Mathematics and Magic Players

[thefreakaccident]

It seems to me that most magic players are also high-level mathematicians...

Is it just me, or is there a correlation here?

Magic is a game of math, with many calculations, simple statistics, and other undeterminable variables.


Is this game more attractive for those mathematically inclined?


A good example to the contrary is my friend, and teammate Colton Geneva, who is one of the funniest guys you could ever know, and isn't a terrible player, but he happens to totally suck at math, but he is the only person I know for this to be true.


I myself happen to be more mathematically inclined however, as it is the only topic I actually enjoyed (until Calc my junior year).

So, I guess it boils down to this:

Since this is a game of math, does it attract people who are good at math?

[Skeggi]

Since this is a game of math, does it attract people who are good at math?

Yes. Not saying I'm good at it, I have computers to do my math :tongue:

[Nightmare]

Many of the people who enjoy this game are mathematically gifted, yes. If you boil the game down, cutting out all the flavor entirely, the game itself is pure mathematics, which is why some people delve into that aspect so deeply.

[Peter_Rotten]

I hate math. I'm terrible at. In fact, sometimes I'll just blindly swing my critters into combat because I don't feel like adding in my head.

The flavor and D&D feel attracted me to the game. I think the poker-like bluffing and watered down chess-strategy keeps me playing.

But to hell with the math.

[montanhas18]

I started playing Magic about ten years ago. Watched people playing the game in a dozen different countries (watched = reporter at GPs, PTs and Euros). To this day we still get a good laugh out of something we witnessed in those first months playing the game: a high school kid sitting down to play the game with a calculator at his side... because he was playing Pox.

A third. "Round up each time."

:smile:

[Dan Turner]

There is a really good article from about 15 years ago called "The Mathamatics of Magic The Gathering" I will see if I can find it on the net or if not I have a copy saved on one of my backup hard drives. I have been thinking of re-vamping it for the way magic is played now since strategy and card draw as well as the way we mulligan has come a long way in 15 years.

And by the way I am a total math geek.

[smoky squirrel]

I have one year to go before I get my PhD in Pure Mathematics. So yeah, make of it what you want :) When I got the time I will put my effort in writing some comprehensive mathematical strategy articles about Magic.

[Nihil Credo]

I'm finishing my 3rd university year in mathematics, and what brought me back to Magic and then into serious play (after a brief casual period back in 2000) was finding all those fascinatingly complex strategy articles around the net.

[Taurelin]

Might be true. I, for example, am a teacher of Mathematics. And I do particularly adore decks like Solidarity. But on the other hand, the maths you need for playing Solidarity is something you learn in 7th grade (y = 3*x). And I don't calculate statistics while mulliganning or playing spells.

Maybe it's rather a general mathematic way of thinking, since Magic also follows the rules of logic very much. And as mathematicians we probably have something like an intuitive affinity for that.

Sadly, this advantage is neutralized by my lack of psychological skill (mental gaming). I would also be a lousy poker player. :smile:

[Skeggi]

Might be true. I, for example, am a teacher of Mathematics.

Well, you know what people say: "Those who can't, teach." So I guess you're another exception on the rule :tongue:

[Finn]

I hate math. I'm terrible at. In fact, sometimes I'll just blindly swing my critters into combat because I don't feel like adding in my head.++

Actually, I am not terrible at it. But I don't like it. Calculating blocking scenarios and return attacks bores me, so I typically take a guess here as well. Oh yeah, and I am a math and programming teacher for profoundly gifted students. Go figure.

BTW, the game's rules are both mathematics and logic on its underbelly. I.e. "the stack" is a programming and computer software concept that functions essentially the same way the game uses it. And also, Mark Rosewater has gone into detail about the mathematical side of card design. But I think that it is a mistake to say that the game can be boiled down to numbers. On the creative facets there is so much more than that.

[Anusien]

Wait... you're telling me over-intellectual geeks are attracted to complex strategy games?

[Dan Turner]

FOUND IT:

http://www.kibble.net/magic/math.php

[freakish777]

It seems to me that most magic players are also high-level mathematicians...

I guess that depends on your definition of high-level mathematicians...

Under my definition of high-level mathematician, most magic players aren't.

