to being wrong you know there's some
people that have this saying that
numbers don't lie but in reality the
data are always trying to trick you
they're very mean so once we learn some
basic statistical tools like mean median
standard deviation standard errors the
z-test statistical significance then we
dive into analytics to learn about what
kinds of numbers we should record for a
game and how we would use the results to
determine whether the game was balanced
or not fighting and brawling games and
MOBAs are great with this because you
have a ton of characters that all have
to be balanced against each other in
ways that don't easily lend themselves
to being analyzed purely through math
formulas and spreadsheet that relate
them to one another one exercise I like
to do is give them is to come up with
metrics have them come up with a metrics
plan for a game that they're working on
themselves like if you you might be
working on some small passion project
like a like a simple board game or
something but if you had a few thousand
play tests and we could record any data
you wanted give me a question that you'd
want to know the answer to and then list
what data you would collect to get an
answer to that question and then how
would you interpret that data to get an
answer like what would a positive or
negative result look like and this is
yet another place where professional
ethics is discussed in regards to
metrics driven design if you find out
for example that changing a certain
number or mechanic or whatever leads to
greater revenue but also reduces player
enjoyment such as might be the case with
mechanics that hold your players
accounts for ransom or that create
intentionally create pain points that
can only be removed by paying money is
that something that's good is that
something that's unfortunate but
necessary
or is it something that's a breach of
professing professional ethics as a game
designer and as with other ethical
questions raised in this class I don't
give any answers or opinions I just
point out that these are things that a
game designer should be thinking about
and forming an opinion about because if
you don't then someone else will make
that decision for you the last thing we
cover in the class is in France ative
mechanics that is things like Rock Paper
Scissors where there's no concept of
better or more powerful because it all
depends on what your opponent is doing
something is strong against one thing
and weak against another and this is
where we get into the fields of linear
algebra and game theory dealing with
payoff matrices and Nash equilibriums to
solve these kinds of problems
mathematically I think it's pretty
fascinating that you can ask a question
like suppose we're playing
rock-paper-scissors but if I win with a
rock it counts double and if you win
with the Rockets just normal and we're
playing to best of ten you can actually
use matrices and systems of equations to
come up with a solution of exactly how
often both of us should choose each
throw and how big of an advantage this
is for me you know so this is some of
the matheus tedious math that I cover in
the class and frankly it's not all that
useful in a lot of games because it's a
very pure and it's very work intensive
but there are a lot of games where that
have some kind of intransitive
relationships any situation where you
might use terms like hard counter or
soft counter which would include units
and RTS is characters and fighting or
brawling games or MOBAs character
classes and mmo's decks and strategies
and TCG's all kinds of things like that
and so like Markov chains I don't think
that game theory is used a lot in the
field but I do find it to be a really
fascinating tool that's very powerful in
the right situation so I want my
students to encounter it so one thing I
want to point out here is that actually
playing games either in class or as
homework or maybe home play is really
important in this class math is not
always intuitive if you just write a
bunch of equations on the board but if
you can see it in action it's a lot
easier to grok what's going on it's also
useful to provide context that the
concepts we're learning here are useful
and can be applied directly to analyze
games or solve real-world balanced
problems in all the years I've been
teaching this I have not once been asked
the question when will we ever use this
so students are seeing the theory and
the application at the same
time that helps keep the students
engaged plus they love playing games as
part of a course requirement and it lets
me introduce them to a number of games
that I wouldn't normally be able to get
them to play otherwise so that lets me
add to their personal game Canon as well
another thing this class lends itself to
really well as PvP mechanics having
students compete in some kind of game
balance or mathematical analysis test
where the final answer isn't clear isn't
obvious and there are multiple layers of
potential analysis I have players either
play on their own for a high score or
play against each other in class in a
tournament and I usually modify these
games slightly both to simplify the
constraints so the analysis space isn't
as huge and also to prevent the students
from just using Google to find optimal
strategies I also try to find a ver
games that can be solved in a
spreadsheet because spreadsheet eating
skills are really important for game
designers and for game balance in
particular so this serves as a good
practice for them cookie clicker and
desktop tower defense I've mentioned
already
bable bable was actually presented here
by Eric Zimmerman last year and it's
been a wonderful in-class exercise for
me korto minuet is a game designed by
Jason Rohr that is a pure game theory
problem with and there I had to do some
very heavy changes to that because two
elements of the original game are real
money gambling which is required and
also satanic seems so I had to remove
those things obviously Pig is a
traditional dice game that's a great
example of calculating probabilities and
Goku is an intransitive game from the
Secotan series of RPG RPGs we could just
look all those up and and probably
figure out what's going on with that
another important topic that's
distributed throughout the class is how
to use spreadsheets because the vast
majority of game balance problems can be
solved in Excel and I want students to
be strongly proficient in spreadsheet I
