---
title: 'How to break Magic the Gathering.'
source: 'https://youtube.com/watch?v=x3dE-NJ1UDQ'
video_id: 'x3dE-NJ1UDQ'
date: 2026-06-29
duration_sec: 978
---

# How to break Magic the Gathering.

> Source: [How to break Magic the Gathering.](https://youtube.com/watch?v=x3dE-NJ1UDQ)

## Summary

This video explores an astronomically large but finite number generated in Magic: The Gathering through a specific three-card combo. The host explains the game's rules that limit infinite loops and uncomputable numbers, then demonstrates how the combo creates a recursive doubling effect that yields a number too large to calculate.

### Key Points

- **Biggest number in a game** [0:00] — The video claims the biggest number ever used in a game comes from Magic: The Gathering.
- **Magic's complexity and rules** [1:13] — Magic has nearly 30,000 cards and rules to prevent infinite loops and uncomputable numbers (e.g., rule 107.2: uncomputable numbers equal zero).
- **The three-card combo** [3:14] — Cards: Double It (doubles token copies), Astral Dragon (makes two token copies of Double It), and a third card that creates an extra token copy of Astral Dragon.
- **Exponential growth loop** [4:20] — Playing Astral Dragon triggers multiple doublings, leading to 32 Astral Dragons, each generating more Double It tokens, resulting in a power tower 30 layers high.
- **Scale of the number** [8:04] — The number has over 22 digits initially, then grows to a power tower of 10^3.6×10^20, far exceeding atoms in the universe.
- **Rule 107.2 nullifies the number** [12:43] — Since the number is uncomputable, rule 107.2 makes it zero in an actual game, turning the combo into zero dragons.

### Conclusion

The video demonstrates a mind-bogglingly large but finite number from a Magic card combo, only to be nullified by the game's rule that uncomputable numbers equal zero.