[thefreakaccident]

Well, Me and most of my magic buddies are honors math students, with four of us having taken either AP Statistics or Calculus... and the others just being honors math students up until something like PreCal, or something to that extent.


The point was that I am finding that a good deal of magic players are in fact good at math in general... or at least, that is the correlation I have found with this sample (although, there is some bias here, as they are my group of friends, therefore similar intellectual capabilities/interests...).

[Lukas Preuss]

This:

I'm finishing my 3rd university year in mathematics...

and this:

Might be true. I, for example, am a teacher of Mathematics. And I do particularly adore decks like Solidarity.

I too am finishing my third year of university to become a math (and English and history) teacher. The complex mathematical aspect of the game fascinates me the most... one of the reasons why I really like Solidarity.

[jbmulder]

I do have a BA in math, but I don't play Magic because it's essentially a math game.

I do meticulously calculate the blocking/attacking numbers, though. I enjoy reading statistical breakdowns as well, but stats was always a weak point of mine. I'd like to work on that.

I enjoy the math involved in games a lot though. Especially in poker. However, it's no substitute for the moments when you just have to go with your instincts.

@squirrel:
What are you studying? My favorite math classes were always the pure math classes. Group theory ftw

[freakish777]

Well, Me and most of my magic buddies are honors math students, with four of us having taken either AP Statistics or Calculus... and the others just being honors math students up until something like PreCal, or something to that extent.


The point was that I am finding that a good deal of magic players are in fact good at math in general... or at least, that is the correlation I have found with this sample (although, there is some bias here, as they are my group of friends, therefore similar intellectual capabilities/interests...).

Sure, that's probably reasonable. Claiming "high-level mathematicians" though isn't (I definitely don't define high school level math classes, AP or not, as high level, if you're doing grad work in Math, then I'd consider it high level, and for the record, I hold no degrees in Mathematics). That doesn't mean you and your friends aren't good at math.

[Deep6er]

I'm ludicrously fucking terrible at math.

Not going to lie here, but I failed fucking Geometry. No lies. Also had a devil of a time in Algebra 2.

I calculate scenarios for blocking and attacking just fine, but when it comes down to statistics, I'm pretty awful.

I would say that Solidarity wasn't really based off of mathematical principles as much as it was based off of keeping things straight. Knowing how much mana you had floating, how many spells were played, and how many cards your opponent had left in his library were slightly less valuable than playing around your opponent's hate. Then, when you went off under a high stress scenario, it was more a logic puzzle that also included elements of math.

Seriously though, I'm terrible at math, and I hate it. Fuck math.

[Nightmare]

I'm ludicrously fucking terrible at math.

Not going to lie here, but I failed fucking Geometry. No lies. Also had a devil of a time in Algebra 2.

I calculate scenarios for blocking and attacking just fine, but when it comes down to statistics, I'm pretty awful.

I would say that Solidarity wasn't really based off of mathematical principles as much as it was based off of keeping things straight. Knowing how much mana you had floating, how many spells were played, and how many cards your opponent had left in his library were slightly less valuable than playing around your opponent's hate. Then, when you went off under a high stress scenario, it was more a logic puzzle that also included elements of math.

Seriously though, I'm terrible at math, and I hate it. Fuck math.

This just in - I'm more asian than Dave Gearhart.

You've failed your racial profile, Dave.

[Deep6er]

Yeah, turns out I'm also nowhere near insane enough at video/computer games to be asian too. I'm pretty sure that I'm going to get a letter in the mail soon about how I'm no longer asian enough to be half-asian. :(

But hey, it's cool, because I'm also white which means... wait, what does it mean again? Damn. :(

[TheInfamousBearAssassin]

But hey, it's cool, because I'm also white which means... wait, what does it mean again? Damn. :(

You get a free yacht. But you have to be all white. And no Irish.

[Deep6er]

Badass, since I'm getting kicked out of the asian kids club, that means I get a free yacht? That's cool. I can deal with that.

[Dan Turner]

You get a free yacht. But you have to be all white. And no Irish.

Damn and I am half Spanish, and my white half is Irish guess I am just screwed.


NO YACHT FOR ME

[feuerizer]

I can support your theory at all!

All my friends who play magic are engineers which means they are somehow related to math.

I am a teacher for math and physics.

