How to balance your Game

How to balance your Game: A case study on Game Balance

In this 2016 GDC session, game designer and educator Ian Schreiber presents a summary of his college-level course in game balance, examining the major topics covered in the syllabus and a set of assignments that can be used to further build balance skills by putting the theory into practice.

Part of the information on this topic can be found on the free course https://gamebalanceconcepts.wordpress.com/

How to balance your Game table of Contents

GDC Talk Video

How to balance your Game – A course about game balance

A course about game balance GDC talk Transcript

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.

design how many of you have an offering

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.

tracks or course sequences should

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.

the course for

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.

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.

the game in order to choose the most

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.

It is Also needed to point out to 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.

the class and everyone's been given the

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.

that's all you're doing

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.

game balance

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.

actually just talked about this in the

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.

& 1

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.

I throw

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

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

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.

jail when you roll three doubles in the

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.

how to balance

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.

answer is that you come up with some

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

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

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.

people that have this saying that

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.

mechanics that hold your players

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.

point out that these are things that a

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.

have some kind of intransitive

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.

time that helps keep the students

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.

already

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.

that you would have to comment your code

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.

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.

I've been able to actually send the

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

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 hi as a game designer actually run into this issue.

hi as a game designer actually run into

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?

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.

hi I work with a lot of teenage students

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.

that

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?

two questions

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.

are certainly things in there that I

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.

and it certainly has a lot of

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.

you're once you're games get

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

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