Theory Strategies Explained

Guide written by spqcey originally. Contributions from everyone who has innovated new strategies and the Amazing Community.

Feel free to use the glossary as needed.

The theory sim (simulation) we currently recommend was originally made by XLII, now maintained by the sim team and can be accessed here.

Modulus Explanation #

A “%” can be seen in the table of some strategies. The “%” indicates modulus, which to simplify, is the remainder of a division.

So,

13 % 10 = 3

21 % 10 = 1

20 % 10 = 0

Because the modulus used is mod10, and we use a base 10 numbering system, we can look at the last digit of the level to easily find the result of the modulus.

So, 2145 % 10 = 5

List of Strategies #

Official Theories #

Theory 1: Recurrence Relations #

T1 is one of the theories that benefit the most from active strategies. T1SolarXLII xexxx improves slightly on T1Ratio.

T1SolarXLII xexxx — Very Active
T1Ratio — Active
T1C34 — Idle
T1C4 — Idle

Theory 2: Differential Calculus #

T2 is the only theory without an active strategy after all milestones are bought, despite attempts.

T2MC — Semi-Idle
T2MCAlt2 — Semi-Idle
T2MCAlt3 — Semi-Idle
T2MS — Active
T2QS — Semi-Idle
T2 — Idle

Theory 3: Linear Algebra #

T3 has the most variables of any theory and has benefitted the most from player-created strategies. T3Play2 is currently the best active strategy above e350 $ρ$ . T3ρ2C23d is an easier version being 10-15% slower.

T3SNAX is currently the best idle strategy above e200 $ρ$ . T3SNAX2 is similar to T3SNAX but is designed to be QoL compatible.

T3Play2 — Very Active
T3Play — Very Active
T3SNAX — Semi-Idle
T3SNAXdC12 — Active recovery, then Semi-Idle
T3SNAX2 — Active
T3ρ2C23d — Active
T3ρ2C23 — Idle
T3ρ2C23C33d — Active
T3ρ2C23C33 — Idle
T3NoC11C13C21C33d — Active
T3NoC11C13C21C33 — Idle
T3NoC13C33d — Active
T3NoC13C33 — Idle
T3NoC11C13C33d — Active
T3NoC11C13C33 — Idle
T3NoC13C32C33d — Active
T3NoC13C32C33 — Idle
T3C11C12C21d — Active
T3C11C12C21 — Idle

Theory 4: Polynomials #

T4 is the third-strongest theory in endgame, only behind T5 and T6.

T4C3d66 — Active
T4C3coast — Semi-Idle
T4C3 — Idle
T4C3dC12rcv — Active
T4C356dC12rcv — Active
T4C456dC12rcvMS — Active
T4C123d — Active
T4C123 — Idle
T4C12d — Active
T4C12 — Idle
T4C56 — Idle
T4C4 — Idle
T4C5 — Idle
T4 — Idle

Theory 5: Logistic Function #

T5 is the second-strongest theory in endgame, only behind T6.

T5AI — Active
T5Idle xexxx — Semi-Idle
T5 — Idle

Theory 6: Integral Calculus #

T6 is the most powerful theory in endgame, with several players reaching well over e1300𝜏 on their main save, some even over e1400𝜏.

T6AI — Active
T6SNAX x.xxexxx — Semi-Idle
T6NoC34d — Active
T6NoC34 — Idle
T6NoC1234d — Active
T6NoC1234 — Idle
T6NoC345d — Active
T6NoC345 — Idle
T6C4d — Active
T6C4 — Idle
T6C3d — Active
T6C3 — Idle

Theory 7: Numerical Methods #

T7 is the third-weakest theory in endgame, ahead of T2 and T8.

T7PlaySpqceyX — Active
T7C3d — Active
T7C12d — Active
T7C12 — Idle
T7C123d — Active
T7NoC12 — Idle
T7NoC123 — Idle
T7NoC124 — Idle
T7NoC1234 — Idle
T7 — Idle

Theory 8: Chaos Theory #

T8 is the weakest theory in endgame and has the most active strategy of any main theory (T8PlaySolarSwap).

