So... Miirym + Astral Dragon + Parallel Lives... I need a maths wizard, please.
Asked by TypicalTimmy 1 year ago
I was messing around with my deck and it's newer interactions and brought out Astral Dragon. Miirym, Sentinel Wyrm made a token copy of it, but then Parallel Lives doubled that so I ended up with 3x Astral Dragons in play.
- Trigger time.
OG Astral Dragon, for shits and giggles, targets Parallel Lives and makes 2 token copies. But, the OG Parallel Lives sees these being produced and doubles them. So, I instead create 4 total token copies that are 3/3 Dragons with flying.
From here, the 1st of the two token copies of Astral Dragon also is directed to make 2 token copies of Parallel Lives. This time, I have a grand total of 5 Parallel Lives on the battlefield. So, we double 2 five separate times.
2 doubled into 4, 8, 16, 32 and lastly 64.
Now I have a grand total of 64 + 4 + 1 Parallel Lives on the battlefield, or 69 (Nice).
And you guessed it. 2nd Astral Dragon makes 2 token copies of Parallel Lives. Which now means I must double this, 69 times.
So, 2 doubled into .... uh.
Google says 1.1805916e+21.
Is... is that right? That can't be right.
Is that right??
1,180,591,600,000,000,000,000. One sextillion, one hundred and eighty quintillion, five hundred ninety one quadrillion, six hundred trillion. Some measure of rounding error, thanks to technological limitations I'm not going to work around.
The same number of seconds in thirty trillion years. The age of the universe, in seconds, two thousand times over.
The distance from here to the edge of the known universe, in 500-mile increments. The diameter of the Milky Way in yards/meters.
All the money on Earth converted to USD, one trillion times over.
You can dump all the oceans into that many 4" x 4" x 5" (10 cm x 10 cm x 12.5 cm) containers.
Exponential growth is fun.
For the sequencing, let's call the Parallel Lives in play PL(1) and the nontoken Astral Dragon AD(1) and count from there.
You cast AD(1), and Miirym, Sentinel Wurm creates a copy of it. PL(1) sees that token and turns it into twice as many. Let's call these two token copies AD(2) and AD(3). Miirym's job is done, since we'll be dealing with tokens going forward.
AD(1), the original nontoken Astral Dragon, copies PL(1), the original nontoken Parallel Lives. AD(2) and AD(3)'s triggered abilities are still on the stack. AD(1)'s ability resolves, and you create two times two, or four, Parallel Lives tokens. These will be PL(2), PL(3) PL(4) and PL(5).
AD(2)'s ability resolves from the stack, also targeting PL(1). PL(1) through PL(5) each make twice the number of tokens, from two from the original effect, to 4 from the effect of PL(1), to 8 from PL(2), to 16 from PL(3), to 32 from PL(4), to 64 from PL(5). These will be PL(6) to PL(69). So you're correct so far.
Finally, AD(3)'s ability resolves, also targeting PL(1). The original two copies are copied 69 times. One doubling effect creates 2^2 = 4 tokens, two doubling effects creates 2^3 = 8 tokens, three doubling effects would create 2^4 = 16 tokens, so 69 doubling effects would create 2^70 tokens. This does work out to your 1.1805916e+21 answer.
So yeah. Lotta tokens.
June 14, 2022 4:49 a.m.
Assuming you use standard-size M:tG cards for all of these copies, the stack would reach 38 light years into space, deep into interstellar distance. If you wanted to lay them flat, you could just about cover the surface of the sun.
I can't come up with a good comparison for the size of a big messy pile, but it's somewhere between the asteroid that killed the dinosaurs and the asteroid Ceres.
June 14, 2022 5:37 a.m.
its equitable to A whole lotta dead losers sitting at your table BAM I figured it out for you
June 16, 2022 3:58 p.m.
TypicalTimmy says... #5
Someone mentioned to me that Rakdos Charm says hello lmao
June 16, 2022 4:18 p.m.
Dragondeckbuilder says... #6
You're thinking way too small, if you stack the triggers differently, have the first astral dragon trigger happen first, you make 4 more parallel lives, totaling five. Now have miirym trigger, making a token of astral dragon, which thanks to the 5 parallel lives actually makes 2^5 or 32 astral dragons. Now all of those triggers go on the stack and after the first trigger you have your 69 parallel lives, except this time you still have 31 triggers to resolve. The second resolves and now you have your number plus 69 parallel lives, and a trigger after that nets you 2*2^(1.1805916e+21+69) + 1.1805916e+21 + 69, or an ungodly amount of dragons. I messed this up previously and so this quote of mine is quite off, and will actually be smaller than the true number, but it should still get the point across "By this third stack, there are now more parallel lives, which are dragons and can attack your opponents, then there are particles in the known universe. To put this in almost understandable terms, in order to have a token for each parallel lives you’d need 10^10^20.25 universes worth of particles. And that’s still only the third trigger out of 32 triggers"
September 13, 2022 2:45 p.m.
ZoDoneRightNow says... #7
The recursive function that models this question is: find f(32) given:
f(0) = 5
f(x) = f(x-1) + 2 ^ (f(x-1) + 1)
Explanation of the function:
f(0) = 5 because when the first Astral Dragon comes into play it makes 2 Parallel Lives which is doubled to 4. 4 + 1 = 5. We are looking for f(32) because 2^5 Astral Dragons are created by Miirym, Sentinel Wyrm because we have 5 PLs in play.
f(x) = f(x-1) + 2 ^ (f(x-1) + 1) because the number of Parallel Livess after each Astral Dragon enters = Number of existing Parallel Livess + number of new Parallel Livess (2 ^ (f(x-1) + 1)). The number of new Parallel Livess is (2 ^ (f(x-1) + 1)) because Astral Dragon creates 2 which is doubled a number of times = existing Parallel Livess
I plugged this function into Hypercalc, a calculator for very large numbers ()
The answer is 30 PT (3.553934904655 × 10^20)
Which means a power tower of 10s, 30 high with (3.553934904655 × 10^20) on top ie: 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^(3.553934904655 × 10^20)
TypicalTimmy says... #1
Also, what even is 1.1805916e+21? Like, I never made it that far in math. It's my worst subject. Only class I ever failed my entire educational career.
June 14, 2022 1:08 a.m.