Magic: The Gathering Drive to Work Podcast - #681: Math in Magic

Episode Date: October 18, 2019

In this podcast, I talk about how Magic design involves a lot of math.

I'm pulling up in my driveway. We all know what that means. It's time for another drive to work. Okay, so today's topic is math in magic. Yes, math. So, I'll begin by telling a little story, which was, I don't know whether this was junior high or high school, probably was junior high, where I was in some math class, and I was frustrated by whatever the math was. And I'm like, why do I have to take so much math? When am I going to use math? Because I was sure that I was going to grow up to be a screenwriter. That's what I wanted to be.

And I'm like, I have to count pages in my salary. That's it. I don't need math. I don't need math. But I took math classes nonetheless. And interestingly, I now have a job with a lot of math. So I did an interview not so long ago with a podcast called Working. And on it, one of the topics that came up was how much math we had. And he was fascinated by it.

And I realized it might be an interesting podcast topic because I'm not sure if it's obvious how much math there is in the making of magic. There's a crazy amount of math. And so today, I'm going to try to convince you that that math class that you took or are currently taking has some value if your goal is to ever make magic. So I thought it'd be interesting, just a different way to look at magic, talk about a different aspect of magic. I know we, I always examine magic design from many angles, but I've not examined it from the math angle. So today I thought I would talk about the multitude of math in magic. Very literate

of title there. Okay, so let me start with my math. Let me start with the math that I care about in vision design, and then I will start getting into math that other people care about. Okay, so first thing you have to understand, to understand the math that I have to worry about, is the fact that we have a trading card game. And what that means is that normally, if I sell you a game, if I'm selling you Monopoly, I sell you Monopoly, I sell your buddy Brad Monopoly. I sell your buddy Jamie Monopoly. All of you guys are going to open the exact same thing. The same board. The same pieces. You are all getting the exact same experience. But in a trading card game, that is not at all true.

You'll open some cards and your friends will open different cards. Each friends will open different cards, that each person who experiences a game experiences through the lens of a random assortment of cards. Now, that makes some challenges when you're making a magic set, because if I know exactly what you're getting, if everybody's getting the same thing, I mean, not that there's not math there, but there's a little bit more math for me,, and when I say me, I mean my team and all R&D, because if I want to make a set and I want to have a theme in the set, I have to care about how often that theme shows up.

shows up. Because what I don't want to do is I have a theme and you open up ten booster packs and you have no idea what the theme is. For example, Champions of Kamigawa had this legendary theme, but all the, or most of the legendaries were at rare. There were a few uncommons, but most of them were at rare. And now all the rare creatures were legendary. But how many packs do you have to open up before you figure out that's what's going on? Because not every pack has a rare creature. And even if you open up a rare creature

and it's a legendary creature, there are legendary creatures in the set. Like, how many do you have to open before you're like, oh, this is atypical. Wait a minute, I think there's something going on. And the problem there was it required a lot of packs. You really, like, it was not a theme you got pretty early.

And that's the problem. You know, we want you to open up one booster pack and have some idea what the theme is. And if you open up multiple, you know, three, four booster packs, for sure you should know what the theme is. And so in order to make that happen, we have to care. So this is a term I use from time to time called ASFAN. Regular listeners should know.

It stands for ASFAN. So what ASFAN means is when you open up a booster pack, what percentage of the cards are any one thing that you care about? And the reason this is so important is, let's say I have a theme. Let's say it's a set about artifacts or a set about enchantments or legendaries or whatever my theme is, whatever we care about. I have to be conscious of how often that appears. And in order to do that, we have to think of

the way Aspen is calculated is, in a booster pack there are 15 cards. One of them is a basic land, ten of them are commons, three of them are uncommons, one of them is a rare, although one out of eight times that rare is replaced with a mythic rare. Once again that is on average what you get. There's shenanigans with printing that can make weird things happen, but on average that is what you get. So what that means is when we're trying to calculate we have to figure out, okay, how many commons are there? So for a large set, usually there's 101.

How many uncommons are there? There's normally 80. How many rares? Normally 53. How many mythic rares? 15. So we have something showing up in some number of commons. We have to care about how many commons have that thing and then calculate in a booster pack that times 10 because there's 10 slots where a common could show up.