Although I got into magic in `96 as a schoolboy...
Nevertheless I had liked math back in the days.

[thefreakaccident]

I'm ludicrously fucking terrible at math.

Not going to lie here, but I failed fucking Geometry. No lies. Also had a devil of a time in Algebra 2.

I calculate scenarios for blocking and attacking just fine, but when it comes down to statistics, I'm pretty awful.

I would say that Solidarity wasn't really based off of mathematical principles as much as it was based off of keeping things straight. Knowing how much mana you had floating, how many spells were played, and how many cards your opponent had left in his library were slightly less valuable than playing around your opponent's hate. Then, when you went off under a high stress scenario, it was more a logic puzzle that also included elements of math.

Seriously though, I'm terrible at math, and I hate it. Fuck math.



Ironic, that you made one of the most mathematical decks ever to see play in the format... and yet you claim to suck at math... funny.

[Kuma]

Statistics major here, and yes I'm attracted to the statistical side of the game. I love calculating the probabilities of drawing X, Y, and Z, in N cards, etc.

BTW, the odds of a turn one moon effect in your opening seven in Dragon Stompy is ~34% on the play and ~50% on the draw. The odds of mulling to get a certain card, i.e. Leyline of the Void, is ~80% if you're willing to go down to a single card.

Just in case anyone cares. ;)

[jbmulder]

Statistics major here, and yes I'm attracted to the statistical side of the game. I love calculating the probabilities of drawing X, Y, and Z, in N cards, etc.

BTW, the odds of a turn one moon effect in your opening seven in Dragon Stompy is ~34% on the play and ~50% on the draw. The odds of mulling to get a certain card, i.e. Leyline of the Void, is ~80% if you're willing to go down to a single card.

Just in case anyone cares. ;)

Yes! I love this stuff!

[Zach Tartell]

<- this guy has difficulty counting past ten without taking his socks off.

[smoky squirrel]

@spidey Crystalline Graded Rings with zero degree part a Dedekind Domain.

Oh and in my spare time: game theory. But magic is usually a game of imperfect information, and imperfect decisions by both players, and that makes things very difficult. Mindless combo decks like belcher (usually) can be described adequately though. Is there anything you guys want to see mathematically explained about magic? I will try to do that if I can.

[Pinder]

Math nerd sounding off here.

I stopped taking math at my community college because I had run out of math classes to take. The series they had stopped at Differential Equations. Not that Differential Equations really helps that much with Magic, but I did solve a hypothetical murder once by deriving a corpse's time of death based on his body temperature, both before and after he was moved into a freezer. So that was cool.

I sort of sucked at Linear Algebra though. It's because I hate matrices. Fuck matrices.

[Sanguine Voyeur]

I've never learned about matrices. I did, however, 'review' matrices every year in high school.

Other then that, I can handle complex concepts, but can't aptly solve simple math problems and I frequently make small errors.

EDIT: Make that stupid errors.
I do believe, although I'm not positive, that the chance of it not happening is 88.7%. So the chance of it happening should be 22.3%.

[Pinder]

Other then that, I can handle complex concepts, but can't aptly solve simple math problems and I frequently make small errors.


This is what it is for me, too. I have a tendency to overcomplicate things, and I tend to miss the really simple solutions. So I look really smart, unless I'm trying to do something really easy, in which case I try to do it as complicated as possible.

It extends into Magic, too. I often fall into the "danger of cool things" zone.

[DeathwingZERO]

Like Spell Snare on a Daze?

I never bothered going past Algebra 2 in high school, but had I actually cared about high school enough to stick around I would have probably ended up in Calculus or AP Calc at some point. Math was probably my favorite subject, and constantly having problems requiring me to sound like I'm trying to figure out the values of letters in the alphabet was cool.

[Mayk0l]

I'm going to have to go with Mr. Rotter on this one. Initially, the flavor dragged me into the game, it had nothing to do with math or the game mechanics or why it's so awesome to have exactly 60 cards in your deck. I was, however, mathematically proficient enough to realise that 1 Quicksilver Dragon was not good enough, because they looked awesome. I needed more!

Oh, and Merfolk.

Math? Nah, I suck so hard at math I can't even tie my shoelaces properly. I'm glad my future profession and job description do not include me doing any adding, substracting or counting. That'd just be a bad idea.

