A Course About Game Balance

Summary

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

00:00

📚 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。

05:01

🎮 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。

10:02

🎲 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。

15:04

🔢 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。

20:05

🏆 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。

25:05

📈 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。

30:06

🤹‍♂️ 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。

Keywords

💡游戏设计

游戏设计是指创造游戏的过程，包括游戏规则、故事、角色、界面和用户体验等方面。在视频中，游戏设计课程提供了多种专业主题，如严肃游戏、叙事世界构建、游戏平衡等。

💡游戏平衡

游戏平衡是指在游戏中创造公平性的外观，涉及玩家感知和实际游戏机制的平衡。视频中提到，游戏平衡是游戏设计中的一个重要组成部分，需要数学、系统和心理学的综合运用。

💡概率

概率是数学中的一个基本概念，描述了某个事件发生的可能性。在游戏设计中，概率用于处理游戏中的随机性和不确定性，如骰子投掷和卡牌抽取。

💡数学建模

数学建模是使用数学工具来理解和预测现实世界现象的过程。在游戏设计中，数学建模帮助设计师理解游戏元素之间的关系，并通过数学工具来优化游戏平衡。

💡游戏理论

游戏理论是研究具有冲突和合作特征的决策问题的数学理论。在视频中，游戏理论被用来分析如剪刀石头布这样的非传递性游戏机制。

💡认知偏差

认知偏差是人类在处理信息和做决策时的系统性错误。在游戏设计中，了解玩家的认知偏差有助于设计更符合玩家直觉的游戏机制。

💡伦理

伦理涉及道德原则和行为规范。在游戏设计中，伦理问题包括是否应该诚实地呈现游戏概率，以及如何平衡玩家体验和商业利益。

💡游戏分析

游戏分析是指对游戏的各个方面进行深入研究，以理解其工作原理和玩家体验。在视频中，学生通过分析现有游戏来学习如何平衡游戏。

💡电子表格

电子表格是一种用于组织、分析和存储数据的软件工具。在游戏设计课程中，电子表格被用来解决游戏平衡问题，提高学生的数据处理能力。

💡游戏开发

游戏开发是指从概念到完成游戏的整个过程。视频中提到，学生通过设计和分析游戏来学习游戏设计的各个方面，这是游戏开发教育的一部分。

💡游戏测试

游戏测试是游戏开发过程中的一个重要环节，目的是发现和修复游戏中的问题。在视频中，游戏测试被用作一种方法来帮助学生理解游戏平衡。

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]