So let's say, for example, we have 101 cards. And let's say your theme shows up in, okay, for math purposes, I'm going to say 100 commons. It's really 101. So the math's harder that I'm leading on. But just for simplicity's sake, let's assume it's 100. Okay, let's say I, at common, 10 of the cards have my theme. So that means one out of 10, one tenth, 10% of my cards had the theme. So what happens is, when I'm figuring out the math for the booster for Asfan, I say, okay, there's a one

in 10th chance that you're going to get one of those cards. One of the cards that I care about, the theme that I care about. And then, since you have a, every common slot gives you a 1 in 10 chance, that means for each of the 10 slots, you have a 10% chance, a 1 in 10 chance. Now, if you have 10 slots and a 1 in 10 chance, that means you have a 1.0. Your as-fan right now is 1.0. The reason for that is, on average, if you open up a booster pack, so let's say, for example, the theme's only a common, only in 10 cards. That's an as-fan of 1, because out of 100 cards, you have 10. It's 0.1 or 10%. But if that happens 10 times, your average is, oh,

I will get one of the cards in question. So my as-fan is one. Now, sometimes you might put something at higher rarities as well. So like uncommon. So let's say uncommon, you decide that you're going to put in

four of the cards in question. We'll make it easier. We'll say eight of the cards in question. So you in four of the cards in question. We'll make it easier. We'll say eight of the cards in question. So you put eight of the cards in question. So common has ten, uncommon has eight. Well, eight out of eighty is ten percent as well. So now if that were the case, you would have ten percent in each of the commons

and ten percent at the three uncommon slots. So you would have a one point three asan now. Because that's saying that if you open up your Butcher Pack between your common

and uncommon slots and based on how they are on the set, you now have a... On average, when you open up a set, you have 1.3 cards of the thing in question.

It's an As-Fan of 1.3. Now, let's say, for example, at Rare, I also want to have a 10% chance. There's 53 rares. Basically, you get a rare seven out of eight times. You get a mythic rare one out of eight times. So let's say I want a 10% chance of getting mythic rare. There's 53 of them. So 5.3 is 10%. So let's just say 6. A little bit over 10%, but close. So let's say we put 6 Rares in. Then, because

there are 53 slots, you get 6 Rares. That's roughly 10%. And you get 1 slot that shows up 7 8ths of a time. So if it was 10%, then it would be 7 8ths of 10% because the slot shows up 7 to the 8th of the time. Likewise, Mythic Rare, that shows up 1 to the 8th of the time. So it's whatever the percentage times 1 to the 8th. And then you add all those together. That's how you figure out you're an As-fan.

I have to be very conscious of that because if I'm making a certain set, I have to figure out how often does that show up. Now it can get even more complicated. Let's say I have an A-B mechanic. So what that means is, a good example of an A-B mechanic might be madness. Madness says, whenever I discard, if this card gets discarded, I can pay a certain cost to cast it. Well, madness doesn't mean anything unless I have cards that make you discard. So that's what we call an A-B mechanic.

Well, A is cards that make you discard, and B are madness, cards that trigger when discarded. So if I want to put an A-B mechanic in, not only do I have to figure the As-Fan of A, but the As-Fan of B. Now, the other thing that makes the math even more fun an As-Fan of A, but an As-Fan of B. Now, the other thing that makes the math even more fun is right now I'm assuming that when I talk about As-Fan,

I'm talking about general As-Fan, just in a random booster. But not everybody's playing every color. So not only do we have As-Fan, we have As-Played. And what that means is not just looking at what is in the booster, but what is most likely to actually see play. Because one of the things that we do is we grade all the cards on how likely they are to get played in limited, and then there's gradings for constructed. And so we have to figure out sort of, as played means,

okay, these are the percentages based on cards you're more likely to play. Now, it gets extra complicated because of colors. So I might have a theme, but my theme might not universally show up in all the colors in the same rate. And so one of the things that we're trying to figure out is not just as fan, but sometimes what's the as fan for color?

What's the as fan for black? What's the as fan for red? And there's a lot, like I said, a lot of us trying to figure out what we're doing is trying to make sure that whatever it is we're giving you, that we're putting it in at a rate where it's going to show up in the right amount. Now, there's some tricks we get to use to circumvent the math. For example, War of the Spark had a Planeswalker theme,

and Dominaria had a Legendary theme. But one of the things we did in both of those packs is we dedicated a slot to the theme. So what that means is every time you open a Dominaria pack, you were guaranteed getting a Legendary. And every time you opened up a War of the Spark pack, you are guaranteed getting a Planeswalker.