## Transcript

Are you ready for the biggest number I believe 
has ever been used in a game? And the way it's  
generated, I think is like super interesting. 
It happens to come out of the game of Magic  
the Gathering, which is why I have all these 
cards around me. Now, I don't play Magic. Um,  
friends of mine do, who are massive dorks, and 
they assure me, and they're in the room right  
now. They assure me it's a lot of fun, and I get 
it. There's lots of cards. The cards interact,  
which is how we get this ridiculous number. 
You got some uh like creatures. So, here I've  
got a worm spelled incorrectly. And then you 
got spells you can play that change things in  
the game because it's like a two-player 
game against someone else. Uh strangling  
soot. Don't know what that is. Uh and Armageddon, 
destroy all lands. There you are. I'll play that.
I regret calling them dorks.
This video brought to you by Jane Street and their 
brand new neural network puzzle. Details later,  
we're going to need somewhere new to film. 
Right, new location. Now, the thing about Magic  
the Gathering is it's been around for now over a 
third of a century. And if you're thinking that's  
not right, Matt, it came out in 1993. I have some 
terrible news about 1993 for you. But the point is  
it started well it was the brainchild of someone 
with a PhD in mathematics and it's only got more  
complicated since and over the three decades 
since then every possible edge case has come  
up. There are now almost 30,000 different cards. 
And so the way they interact has become just an  
unwieldy level of complex. And for that reason, 
they've had to introduce some rules to stop things  
from getting too out of hand. Because a lot of the 
cards involve calculations and numbers, regulation  
107.1 states that only whole numbers are allowed, 
only integers. Let's try and keep this nice and  
simple. If it's something you can't calculate 
using integers, well, regulation 107.2 says,  
tough. If you can't calculate it, you get a zero. 
We're keeping it neat. Now, once you get to loads  
of cars interacting, you think, well, hang on. 
What if there's like a runaway feedback loop?  
Well, regulation 104.4B says no to that. If you've 
got some kind of, you know, feedback cycle, which  
is going to carry on infinitely long, no deal. 
The game is officially a draw. And that's assuming  
it's a cycle where no player can stop it. If a 
player can stop it, then that's fine. and they can  
choose some some arbitrary level at which at which 
they quit. And so within those rules, in theory,  
you can only play moves which will give you a 
manageable end result. And that worked. Everything  
was nice and manageable for a very long time 
until someone found a loophole somewhere above  
big numbers, but before infinity. Our ridiculous 
combination involves these three cards which we  
have managed to get our hands on the original. 
However, for us non-magic the gathering people,  
h they are dense. There's a lot of like wonderful 
artwork. There's a lot of information on these.  
And so what we've done is we've made three 
simplified standup maths versions and we're  
going to use those to explain how it all works. 
Starting uh with this one, card A, double it. Now,  
this card doubles the number of tokens that are 
put into play. And the one nuance here is you'll  
have like your original creature cards or like you 
know, spell cards. And you can also have copies of  
them that are called tokens. And the game deals 
with them subtly differently. The original and  
all the token copies. This is if you're putting in 
token copies of something, they get doubled. Now,  
we'll get to card B in a moment because before 
you play B, you have to have card C in action. And  
card C says once you do play B, you're going to 
get another token copy of it appearing. And once  
you've got A and C ready, our ridiculous loop is 
set to kick off. Now, it's time for card B, which  
in the original is called Astral Dragon. We've 
just called make two because when you play this,  
you make two token copies of A. So, in theory, 
we need two copies of this to now enter the game.  
But because they're tokens entering the game, 
card A's power is to take entering tokens and  
double them. So, we'd actually get four. So, 
just by playing this one card, we should get  
four token copies of A appearing as if by magic, 
the gathering. Now, to get those copies, well,  
okay, this card over here, I know I'm going 
a little off. Um, this mystical teachings  
card says I can search search your library. So, 
I'm going to use that to head to the library.
So, at my local library, I was able to make some 
extra photo copies of card A, which if I now cut  
them apart, gives us four token. And you can tell 
they're token cuz they're now grayscale copies of  
of A. So there we are. We can put them all into 
play. I'll just put them down here. We're now  
going to resolve the C issue, which is by playing 
B, we also get an extra token copy. And I've  
got a couple down here. I've made these a little 
smaller. You'll see why in a moment. So we put one  
token copy in of B because of C. But look at this. 
There's five A's over here. And they all see this  
happening. And each one of them, well, the first 
one here decides that it's going to double this  
one coming in. Okay, so now we got two of those. 
And then the next one sees both of these coming  
in, so it doubles those. And now we've got four 
of them. And then the next one sees these four  
and doubles them. Then we get eight. And well, 
there's five of them. So we have to double it five  
times. So we get two to the power of five token 
copies of B. There are now 32 extra B's in play.  
We've just put in 32 newbies. And every single 
one of these tokens says, "When this enters play,  
put two token copies of A in." So, I need to 
add another two token copies of A. But guess  
what's over here? Already five A's. And they're 
going to do the same thing to the incoming two  
A's I did to the incoming 1B. Now, a single 
B got doubled five times. We had 32 of them.  
If we have two A's coming in, it's going to 
get doubled five times, which would be 64.  
So, here we have this is 64 A's, which 
I'm now going to add in to our A pile. Oh,  
no. Because if I put these in, we now have a total 
of 69 A's over here. And we've only deployed one.  
We've done that one. We've done one of our 32 Bs. 
So now the next the next B comes in. It's going to  
make two new A's and they're going to be seen by 
69 pre-existing A's. So it's the two is going to  
get doubled 69 times. Wow. We're about we're going 
to have to add two to the 70 A's. And here we go.  
So, I have put these um we're now running 64 to 
a sheet and we have an additional 2 to the 70  
copies of A plus the 69 that were already here. 
How many do we have? Could we work it out? I've  
worked it out. Is that many? Look at that. It's 
a number with 22 digits. Oh, little confession.  
I didn't photocopy them all cuz if we wanted 
to have This is basically 10 to the 21. And  
if we wanted that many card A's at this scale, the 
amount of paper it would take would fill more than  