divide these things up and introduce
them a few at the time each a few at a
time each week using the ones that are
relevant to the problems that need to be
solved that week I go into a lot of
detail with this mostly just pointing
out features in Excel that are useful
and then asking them to use those
features in their design work for the
week we cover formatting to make the
spreadsheets look more readable and
usable various types of graphs and
charts that can be used to visualize
data how to comment your worksheet
properly the same way so the same way
that you would have to comment your code
how to use formulas at a very basic
level doing sorting and data validation
dealing with multiple worksheets and how
to format them for readability and
usability dealing with all the different
ways to fill or copy and paste to save
time and showing them a wide variety of
useful functions of which there are too
many to list in this slide one notable
exception here is I do not get into
writing scripts such as VB script in
Excel or the scripting language that
they have with Google sheets because 99
times out of 100 it isn't necessary and
it just makes things way more
complicated and I get a lot of
programming students that tend to
default to writing script rather than
learning to think in spreadsheets I want
students to be able to think in terms of
formulas here not code a typical case is
a student who will write a thousand line
script to implement an AI to play a game
and then all have to walk through it
with them line by line to show them how
to do exactly the same thing in about 50
cells instead greatly condensed and way
more readable the class also lends
itself to multi-part projects that are
longer-term one is designing doing a
design analysis of an existing game or
part of an existing game I've had
students do the math to derive the
design thinking behind hearthstone
Dominion netrunner and a number of other
card games figuring out the relationship
between costs and benefits and then
creating a new 5 to 10 card mini
expansion for the game with cards all
focused on a single mechanical theme
that requires the student to invent a
new mechanic and then figure out how
much it costs this kind of thing becomes
particularly awesome in cases where I
happen to know the designer of the game
that the student is analyzing in a lot
of cases designers are particularly
amused that their own creative work
their own commercial work is being used
as a class assignment and they're
usually very happy to be available for
questions from students though in my
experience the students are usually too
intimidated to take advantage of this in
the future I'll probably organize a
required Q&A or something like that
the other benefit is that in some cases
I've been able to actually send the
student work to the designer for
consideration in using their expansion
as part of a future release having a
professional design credit for a class
project is a kind of holy grail for the
student in my class it has not happened
yet but these things are slow and the
possibility is there for students
working on other games or for a
different class or just on their own
passion projects analyzing their own
games from a balanced perspective and
creating mathematical models to improve
the balance of their game is also a
useful way to go about this
or just give them tagged aim to balance
I created a game called harmony that I
presented before it's a very simple TCG
with just four mechanics and the goal is
to balance those mechanics with each
other
starts off completely broken
intentionally and students have to
figure out how to relate these things to
each other projects in this class are
super important but to practice these
skills on real games because it's one
thing to say make a game as a project
it's another to say now balance second
I've also been working over the past
couple of years to document everything
in this class and I now have the first
draft manuscript for a complete book the
first draft is done and I will be
talking to publishers here at GDC and
shortly after so if you want to run a
class like this and you can wait a year
or so to get it into your curriculum I
should have a textbook ready for you
before too long in the meantime feel
free to use what's available on game
balance concepts even if it's an earlier
iteration and feel free to write me
after the show if you have any questions
about it or anything thanks for
listening and now I will be happy to
take a couple questions
[Applause]
hi as a game designer actually run into
this issue a lot in that I too am
usually running adverse sorry as a
programmer I'm usually writing a lot of
code and I'm trying to code my way
around the things you're talking about
with the spreadsheet it occurs to me
that actually probably one of their
advantage in doing so much design
through the spreadsheet is it probably
creates a natural limitation as well to
the scope so does it am i correct and
that actually probably helps to prevent
scope creep released um within ourselves
I would say that probably is true so the
question is would learning to do things
balance in spreadsheets as opposed to
code you know limit artha limit this
helps to limit the scope of complexity I
think that's definitely would be true
you know usually I have to usually I
have to go the other direction in that
trying to get them to stop using code in
the first place and just getting them to
sink in spreadsheets being able to think
in terms of formulas in terms of
relationships between mathematical
things if you've got something and you
know a algorithm that's super super
complicated then analyzing it is very
difficult and if something is too
difficult for you to analyze that's too
diffident it's too complex to be put in
the game so yes do you ever talk about
logic and how logic can connect to
balance when it comes to design okay
yeah can you uh can you clarify what you
mean by logic because that's a very
large term okay so I often with my
students realize that they don't
understand the logic generally of maybe
the puzzle or challenge that they're
putting together and then when it comes
to balancing that experience in the game
like what's the difference between level
one and level two in the difficulty
because they're not following they're
not they're not thinking through the
logical problem they're having trouble
just putting their head around what is
the balance then of that player