And so, that ups your AS fan, because you have a guarantee that you know. And that allows us to tweak. Now, the other thing is with Collation, there's a lot of things we can do depending on is your ASFAN, for example, on its own sheet? If the ASFAN

is on your own sheet, you have a lot of control of how many times you print that sheet. If the ASFAN is mixed in on a normal sheet, then once again you're more at the mercy of the math to figure it out. So there's that. There's all the as to that. That's probably the most complicated math that I have to worry about because I need to figure out the right amounts of things. And a lot of that, by the way, also comes from playing

and getting a sense of how often do you need to see things and how often do you want them and how often do they have to show up in certain colors and stuff like that. The other big math that we have to care about is there is a lot of math about trying to make sure that things can work um while vision is not responsible for final costs or anything there also is some math to make sure that um you know when we try to get a mechanic and we want to make sure that what we're doing can work, there is a little bit of we do what we call curving. So what curving is, is we want to make sure

that when you're playing, that you have a good mix of cards at the different cost levels. Especially for limited, for example, that if I want to make a limited deck, I have to think about how often I have things that, like, if you made every single card in your limited deck a four drop, you'd have a problem. First off, you have nothing to do for the first three turns, and then, once you get your fourth land, which might not even be on your fourth turn,

if everything's four, then it's all getting gummed up. What you kind of want to do is have some ones, some twos, some threes, some fours, and actually, you skew a little bit lower because you can cast the smaller cards earlier and the later cards can't get cast until you have more mana. So you don't want too many of the larger cards

just because you can't cast them anyway until you get to there. So there's a whole math to how the players want to build their deck. So the math goes on our side on making sure that we are representing that. Like, if we want players to be able to sort of fill up their deck mana-wise, we have to give you choices mana-wise. So that's something we constantly have to do, is figure out sort of where things are being positioned. And not only do we have to be concerned just about the mana cost, but we also have to think

functionally, how does the card function? You know, like, sometimes we have additional costs, like Kicker is a classic example, where we have to think about the card in both versions, like, oh, you could play this as a 2-drop or as a 5-drop. Okay, well, we have to figure out how often you're playing it as a 2-drop

and how often you're playing it as a 5-drop. I mean, hopefully my goal here, as you can see, like Richard Garfield, obviously the creator of the game, was a math professor. So it is no surprise that there's a lot of math baked into what we're doing. Like I said, I think the biggest part of it in general has to do with the fact of the randomness of the trading cards.

But there's just a lot of just general math. Like one of the things that we are always conscious of is how much math gameplay requires of you. How much tracking, you know, how much math do you have to do? And here's a very simple example, which is when something has to change its power and toughness,

we've learned there are things that you can do that are easy for the mind to sort of calculate, and there are things that are tough. For example, adding plus one plus one, or adding plus n plus n is the easiest, just because, I mean, the simplest thing to do is have square stats, I'm a 2-2, I'm a 3-3, and then I give you plus n plus n, meaning the boost is the same for power and toughness. So the idea is I'm a 2-2 and I get plus 3 plus 3. I'm like, oh, very easy.

2 plus 3 is 5. I'm a 5-5. That's very easy to calculate. Sometimes, but the problem is if we always did square stats with square boosts, it's very limiting what we can do. So the next thing we can do to make it easy for you is, sometimes we'll have non-square stats. And usually with non-square stats, we most often will give you square boosts. But sometimes what we'll do is, if a creature is giving itself a boost, one of the things we'll do sometimes is,

let's say you have a creature that has a different power and toughness. You can swap its boost so that it ends up even. So I have a 2, 3 that I give plus 3, plus 2 to, meaning it turns into a 5, 5. Then I have to realize it's 3, plus 2, and 2, plus 3, but the inverting of them is a little bit easier for people. The other math that's also a lot easier is only changing the power and not changing the toughness. A lot of the difficult

math and understanding what is going on on the board has to do with the toughness because you're trying to figure out if things survive. If you change power of things, it's a little bit easier to track. So you'll notice more often we'll change just power. We don't often change just time. We do every once in a while. But we more often change just power. Plus N plus O is a lot easier to track.

And so one of the things that we're always trying to do is not only behind the scenes do the math, make sure that the math is working out and making the game run smoothly. But we also want to make sure that any math that you, the player, have to encounter, that we're doing things to help you. That we're doing things to make it a little easier to process. And sometimes what we find is there's certain like a good example of math that didn't work out is

in Unhinged, I did fractions. I did half. And on the surface, it's like, oh, cute, it's a half-half creature, whatever. What we found in practice is people are not used to subtracting halves. So, for example, you know, you're at 16 and you get hit for two and a half damage.