one entire shipping container with just paper. In 
fact, it would fill multiple shipping containers.  
It would fill enough shipping containers to 
fill 1 million shipping container tankers. Uh,  
that's a lot of paper. We'll talk more about 
outrageously big numbers in a moment. But just to  
complete this journey, we're going to keep going 
through B's. And each time we go through B's,  
we get a number of additional A's equal to 2 to 
the power of the number we have already + one.  
So our sequence is each next term in the sequence 
is the previous term plus 2 to the power of the  
previous term plus one. And we should do that 
well through all 32 of the new bees that showed  
up. And so the sequence goes five 69 that a lot 
and then a lot a lot a lot a lot. You get the  
idea. Now to deal with the elephantized number in 
the room. What does a 22digit number even mean?  
And a lot of people when I said a big number 
in a game might be thinking about the classic  
52 factorial because if you take a deck of 52 
cards, you give them a decent shuffle. There's 52  
factorial possible arrangements of this deck. But 
here's the thing about that number and the card  
number. We could write them down. I mean, I have 
written that one down. You could write down 52  
factorial. But the next step up of this, could you 
write that down? because it's going to h well in  
binary it'll have that many digits because that's 
the rate at which this is growing and in base 10  
we just divide it by it's about a third going from 
base 2 to base 10 so it would have a third of that  
many digits in base 10 the next one up and there's 
no way we can write that down the one after that  
absolutely not the number of atoms in the knowing 
universe we believe is about this many Now, um,  
I've made that number up. That's 81 random digits. 
It's about 10 to the 80. So, it could be this.  
The exact number it happens to be right now will 
look exactly like this. And anything above that,  
there aren't enough atoms in the universe, one 
per digit, to write them down. And this very  
quickly exceeds a power bigger than the number of 
atoms in the universe. So, the order of magnitude  
is just nuts. In fact, if you put this whole 
recursion thing, I mean, we tried it in Excel,  
that crashes real fast. We put it into Python, 
that's as far as it gets. We then use something  
called hypercal. And if you do continue the number 
of iterations, you can represent the number as  
this, a power tower that's 30 high. So, what we 
have here, a power tower. You start at the top,  
you work your way down. At the top, we have 10 ^ 
3.6 * 10 20. And we could write all those digits  
out. There's a lot. um if we could even work them 
out. And then the next one down. So you calculate  
each layer as you go down. There are 30 of these. 
As you go down each one, the next one has as many  
digits as the value of the one above. And it's 
nuts how fast you you run out of universe to  
write this in. Like this is just an insanely 
large but finite and very specific number. So,  
what's amazing about playing this in Magic the 
Gathering is that you are technically playing  
an exact number of Astral Dragons. And I reckon 
if you got that many, I mean, you might win this  
game. And you can argue it's not infinitely large. 
It's finite. And it's an exact an exact value.  
Now, this is a lot smaller than Graham's number. 
Graham's number is just it's like iterative power  
towers or power towers although it was just 
a threshold. It was just like an upper bound  
below which the value to the problem must exist. 
And even though this is vanishingly smaller for  
some definition of vanishing and smaller, it's an 
exact value that exactly solves this problem. So,  
in that regard, this could arguably be the biggest 
number that's ever actually been used by humans in  
this game. It just so happens that it's so big, 
we're unable to compute it. Oh, wait a minute.  
You remember rule 107.2. If you can't calculate a 
number, it equals zero. You can't calculate this  
number. It exists. It's it's exists as much as 
the number seven does. And compared to infinity,  
it's about as big as seven. But as humans, we 
can't compute that. So if you did ever play  
the shenanigans in an actual game, and there's 
only three cards, easy to achieve. We found them  
all. Like some of them are a little obscure, but 
these are all absolutely attainable cards. If you  
somehow contrived to play this in a game, depends 
if if the adjudicators will let you get away with  
this. If they insist you need to be able to 
calculate the integer value other than just  
proving the integer exists, you've now got zero 
dragons. And that's the smallest possible number  
of dragons. Now, if you've enjoyed following 
along with Oh, this ridiculous. My goodness,  
you might be the perfect person for what the 
sponsor of this video, Jane Street, has in store  
for us. Because speaking of shuffling things, 
they have a machine learning neural network  
puzzle which is going to be explained by exploded 
matt. If you're not familiar with Jane Street,  
they are a research-driven trading firm where 
curious people work on deep problems and they  
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They also have to build the infrastructure 
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that research. If you're at all interested in this 
kind of neural network research, Jane Street's  
machine learning team have put together a neural 
network puzzle. They trained a neural network with  
96 layers and then they shuffled them and you 
got to put them back in order. And you know,  
forget 52 factorial. To my naive understanding, 
this is like 96 factorial. That's not a hint. I  
mean, I had a look at it. I couldn't solve this. 
But some people watching the video probably can.  
If you do think you've solved it, please send 
your answer into Jane Street. I would love to  
see how many viewers of Standup Math videos can 
solve this neural network challenge. Anyone can  
do the puzzle. You don't have to care at all about 
a career in finance. But if you are curious about  
Jane Street and the work they do with machine 
learning, I will have a link below and there's  
like a QR code somewhere on the screen. You can 
check out their open roles and available programs.  
That's the video. Thank you so much for watching. 
I really appreciate it. I also want to thank  
Tabitha Grove who designed these phenomenal cards. 
And if you support me on Patreon, we're going to  
put some extra content up on there about how 
Tabitha designed uh these fantastical artworks.  
And uh big thanks to Matthew Franklin who is the 
viewer who wrote in and mentioned this ridiculous  
thing in Magic the Gathering. And if you know 
any other ridiculous maths things in games,  
gathering related or otherwise, please do let 
me know. And um yeah, we'll also link to the  
original Reddit post and whatnot um below. 
Uh that's it. That's the whole video. Um if  
you're wondering why the table's shaking slightly, 
Skyabad the dog has come through. Skye, over here,  
over here. Over here, and around. You got to say 
goodbye. Over Sky, here. And up. And goodbye.