T8PlaySolarSwap — VERY Active
T8Play — Active
T8SNAX — Semi-Idle
T8NoC35d — Active
T8NoC35 — Idle
T8NoC5d — Active
T8NoC5 — Idle
T8NoC3d — Active
T8NoC3 — Idle
T8d — Active
T8 — Idle

Official Custom Theories #

In chronological order of release. Read more about custom theories in the Custom Theory Guide.

Custom Theory 1: Weierstraß Sine Product #

The first official custom theory, abbreviated WSP, was created by xelaroc and released on January 15, 2022.

WSPdStopC1 — Active
WSPStopC1 — Semi-Idle
WSP — Idle

Custom Theory 2: Sequential Limits #

The second official custom theory, abbreviated SL, was created by ellipsis and released on January 22, 2022.

SLMS — Active
SLMSd — Very Active
SLStopAd — Active
SLStopA — Idle

Custom Theory 3: Euler’s Formula #

The third/fourth official custom theory, abbreviated EF, was first planned by Snaeky, coded by peanut, and balanced with help by XLII. It was released on May 4, 2022, in the same update as CSR2 and the $τ$ cap increase.

EFAI — Active
EFSNAX — Semi-Idle
EFd — Active
EF — Idle

Custom Theory 4: Convergents to √2 #

The third/fourth official custom theory, abbreviated CSR2 or CS2, was created by Solarion. It was released on May 4, 2022, in the same update as Euler’s Formula and the CT $τ$ cap increase from e100 to e150.

CSR2XL x.xx — VERY Active pre-e500 $ρ$ , Active post-e500 $ρ$
CSR2d — Active
CSR2 — Idle

Custom Theory 5: Fractional Integration #

The fifth/sixth official custom theory, abbreviated FI, was first planned by Snaeky, coded by Gen, and balanced with help by XLII. It was released on April 1, 2024, in the same update as Fractal Patterns and the CT $τ$ contribution rate increase by x4.

FId — Active
FI — Idle
FIMSd — Active
FIMS — Active
FIdPermaSwap — Active
FIPermaSwap — Semi-Idle
FIMSdPermaSwap — Active
FIMSPermaSwap — Active

Custom Theory 6: Fractal Patterns #

The fifth/sixth official custom theory, abbreviated FP, was created by XLII. It was released on April 1, 2024, in the same update as Fractional Integration and the CT $τ$ contribution rate increase by x4.

FPmodBurstC1MS — Active
FPdMS — Active
FP — Idle

Custom Theory 7: Riemann Zeta Function #

The seventh official custom theory, abbreviated RZ, was created by prop and released on December 15, 2024.

RZdBH — Active
RZBH — Idle
RZSpiralSwap — EXTREMELY Active
RZdMS — Active
RZMS — Semi-Idle
RZd — Active
RZ — Idle

Custom Theory 8: Magnetic Fields #

The 8th/9th official custom theory, abbreviated MF, was developed by Mathis. It was released on March 10, 2025 alongside BaP.

The strategies listed here are only variable buying strategies. For resets, please check the sim’s variable buy list (which contains resets highlighted) or the MF guide.

MFd2 — Very Active
MFd — Active
MF — Semi-Idle

Custom Theory 9: Basel Problem #

The 8th/9th official custom theory, abbreviated BaP, was developed by Python’s Koala. It was released on March 10, 2025 alongside MF.

BaPAI — Active
BaPAIMS — Active
BaPcoast — Semi-Idle
BaP — Idle

Theory 1: Recurrence Relations #

T1SolarXLII xexxx #

Class: strat; Caption: T1SolarXLII xexxx;

INVIS	Below xexxx $ρ$	Above xexxx $ρ$
$q_{1}$	When $q_{1}$ cost $\times (6 +$ lvl% $10) < q_{2}$ cost and $q_{1}$ cost $\times (15 +$ lvl% $10) < c_{4}$ cost and $ρ > 5 \times$ cost	REDX
$q_{2}$	when $ρ > 1.11 \times$ cost	REDX
$c_{1}$	See T1Ratio	REDX
$c_{2}$	See T1Ratio	REDX
$c_{3}$	See T1Ratio	REDX
$c_{4}$	CHECK	REDX

The “xexxx” is returned by the recommended theory simulator. For example, it could say:
T1SolarXLII 3e647.