It takes people a little while, a little longer to calculate that than we realize. That is something we should have caught in playtesting that we didn't. Oh, unhinged my... Of all the sets I've worked on, the one I'm most disappointed in is that I made a lot of mistakes in it. And I look back. I mean, given it was a long time ago, but still. I don't get to make that many unsets. When I make one with lots of mistakes, it haunts me. Anyway, so there's that.

The other thing in general we want to think about is not only creatures that can change themselves, but also things that affect other things. Things that can change themselves, you're a little more locked in saying, okay, well, I know what this is and I know what is changing, so I understand the math I have to do directly.

When you do change effects that are can affect anything, you have to be extra careful. That's why you'll notice that most giant growths tend to be plus n plus n, meaning plus 3 plus 3 plus 2 plus 2 plus 4 plus 4. Just because when you can target anything, we know that math can get extra hard

because we don't know what you're targeting. So we're more likely in those scenarios. Also, for example, when white boosts everybody, it tends to be plus 1 plus 1. Everyone's probably going to do plus one, plus one. Every once in a while we do plus two, plus one. Um, that's really the only non-square stat that we do in white where we boost people. Um, and once again, um, people are a little easier time with the power than the toughness,

but. Okay. So in design, there's a lot of math that has to do with figuring out how often things show up and how much they interact with each other. There definitely is some math that goes into the mana, meaning there's math on trying to understand when to cast something, how much it should cast, and when it's supposed to cost one colored mana or two colored mana. That is not something I do tons with. But one of the things is we normally have a play designer on our team so we can cost things. And I do enough costing that I have a general sense. I'm not quite as fine-tuned as our play design department.

But I do get a sense of trying to figure out when we care. And one of the things, by the way, colored mana, how much colored mana you have, that's another sort of mathy thing you have to keep in track of. Oh, and that reminds me, another kind of math related thing is understanding your land. Understanding how to give people access to the colors they need in a way that gives them enough access that they can play what we're trying to let them play, but not so much so that they can just play whatever they want. And the more colors you're letting people

play, the harder it is. Like, if I let you play three colors, and I want to give you the tools to play three colors, it is tricky not to let you play four and five colors. And even with two, for example, when you're playing two colors, just letting people get to the third color, it is tricky to sort of find the right amount. There's a lot of math that goes into that as well. And like I said, there's a lot of math in the nook and crannies, you know, trying to figure out, like, whenever we have a number, whenever we're trying to figure out power toughness, or trying to figure out mana cost, or activation cost, or, you know,

whenever there's something, there's a number there, that number revolves, That number is going to revolve a little bit of math and sometimes a lot of math depending on what it is. Okay, so now I've gotten through that. That's all stuff I worry about. I'm making the game. But the math gets much more complicated once we get outside of just the mechanics within the game itself. For example, we make a lot of different versions of magic. Right now, there's 11 languages of magic. So one of the things we have to figure out is print runs.

We have to figure out how much are we supposed to print of each thing. And in general, the idea is, the goal of a print run is, we want to make enough magic that we're meeting the supply of the audience. But, at the same time, we don't want to overshoot because we're collectible. We want there to be enough for people to get, but not so much that it's just sitting around the shelves, right? We kind of want to make it, want people to buy it, and then want it over some period of time to be sold.

Now, normal magic sets, standard legal sets go on sale for a while, you know, we will reprint things, but there's a lot of math at figuring out print numbers. You know, what's the right amount to print so that we because if you err on one side, then you short the market and people can't get the stuff and you're losing money. You err on the other side, you overprint, and then part of

making a collectible is people want to get it and it being something that's exciting and has... You know, you want it to be something that people can value. And so there's a balance there. Now, it's complicated by the fact that not only are we printing in one language, but we are printing in 11 languages.

And each language has its own sales pattern and has its own need. So not only are we trying to figure out individually what each language wants, but then, on top of that, we're trying to justify and make sure that there's enough of, like, one of the things that we're careful of is, because it's a collectible, we don't want to print any one thing in too small a number. We want to make sure that everything is relatively collectible. Now, in English, we print lots and lots of English. That's not an issue. But as we get into smaller languages, that becomes more complicated. Now, added to that, the added thing is, you know, we also do things like foils. We have to understand the rarity of foils. And we're starting to do stuff like booster fun. And not only do we have to do those things for, we have to do those things for, um, we have to do those things for each market and understand when and where and