[Nihil Credo]

Ok, let's get some actual maths in this thread:

Has anyone looked into finding a set of differential equations to describe the evolution of a metagame (= finite, small, fixed set of Magic decks, each of which is played by a variable subset of a large, fixed-size set of players)? I messed around with that a while ago after learning about the Lotka-Volterra predator-prey model, which however clearly does not apply to metagames (ex. decks have no intrinsic growth rate). I then tried to develop a model on my own, but hit a stumbling block when trying to reconcile the following hypotheses:

- A deck's popularity increase rate (dP/dt) is a strictly increasing function of the deck's overall winning chances.
- The limit of a deck's popularity increase rate (dP/dt) tends to +inf or -inf as that deck's overall winning chances tend to 1 or 0, respectively (they're never 1 or 0 because every deck is 50/50 against the mirror).
- The collective popularity of the decks has the zero-sum property (due to the constant number of total players).

Any takers, or do you know of any model that might be more appropriate for this scenario?

[Deep6er]

I like how I literally didn't understand any of that.

Go me.

Also, on another note, fuck math.

[TheInfamousBearAssassin]

Dave and I once created an imaginary number named Frank that was a post-infinite number with the ability to multiply zero into something. We created it to describe how much better I am at everything than Dave.

[CynicalSquirrel]

I'm also beyond bad at math. I don't like it and I'm not good at it. Barely got through high school math, although that also had to do with me not doing the homework since I hate math. I just never understand how people could find it interesting.

[Deep6er]

Dave and I once created an imaginary number named Frank that was a post-infinite number with the ability to multiply zero into something. We created it to describe how much better I am at everything than Dave.

You know, if I recall correctly, that number was there to describe the hate that I had for Ramsapoop, and now, by extension, you.

Fuck you Jack.

[The Rack]

I hate math, but I'm good at it.

Fuck math.

[Fred Bear]

Ok, let's get some actual maths in this thread:

Has anyone looked into finding a set of differential equations to describe the evolution of a metagame (= finite, small, fixed set of Magic decks, each of which is played by a variable subset of a large, fixed-size set of players)? I messed around with that a while ago after learning about the Lotka-Volterra predator-prey model, which however clearly does not apply to metagames (ex. decks have no intrinsic growth rate). I then tried to develop a model on my own, but hit a stumbling block when trying to reconcile the following hypotheses:

- A deck's popularity increase rate (dP/dt) is a strictly increasing function of the deck's overall winning chances.
- The limit of a deck's popularity increase rate (dP/dt) tends to +inf or -inf as that deck's overall winning chances tend to 1 or 0, respectively (they're never 1 or 0 because every deck is 50/50 against the mirror).
- The collective popularity of the decks has the zero-sum property (due to the constant number of total players).

Any takers, or do you know of any model that might be more appropriate for this scenario?

If I understand you correctly, you are saying...

(a)

dP/dt = f(W) -> P = f(W,t) where W = f(M) and M = f(D,t)
[ where P = Popularity, W = Winning Chances, M = Metagame, D = Decks Played, t = time]

Popularity increases with time if the deck's winning chance in the current metagame is positive. This is a little convoluted because W itself is a function of time, unless you define the Metagame as static (a constant). But, if you believe the Metagame to be static, the problem becomes moot.

(b)

I believe it is due to that convolution that you are unable to resolve your next statement.

limit dP/dt does not go to infinity (or negative infinity) because W cannot go to 1 (or 0) since the Metagame (and, more strictly speaking, Magic) won't allow it. W can approach 1 (or 0), but you will always have 'a chance' of losing (or winning) any given match which inadvertantly puts a limit on how close to 1 (or 0) W can get within a given Metagame.

As a test, assume one week everyone plays an identical 60 card deck and 15 card sideboard. Everyone has read the same strategy articles and will board in each game identically. [Not necessarily realistic, but a 'textbook' example nonetheless]. I think the expectation should be that the decks popularity will go to 50% the second week (50% of players will be 'disappointed' and switch to a deck which presumable beats the first deck) and so on.

(c)

I'm a little lost on what you mean... I would expect the collective popularity of all decks in the metagame to = 1 (i.e. everyone brings a deck). Maybe you could explain that a little further.