experience okay so we're talking
you know do students have difficult I do
I go into game logic and understanding
these mechanics and how they relate to
each other you know because if students
don't understand how the mechanics of
the game work at a core level then it's
kind of hard to figure out how the
numbers work is that correct that would
yes but also the more sort of formal
concepts of logic like spatial reasoning
versus you know the different types of
lot okay different types of logic in the
current iteration I don't do that as if
you've noticed there's a lot that I am
covering that hasn't been a problem for
me in my experience I think a lot of it
helps that I'm at RIT which has a very
technical focus so I get so students
understanding some kind of propositional
logic and you know lambda calculus and
things like that like they get exposed
to that through their computer science
classes anyway for a less technical
group usually my biggest challenge is
getting them to be able to have the
mathematical thinking to understand at a
just an intuitive level how different
numbers affect each other and so logic
would certainly be a part of that but
I'll take one challenge at a time
hi I work with a lot of teenage students
40 to 70 last week and I was wondering
for a mini course for that age range
what concepts do you think he would
start them on so so this is yeah as
you've noticed I call this a math class
that's cleverly disguised this game
design that's kind of how I pitch it to
other people here so the one thing that
I found is interesting is that even
though we get in some pretty heavy math
because it's contextualized in games
that students already understand and can
already play the math is you know it has
meaning and all of a sudden you don't
really like the prerequisite for this
class in terms of what math you've
encountered in the past is basically you
know can you solve an equation you know
from algebra one if you know how to do
that
I can scaffold everything else on top of
that I would certainly take some of the
more challenging parts like linear
algebra and
and game theory out or at least greatly
simplify it or just say you know this is
something that exists it's a lot part
you know it's a bit harder it's beyond
the scope of this course you know this
is for a audience of of younger younger
children and teenagers you know but most
of this it's you know it I usually it's
not the actual mathematical skills and
it's the challenge it's usually it's
just building up the mathematical
reasoning and intuitive which do you
think it's actually like the most
important concepts or that you should
start in like you're like okay I got 10
hours of you what are you thinking about
right so I would say for yeah if you
only have 10 hours how how would I you
know pick the most important concepts in
this class and that's a good question I
would say I would go through you know
the I would go through numeric
relationships and I would go through the
balance of TCG's just because it's you
know it's very very it's very related to
like algebra so so kind of build on
those skills that are probably going to
be age appropriate at that range it and
and you know and it lets you you know
and it relates it to games that a lot of
them are playing right now already so
thank you that's helpful okay
I'm not sure people are going to be
about but I'll keep answering questions
until someone tells me to stop I have
two questions
so first very simple how long how many
hours well of course and how many hours
are the students represented forth at
which level is given this course and the
second question is we have quite similar
course but we have taken the point of
view that you can explain everything
taking the point of view of game theory
you want to go you made games against
nature to introduce probability and you
can choose a game negotiation to explain
other topics what do you think about
this point of view because I understood
that you're just taking game theory on
only at the informant
nam translated choice system yes so let
me repeat that back because I'm not sure
I quite got that so the first question
is just you know how long this is taking
like how many hours this is a in this
current incarnation it's a three credit
hour class over 15 weeks you know there
are certainly things in there that I
could cut if I had to take it down to
ten you know for the and for the second
question you were asking about the whole
question is in the course well given the
whole the whole content that you have
given is is taken a different point of
view from game theory for example if you
when we introduce public VT went reduce
poverty I'd games against the nature and
thing like that so my question would
okay well it's what you came to only
only at the end okay so yeah the reason
I do game theory at the end is partly
because it ties together a lot of other
things we've been doing in there so it
kind of requires you to understand a
little bit about probability a little
bit about transitive mechanics and how
they relate to things you know there's
all these a little bit about human
psychology and just the idea that you
know we can try to model like the human
brains aren't always mathematical you
know and bringing all you know and also
just encountering things like matrices
and matrix multiplication in when we
talked about Markov chains so all those
things kind of are prerequisites that
lead up to this that's part of the
reason why it's at the end of the course
that I talk about game theory the the
other side of this is yeah I mean like I
said it's not something that's widely
used in the field as a tool and you know
and it certainly has a lot of
limitations to it I just think it's kind
of neat and and certainly you're
absolutely right though that you know
even game theory doesn't always predict
human behavior and that that is worth
mentioning in that section I think
that's it and I do mention that if
you're once you're games get
sufficiently complicated where you need
game theory in order to you know figure
out things and you're working on things
on multiple levels it's probably too
complicated for someone to actually
solve it intuitively anyway and player
behavior is going to diverge from
optimal math but you could at least use
that to write a good AI
okay thank you okay and I'm being told
to stop so thank you all
[Applause]
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