how different things show up. Um, and like I said, one of the things about magic is there's a lot of moving pieces. So I'll just take Throne of Eldraine, for example. Okay. So now in Throne of Eldraine, I have the normal version of every card. I have the premium version of every card. of every card. I have the premium version of every card. For Planeswalkers, I have the normal version of the Planeswalker. I have the normal, borderless version of the Planeswalker. And then I have the premium, borderless version of the Planeswalker. Then for all the cards with Adventure, that's the mechanic in Thorn of Eldraine, that has the storybook treatment. I have to figure out, you know, there is the normal version, there is the non-foil showcase version, sorry, there's a normal version, there's the foil version of the normal version,

there's the showcase version, the non-foil, and the showcase version in foil. And then there's extended art, and the extended art exists, the normal cars, and then the extended art non-foil, and extended art with foil. All those things exist. All those different things. And not everything shows up in every product, and you know, so there's a lot of figuring out when and where and how things show up, and then you've got to do the math to make sure that things show up in the right amount and not just in the right amount in a vacuum but also in the right amount

in totality, how much of the product in general do we want to exist and so there's a lot of a lot of math to figure that out, to try to figure out where and how and how much and how often and what you're doing in different languages and stuff. On top of that, we have logistics, meaning we sell magic at the same day worldwide. So not only do we have to print all these things and print them in the right numbers overall, but we also have to print them within a time frame where we understand where and how

they're going to be all in the same place at the same time. And what that means is we print around the world so that we can ship to a lot of different places, but then we have to figure out sort of how long it takes to print and then how to get where it needs to get such that everything ends up in the same place on the same time so that on the same day worldwide people can release it. And there's a huge amount of math in that. There's a lot of math in trying to understand all the logistics of making the things happen.

On top of that, sometimes we reprint cards. And, you know, we need to be very conscious of how many cards we have. And when we reprint, how many we want to reprint. That's another sort of thing to keep in mind. What we call allocation, which is some things we print to demand, meaning most standard legal sets,

hey, as much as people want, we'll keep printing. And if they want more, we'll go on press and we'll print more. Some things are what we call allocated, which means we don't print, it's not an endless supply. We're only printing so many. Master sets and things that are mostly reprintable in this category, we're like, we're not printing, it's not print to demand, it's we're printing some amount of it. And so we have to figure out what's the right amount of it and what languages it are in. And there's a lot of

deducing all that and figuring out what that has to be. Then there's play design. So play design, like I said, they have a lot to do with figuring out the balance of individual cards, meaning what does this cost? What does that cost? But the other thing that requires a lot of math is they have to balance the play environment. They have to make sure that there is, you know, and like I said, they have to balance the play environment without definitively solving the play environment. Because if they can figure out what the decks are, all of you would figure it out overnight, because there's a lot more of you than us. would figure it out overnight because there's a lot more of you than us.

So a lot of figuring out the environment is not just knowing exactly what's getting played because you don't know that, but it's making sure there's a balance of things so that no matter what happens that there are different outlets for different things. And that requires a lot of combinatorics and figuring out sort of what options and what possibilities happen and what happens if people do this and what happens if people do that. And all this is going along while they're also fine-tuning. All the numbers I was talking about

earlier, play design and set design are fine-tuning all those numbers. Like, we're taking a stab at it and then as we're playing and passing along, set design has to finalize those numbers with input for play design. So, I mean, there's endless numbers in that regard. Okay, but wait, there's more.

So another big thing that we need to do is we need to figure out what players like and don't like. Right? We need feedback. How are we going to get better? How are we going to improve things? So one of the ways we do that is by collecting data. So there's a lot of data we can collect. Data, data, I'm not sure what the correct pronunciation there. I like saying data.

Maybe it's my love of Star Trek Next Generation. So the data is, A, we have sales data because we sell the product. I mean, speaking of math, by the way, there's a lot of math that goes into understanding the business and the markets and stuff. I didn't even get into the business side of math. Then we have data from all the digital inputs. People play Magic at the Arena. They play Magic online. There's a lot of interactions there.

There's a lot of social things we can measure. How many people, you know, how often did this get referenced in social media and where and how and how many impressions. And, you know, there's a lot of stuff we do. Like when we do our advertising, we spend a lot of time and energy tracking our advertising and who clicks through what ad and trying to figure out what spoke to people. We also have organized play data that people play in tournaments and we collect data from that. And we have infinite miscellaneous data. There's a lot of data, especially on the internet, about magic. There's people talking about magic and interacting with magic and there's just lots and lots of data out there.