-FB...

[Pinder]

Dave and I once created an imaginary number named Frank that was a post-infinite number with the ability to multiply zero into something. We created it to describe how much better I am at everything than Dave.

This reminds me a lot of Tacosnape's "Crazy Math". God, weren't those good times?

And Nihil, basically what Fred Bear said. At least, what I understood of what Fred Bear said. I haven't done DiffEq in almost a year now, but what I understood seemed reasonable.

[Mayk0l]

Am I the only one that feels like a complete retard after having read Nihil's and Fred Bear's posts?

[Deep6er]

I like how I literally didn't understand any of that.

Go me.

Also, on another note, fuck math.

You're not the only one Mayk.

At some point, I thought they were speaking another language that looked suspiciously like English, but had no similarities beyond appearance.


... the crafty bastards. They're speaking in code.

We can only hope that whatever diabolical plan they're creating foils itself somehow. Because I sure as fuck can't understand a word the bastards are saying.

[dude 666]

Math nerd sounding off here.

I stopped taking math at my community college because I had run out of math classes to take. The series they had stopped at Differential Equations. Not that Differential Equations really helps that much with Magic, but I did solve a hypothetical murder once by deriving a corpse's time of death based on his body temperature, both before and after he was moved into a freezer. So that was cool.



How is that even possible, what kind of school is that? I'm taking differential equations in high school.

[Maagler]

The only math I have ever been good at is statistics. I hate all other forms. I don't think it hinders me in a game of magic when I cant tell you what the sine or cosine of a circle is. But on the other hand I feel i use statistics more that is possibly necessary when using certain decks.

[KillemallCFH]

I, too, am a math major, but that doesn't really have anything to do with my love of Magic. I got into the game because I am a geek who likes fantasy games, and I stay in the game because I am a geek who likes strategy games. I am way more interested in really abstract math that doesn't have much application in the real world, as opposed to say, Statistics, which I found boring as fuck.

[Pinder]

How is that even possible, what kind of school is that? I'm taking differential equations in high school.

Community College, baby (although I suppose there's still Statistics and other classes I could take, but as far as pure math goes, DiffEq is it). And your high school must kick ass. My high school only went up as high as Calc I (i.e., booooooooooooooring).

[Skeggi]

Because I sure as fuck can't understand a word the bastards are saying.

There's alot of fucking in this thread.

I think it's related to the number of posts Dave made. Amirite?

[Deep6er]

Yeah, I'm a big fan of the casual profanity. It's fucking great. :)

You should hear me speak in real life though, it's even worse.

[Skeggi]

You should hear me fuck in real life though, it's even worse.

Dude...TMI :eek:

Back on topic: I believe the correlation between Math-geeks and Magic isn't explained because Magic is a game of Math. Magic is a game of abstract-logic. The way priority works, the stack, layers and all that stuff, all abstract-logic. People who like abstract logic tend to like Magic. People who are good at math are good at abstract-logic and more likely to like Magic.

I myself am a programmer, not a mathematician, but I do like a fair ammount of abstract-logic, pours straight into Magic.

[Nihil Credo]

If I understand you correctly, you are saying...

(a)

dP/dt = f(W) -> P = f(W,t) where W = f(M) and M = f(D,t)
[ where P = Popularity, W = Winning Chances, M = Metagame, D = Decks Played, t = time]

Popularity increases with time if the deck's winning chance in the current metagame is positive. This is a little convoluted because W itself is a function of time.

That would be correct.


Something I definitely should have made explicit was that I'm assuming continuous, not discrete time. The reason for this choice is clear with the following example: assume the metagame is made of Rock, Paper and Scissors. Let's also assume that at t=0 everyone brings Rock (popularities = (1,0,0)).

With discrete time, you'll end up in a loop: at t=1 everyone brings Paper, at t=2 Scissors, and them the cycle starts again. This is pretty far-fetched.

With continuous time, however, what we'll get is a drastic increase of Paper (vertical tangent at t=0), something like this:


http://xs231.xs.to/xs231/08372/graph466.png


(I drew this quickly with paint.net, apologies for the Bezier curves. Also, the horizontal asymptotes of both curves should be at 2/3 and 1/3.)

which resembles a lot more what actually happens during PTQ seasons - the Anti-Deck and the Anti-Anti Deck rise in popularity, but the original Best Deck (Gifts, Faeries, or whatever) still has a place.

