Goldfish 6: The Desolation of Sardines

We returned to the evolving Goldfish Cube.

Worked scores

SI

This is the worked score for SI's score of 10↑↑↑↑3.334 in the Goldfish 6 Goldfish Draft tournament.

This score requires Knuth's up-arrow notation to calculate and write down, and makes use of the concept of super-logarithms to make suitable approximations during the calculation. Suffice to say, this is almost certainly the largest finite score ever achieved for any game in the entire history of humanity. See the page on Goldfish Scoring for more details on the mathematics involved.

As with all Goldfish scores, this may not be the best score achievable. If you find a better line of play resulting in a higher score, let us know!

Cards drafted

Worked score

Turn 1:
Forest
Fastbond
Forest, Plains, Island, 2×Mountain
Mirari's Wake
(15 life, 0 cards in hand, 6 land in play)

Turn 2:
Sphinx's Revelation, X=9
Forest, Plains, Island, 2×Mountain
Strionic Resonator
Ink-Treader Nephilim
Amoeboid Changeling
Howling Mine
(20 life (15+9-4), 0 cards in hand, 11 land in play)

Turn 3:
(22 mana) Precursor Golem
(17 mana) Regal Force (draw 6 cards)
(10 mana) Plains, 3× Mountain (now 17 life)
(18 mana) Rhox Faithmender
(14 mana) Stolen Identity, targetting Strionic Resonator, cipher onto Ink-Treader Nephilim

2× untapped Resonators total

(8 mana) Attack with Nephilim
(8 mana) cipher trigger on the stack
(8 mana) 2× copy cipher trigger, play Stolen Identity targetting Strionic Resonator (# of untapped Resonators constant)
(4 mana) Amoeboid Changeling gives Nephilim all creature types (including golem)
(4 mana) 2× copy cipher trigger. These and original trigger each target Nephilim

First cipher copy: Nephilim trigger and 1 golem trigger → 4× golems, 2× others
Second cipher copy: Nephilim trigger and 4 golem triggers → 128× golems, 4× others
Original cipher: Nephilim trigger and 128 golem triggers → 10^40.94 golems, 8× others
10^43.687 cards drawn in total from Regal Forces

play 16 lands (now 1 life)
Ajani Goldmane
+1 Ajani, gain 2*(2⁸)=512 life (doubling by Rhox Faithmenders)
Play 512 land
Library of Leng

(1 life, 10^43.687 cards in hand, 543 land in play, 4 Strionic Resontors, 10^40.94 of each golem)

Turn 4:
Attack with Nephilim, cipher triggers 539× copy cipher trigger, use to copy Resonator
Make Nephilim, Faithmender, and Regal Forces into golems with Amoeboid Changelings
(note: many of the copies could be made into golems, but the difference is lost in the rounding).

10^40.94 = 10↑↑2.2074
(using linear approximation of super-logarithm: log*(x) = slog(x); see Goldfish Scoring)
Each time makes 2^x golems, where x was the previous number of golems.
2^x = 10^xlog(2) = 10^{10(log(x) + log(2))}
≈ 10^10log(x) for log(x) >> log(2)
= 10^x
Therefore 2^(10↑↑x) ≈ 10^(10↑↑x) = 10↑↑(x + 1)

4× Resonators copying (plus original cipher) → 10↑↑7.2 golems

The copied Faithmenders and Regals are not golems. But the original cipher (i.e. last to resolve) will create as many Faithmenders/Regals as there were golems before that iteration. So:
10↑↑6.2 Rhox/Regal

The Regal Forces draw 10↑↑6.2 * 10↑↑7.2 ≈ 10↑↑7.2 cards, and the Faithmenders gain 2×2^{(10↑↑6.2)} ≈ 10↑↑7.2 life. More cards are drawn than life is gained, so it is possible to get back down to 1 life and sufficient cards will still be in hand for minor tasks after playing land.

+1 Ajani, gain 10↑↑7.2 life
Play 10↑↑7.2 land.

(1 life, lots of cards in hand, 10↑↑7.2 land in play, 543 Strionic Resonators, 10↑↑7.2 golems, and 10↑↑6.2 other creatuers)

Turn 5:
Attack with Nephilim, cipher triggers
10↑↑7.2× copy cipher trigger, use to copy Resonator, leaving 1086 mana spare.
Make Nephilim, Faithmender, and Regal into golems with Amoeboid Changelings
543× copy cipher trigger and resolve targetting Nephilim
10↑↑550.2 golems, 10↑↑549.2 others
+1 Ajani, gain 10↑↑550.2 life
Play 10↑↑550.2 land

(1 life, lots of cards in hand, 10↑↑7.2 land in play, 10↑↑7.2 Strionic Resonators, 10↑↑550.2 golems, and 10↑↑549.2 other creatuers)

Turn 6:
Attack with Nephilim, cipher triggers
10↑↑550.2× copy cipher trigger, use to copy Resonator, leaving 1086 mana spare.
Make Nephilim, Faithmender, and Regal into golems with Amoeboid Changelings
10↑↑7.2× copy cipher trigger and resolve targetting Nephilim
10↑↑(10↑↑7.2) golems, 10↑↑(10↑↑7.2) others (10↑↑(10↑↑7.2 - 1) ≈ 10↑↑(10↑↑7.2))
10↑↑(10↑↑7.2) land

Play Second Chance.

(1 life, lots of cards in hand, 10↑↑(10↑↑7.2) land in play, 10↑↑557.4 Strionic Resonators, 10↑↑(10↑↑7.2) golems, and 10↑↑(10↑↑7.2) other creatuers)

Turn 7:
Second Chance triggers in upkeep.
Copy trigger with 10↑↑557.4 Strionic Resonators for 10↑↑557.4 extra turns.
Play Second Sunrise, returning Second Chance to play.

Turns 8 to 10↑↑557.4:
Over every two turns:
10↑↑↑x mana → 10↑↑↑x Resonators
10↑↑↑x Resonators → 10↑↑(10↑↑↑x) = 10↑↑↑(x+1) new golems and mana.
Start with 10↑↑557.4 = 10↑↑(10↑↑1.439) = 10↑↑↑2.16 Resonators

After 10↑↑557.4/2 ≈ 10↑↑557.4 pairs of turns, have a total of
10↑↑↑(10↑↑↑2.16) Resonators

On the penultimate extra turn, reduce to 1 life (having stayed at at least 6 life until that point), to trigger Second Chance again on the final turn's upkeep. Copy the trigger with Resonators to gain:
10↑↑↑(10↑↑↑2.16) additional turns

Turns 10↑↑557.4 to 10↑↑↑(10↑↑↑2.16):
As above, finishing with a total of:
10↑↑↑(10↑↑↑(10↑↑↑2.16))
= 10↑↑↑↑(3 + log(2.16))
= 10↑↑↑↑3.334 mana

Convert the mana to points with Strength of the Tajuru + Fling.

Final score: 10↑↑↑↑3.334

mezzacotta | Comic Irregulars' Magic: The Gathering | Goldfish Draft

Last updated: Tuesday, 28 April, 2020; 00:30:32 PDT.
Original material copyright © 2015-2020, The Comic Irregulars. dmm@irregularwebcomic.net