So we need to collect that and understand it and we need to sort it. We have a whole group called BMI. I don't know what BMI stands for. But their job is to collect all their data and then analyze it and get conclusions from the data. So there's a lot of um models and stuff because a lot of trying to understand things it gets complex you know when you're saying what do people feel about this on the internet there's a lot of metrics that you can pull and you can sort of use those and design them um but the other thing that we've learned is we have access to so much so much um data that it's not just a matter, like, it's not just getting the data.

It is processing the data and it is understanding the data, you know, that, yeah, we have a lot of access to a lot of different things, but it's more than just having it. you know, if someone's like, oh, everybody who cares wrote you a letter and we've dumped all the letters on your desk and you now have 80,000 letters, okay, well that that's, you know what I'm saying, there's a lot of process to figuring out how to access and use it, there's a lot of math in that and also, like I said, there's a lot of math in running tournaments in processing, anyone who's ever run a tournament there's a lot in the Swiss pairing

and all the sense of how that happens there's a lot of math in programming, a lot of math in all the digital stuff that we do there is one of the things for example whenever we make something we have to sit down with digital and we have to walk through with them the intent of what we want to do. So, for example, numerous times I've sat down with digital and I want to do something and they're like, oh, well, here's what we need to do to make that work.

And things that you might think of very simple math, like things that the human brain can go, oh, I got it. Sometimes the computer will go, oh, no, that's not straightforward. That is not something, like a computer is really good at saying, if A, then B. But, you know, if like,

well, if A, do B. But when it's A, it's kind of a judgment call. You know, humans are good at judgment calls. The computer is not good at judgment calls. The computers are not good at judgment calls. So there's a lot of figuring out what can get programmed. There's math inherent in there. Then, on top of that, the other thing that play design will look at

is trying to understand how often things get played and what that means. Like one of the data we look at all the time is tournaments and figuring out what gets played. And we look both online and in real life, you know, in tabletop. And trying to understand like, oh, what are the decks and what does that mean? What are the cards that are caring about things? And there's a lot of data crunching to understand. And there's a lot of data crunching to understand.

One of the things that we want to do to get better at understanding sort of how to make the better environments is using the analytical tools to be able to slice and dice what's going on to figure out and process, oh, we made these decisions, and these are the outputs of what we've done to try to understand and get lessons so that we can improve upon that. Actually, what am I missing? Hopefully you can see. I'm almost at work. There is no endless amount of things. The math runs deep. Oh, one of the things that I brought up when I did my interview that was on the podcast was I brought up that we have an economist named Kenny.

And we have so many math problems that are really complex, that are really like very, very important. You know, how much should we print? I mean, that's a very important thing that we, you know, Kenny is able to do a lot of mathematical models and like, you know and do very high-end math. Because there is... Like I said, the math is so deep that we have an economist

and he needs the help of computers to process stuff because it's just so complex. And remember when I did my interview, he was really shocked that we had an economist. But that is how much math that we have in R&D, that R&D needs its own economists. And it's funny talking to Kenny sometimes in that

one of the tricky things in general is not just a matter of understanding what the numbers say, but understanding what you want to know. One of the things that's very interesting that you tend to think of numbers as being very black and white. Like, there is the correct answer and the wrong answer. But one of the things that's very interesting is that as you analyze numbers,

while there definitely is a lot of math that goes into understanding the numbers, it is not nearly as, you know, there's more subjectivity than you realize. Because a lot of it is trying to understand what factors mean and why you can measure factors, understanding the implications can be a lot more complex. And that is something that I don't think I really appreciated until I got here and started watching, like, I'm surrounded by people in R&D that are really good at numbers. I mean, not that I'm bad at numbers, but I'm watching something like Eric Lauer process numbers in his head. I'm nowhere in that ballpark at all.

It's really interesting watching, sort of crunching through in that there's so many problems that come up that someone like Eric, who does high-level math in his head, and Eric will go, oh yeah, we need a computer. Eric will just admit up front, like, oh, yeah, there's no way my brain can process that. We're going to need a computer. It's really interesting.

And like I said, I mean, all those years ago when I swore that I would never need math, but I studied math anyway, I'm glad I did. It actually has paid off. So to all you out there, A, that are in school still and studying math and cursing math, don't curse math. Math is your friend.

Or at least you will need math. Be nice to math. You will need math. Anyway, I'm not sure we thought of today's podcast a little bit different. I like trying different things. I don't know. Give me your feedback on this podcast. Just trying to show you a different side of magic, different side of design.

But anyway, I'm now at work. So we all know what that means. It means instead of talking magic, it's time for me to be making magic. I'll see you guys next time. Bye-bye.