Incidentally, if I were to use discrete time, I'd have to drop the differential notation.



(b)

I believe it is due to that convolution that you are unable to resolve your next statement.

limit dP/dt does not go to infinity (or negative infinity) because W cannot go to 1 (or 0) since the Metagame (and, more strictly speaking, Magic) won't allow it. W can approach 1 (or 0), but you will always have 'a chance' of losing (or winning) any given match which inadvertantly puts a limit on how close to 1 (or 0) W can get within a given Metagame.Actually, I'm assuming a 100% matchup percentage *is* possible; the reason W can't go to 1 is because any deck is 50/50 against the mirror, so even if deck X beats everything else its W will be (1 - (P_x/2)). To be more rigorous, you can only ever get W=1 at the instant when the popularity is zero.

Either way, I don't understand the objection in your paragraph. It reads as if you disproved "X goes to infinity", but as you certainly know, that's not at all the same thing as "limit X goes to infinity".


As a test, assume one week everyone plays an identical 60 card deck and 15 card sideboard. Everyone has read the same strategy articles and will board in each game identically. [Not necessarily realistic, but a 'textbook' example nonetheless]. I think the expectation should be that the decks popularity will go to 50% the second week (50% of players will be 'disappointed' and switch to a deck which presumable beats the first deck) and so on.Why would 50% of them switch and not 100%? It's not unreasonable to assume that people keep or switch decks based on their previous personal performance, rather than metagame analysis, but it doesn't seem very useful given that those who do switch decks still need some criteria to pick their new choice (besides, even if you won with Psychatog through a sea of mirrors, wouldn't you anyway expect an increase in RG Aggro the following week and prepare accordingly?).

It's because of this sort of problems that I think a continuous-time model is more suitable.



(c)

I'm a little lost on what you mean... I would expect the collective popularity of all decks in the metagame to = 1 (i.e. everyone brings a deck). Maybe you could explain that a little further.

-FB...Yes, by "zero-sum property", I meant simply that the total sum of popularities is constant. More specifically, this gave me a linear equation in the n variables dP_i/dt (i = 1, .., n) which I couldn't reconcile with the limit condition (a).

[Anusien]

Blah
Doesn't this sort of analysis assume rational actors? Isn't that a horrible assumption in real life?

[Nihil Credo]

Doesn't this sort of analysis assume rational actors? Isn't that a horrible assumption in real life?

Two separate answers:

First: People's irrational (or budgetary/temporal) reasons to pick their deck are impossible to put in a formula, so the rational assumption is as good as you're going to get. If the non-performance factors become too big (eg. a certain deck is handicapped by being too expensive/complicated), you could try to emulate them in the model on a case-by-case basis (eg. you give that deck a ceiling on metagame presence, or a penalty on matchup percentages).

Second, and much more important, is that a general rule that states "The more element X has an overall positive relationship against the current field of elements, the faster its subset of the total field will grow" can conceivably work as a model for systems other than a Magic metagame. My non-MtG-playing then-girlfriend asked me about it and I described it this way: "A fixed-size population made up entirely of predators (each belonging to one of several species), who randomly fight each other (including those of the same species), each fight having a fixed chance of each outcome depending on the their species."
It's quite conceivable that, say, a bacterial soup or a complex chemical reaction could work like this.

[Pinder]

It's quite conceivable that, say, a bacterial soup or a complex chemical reaction could work like this.

Especially if those bacteria played Magic.

[Fred Bear]

Nihil,

I think we are largely in agreement on the model. I was never suggesting using a discrete time scale, but rather to be able to look at the model after discrete 'chunks' of time. Not many tournaments played have a 'steady-state' metagame breakdown (i.e. as t->oo). Your model should show how a metagame may 'evolve' from tournament-to-tournament (t1, t2, t3, etc.) as the format is 'solved' (i.e. the steady state will result in a collection of Decks A,B,C,etc. in percentages X,Y,Z,etc.). [This is what I assumed to be the goal of your exercise.]




Actually, I'm assuming a 100% matchup percentage *is* possible; the reason W can't go to 1 is because any deck is 50/50 against the mirror, so even if deck X beats everything else its W will be (1 - (P_x/2)). To be more rigorous, you can only ever get W=1 at the instant when the popularity is zero.

Either way, I don't understand the objection in your paragraph. It reads as if you disproved "X goes to infinity", but as you certainly know, that's not at all the same thing as "limit X goes to infinity".

After further thought, I seem to have mispoke. You are correct to say that limit dP/dt is oo. But you must understand that this is a mathematical result, not a 'physical' or real result (I'm actually a physicist by training - math is an unfortunate side effect). If the expectation is for the model to be valid, we have to make assumptions (apply limits) that have real meaning. If your assumption is that W can range from 0-1, then dP/dt=oo can occur within your model (it is possible for P=0 to result in W=1 causing P=1 immediately, i.e. dP/dt = oo). By limiting W to between 0-1 without ever equalling 1, dP/dt can still approach oo, but it can never reach it and the model is 'fixed'. [Note that the converse is not possible, dP/dt will never approach -oo.]


Why would 50% of them switch and not 100%? It's not unreasonable to assume that people keep or switch decks based on their previous personal performance, rather than metagame analysis, but it doesn't seem very useful given that those who do switch decks still need some criteria to pick their new choice (besides, even if you won with Psychatog through a sea of mirrors, wouldn't you anyway expect an increase in RG Aggro the following week and prepare accordingly?).

50% may not be right, but the assumption would be similar to your example. At time, t=0, 100% of people play Rock. There will be a certain percentage of these people who will come back with Rock at the next tournament either because of results or other restrictions (again, our assumptions can take into consideration many things - financial considerations, cards owned, etc.) and a certain percentage of folks will come back with Paper. If the metagame evolves 'faster' than the tournament schedule (probably true for Legacy, say), there will be a percentage of folks showing up with Scissors.

Our differences are in time scale, not continuous or discrete. Most metagames do not 'change' during a tournament, but rather at their completion.

-FB...

[Skeggi]

Guys, this is getting out of hand. You really need to get laid now.

[Mayk0l]

I officially proved my math skills suck to a degree that I can't even get beyond the whole counting numbers thing. I couldn't quite figure out what was wrong with my deck (cause' the 7 piles didn't end at the fourth pile) until Zach pointed out it probably had.. well, at least something to do with the five Putrid Imps :P

[Skeggi]

Lol yeah I had a similar problem. When I first started playing stax I had a list with 3 Ghostly Prison. After some playtesting it became clear I really needed the fourth copy, but I couldn't figure out what to drop for it. FB told me I could just put the 4th Ghostly Prison in my deck as the 60th card: my deck contained 59 cards. Counting = svg tech.

[Aleksandr]

My non-MtG-playing then-girlfriend asked me about it and I described it this way: "A fixed-size population made up entirely of predators (each belonging to one of several species), who randomly fight each other (including those of the same species), each fight having a fixed chance of each outcome depending on the their species."


Beautiful!

[umbowta]

Yeah I admit, I'm totally in love with mathematics. Honestly, I'm working on a bachelor degree in mathematics at the Universty of Michigan. That really just makes me a double nerd. MtG and Math. That's like alpha dork...right? Well maybe, just maybe I'm out dorked by MtG playing english majors. Anyway, I've got to get back to proving that 0<a<b implies 1/a > 1/b > 0 ...and stuff...yeaah.

[Pinder]

Anyway, I've got to get back to proving that 0<a<b implies 1/a > 1/b > 0 ...and stuff...yeaah.

This makes perfect sense when you think about it (i.e., the larger x is in a fraction in the form 1/x, the smaller the fraction is, so if b > a, then 1/b must be a smaller fraction than 1/a...), but the worst part of proofs are always that you have to phrase things mathematically.

[Lego]

Well maybe, just maybe I'm out dorked by MtG playing english majors.

I'm studying for my Masters in English Lit, and am currently editing a paper for publishing on Adam's third choice and the necessity of the Fall in Milton's Paradise Lost. And I know several dead languages. Plus I'm a L1 judge.

Still, I think I'm probably less nerdy than many Math majors/Magic players? Just a guess.

[Mulletus]

I have a physics degree, which I use to stock shelves at Kmart. I also play the magical cards to minimal success.

[Nihil Credo]

I have a physics degree, which I use to stock shelves at Kmart.
Please tell me that means you develop optimal stocking patterns for them.

[Mulletus]

I leave my stocking for Santa.

[umbowta]

)3|^;272666']This makes perfect sense when you think about it (i.e., the larger x is in a fraction in the form 1/x, the smaller the fraction is, so if b > a, then 1/b must be a smaller fraction than 1/a...), but the worst part of proofs are always that you have to phrase things mathematically.
Since 0<a<b, we know a>0 and b>o. By the mulitiplicative property then, ab>o. As such, its multiplicative inverse, 1/ab>0. Multiplying through the hypothesis 0<a<b by 1/ab yeilds 0<1/b<1/a as desired. That one turned out to be pretty easy.

[Deep6er]

I like that the only part of that paragraph that I really got was "That one turned out to be pretty easy."

Also, you misspelled "yields". That's about it. Multiplicative jibber-jabber. Yeah, that one's over my head. Math are the sucks. You know, just letting you know.

[Pinder]

I like that the only part of that paragraph that I really got was "That one turned out to be pretty easy."

Also, you misspelled "yields". That's about it. Multiplicative jibber-jabber. Yeah, that one's over my head. Math are the sucks. You know, just letting you know.


I'll try and put it in layman's terms.

Since we know that a and b are both greater than zero, then the product of a and b, or ab, must also be greater than zero. This in turn means that its multiplicative inverse, 1/ab, is also greater than zero. If you take 1/ab and multiply it by each of the values in 0<a<b, you get (1/ab)*0, which equals 0, (1/ab)*a, which equals 1/b, and (1/ab)*b, which equals 1/a. These new values give you the equation 0<1/b<1/a, which is what you were trying to prove.

God, even then it sounds complicated. I suppose there's just no hope for you,then :tongue:.

[Deep6er]

)3|^;273001']I'll try and put it in layman's terms.

Since we know that a and b are both greater than zero, then the product of a and b, or ab, must also be greater than zero. This in turn means that its multiplicative inverse, 1/ab, is also greater than zero. If you take 1/ab and multiply it by each of the values in 0<a<b, you get (1/ab)*0, which equals 0, (1/ab)*a, which equals 1/b, and (1/ab)*b, which equals 1/a. These new values give you the equation 0<1/b<1/a, which is what you were trying to prove.

God, even then it sounds complicated. I suppose there's just no hope for you,then :tongue:.

I liked the part where you said you'd put it in layman's terms and it was still completely fucking byzantine.

Once you add letters to math, that's where I walk out the door. Letters are for speaking, math is for stupid. Life lesson right there Jimmy (the fucking Hammer).

[Taurelin]

Once you add letters to math, that's where I walk out the door. Letters are for speaking, math is for stupid.

A group of 3 persons is SMALLER than a group of 4 persons.

Hence, if you buy a big pizza and divide it (fairly), each person gets a BIGGER slice if there are only 3 persons compared to a group of 4 persons.

That better? :smile:

[Deep6er]

... I like pizza. Wait, what were we talking about again?

I get it as long as we talk about simple things. You know, like pizza. I like pizza. But when letters are numbers, that's when shit goes haywire. Seriously. Letters are letters and numbers are numbers. Don't go playing with that. It's a recipe for disaster. Not delicious pizza.

[aTn]

I can't speak for the others, but I'm a working mathematician (for a research center for the canadian government), so I'd say I'm pretty mathematically inclined.

As to how far has math helped me playing magic in actual game situations (as opposed to post or pre game analysis), I'd say it made me think systematically through decisions and (on a few occasions) made me choose a play based on the probability of such and such a situation occuring (which I often found out after the game that I had badly calculated :)).

That being said, I make play errors (sometimes enormous) like everyone else and I'm far from being the best magic player out there.

That's my 2 cents.

[thefreakaccident]

... I like pizza. Wait, what were we talking about again?

I get it as long as we talk about simple things. You know, like pizza. I like pizza. But when letters are numbers, that's when shit goes haywire. Seriously. Letters are letters and numbers are numbers. Don't go playing with that. It's a recipe for disaster. Not delicious pizza.

Sigged