This means to begin coasting at $3 e 647 ρ$ .

If you are confused about the “%”, read about it here.

Strategy Credits:

Solarion and XLII for creating and refining this strategy off of the existing T1AI.
rus9384#1864 for implementing coasting and a constant publication cycle for this strategy.

T1Ratio #

Class: strat; Caption: T1Ratio;


$q_{1}$	When $ρ > 10 \times$ cost
$q_{2}$	When $ρ > 1.11 \times$ cost
$c_{1}$	When $ρ > 10 \times c_{2}$ ratio $\times$ cost
$c_{2}$	When $ρ > c_{2}$ ratio $\times$ cost
$c_{3}$	When $ρ > c_{3}$ ratio $\times$ cost
$c_{4}$	CHECK

Do not buy $c_{1}$ or $c_{2}$ after e300 $ρ$ .

For the $c_{2}$ Ratio:

Ratio

For the $c_{3}$ Ratio:

Class: strat; Caption: $c_{3}$ Ratio;


$ρ < e 300$	1
$e 300 \leq ρ < e 450$	1.1
$e 450 \leq ρ < e 550$	2
$e 550 \leq ρ < e 655$	5
$ρ > e 655$	10

Strategy Credits:

XLII

T1C34 #

Class: strat; Caption: T1C34;


$q_{1}$	CHECK
$q_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	CHECK

T1C4 #

Class: strat; Caption: T1C4;


$q_{1}$	CHECK
$q_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	CHECK

Theory 2: Differential Calculus #

T2MC #

Class: strat_separated; Caption: T2MC;

Pub. Mult.*	$< 1150$	$1150 - 2250$	$2250 - 2900$	$2900 - 4650$	$> 4650$
$q_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$q_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$q_{3}$	CHECK	CHECK	REDX	REDX	REDX
$q_{4}$	CHECK	REDX	REDX	REDX	REDX
$r_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$r_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$r_{3}$	CHECK	CHECK	REDX	REDX	REDX
$r_{4}$	CHECK	REDX	REDX	REDX	REDX
					[FOOT;]* Publication Multiplier

Strategy Credits:

rus9384#1864
XLII, whose theory simulator was used to develop and test this strategy.

The “MC” in T2MC stands for MultivariableCoast.

T2MCAlt2 #

Class: strat_separated; Caption: T2MCAlt2;

Pub. Mult.*	$< 550$	$550 - 2050$	$2050 - 2700$	$2700 - 3500$	$> 3500$
$q_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$q_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$q_{3}$	CHECK	CHECK	REDX	REDX	REDX
$q_{4}$	CHECK	REDX	REDX	REDX	REDX
$r_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$r_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$r_{3}$	CHECK	CHECK	REDX	REDX	REDX
$r_{4}$	CHECK	REDX	REDX	REDX	REDX
					[FOOT;]* Publication Multiplier

Strategy Credits:

hotab (better multipliers for the strat)
rus9384#1864
XLII, whose theory simulator was used to develop and test this strategy.

The “MC” in T2MC stands for MultivariableCoast.

T2MCAlt3 #

Class: strat_separated; Caption: T2MCAlt3;

Pub. Mult.*	$< 750$	$750 - 1700$	$1700 - 2650$	$2650 - 3700$	$> 3700$
$q_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$q_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$q_{3}$	CHECK	CHECK	REDX	REDX	REDX
$q_{4}$	CHECK	REDX	REDX	REDX	REDX
$r_{1}$	CHECK	CHECK	CHECK	CHECK	REDX
$r_{2}$	CHECK	CHECK	CHECK	REDX	REDX
$r_{3}$	CHECK	CHECK	REDX	REDX	REDX
$r_{4}$	CHECK	REDX	REDX	REDX	REDX
					[FOOT;]* Publication Multiplier

Strategy Credits:

hotab (better multipliers for the strat)
rus9384#1864
XLII, whose theory simulator was used to develop and test this strategy.

The “MC” in T2MC stands for MultivariableCoast.

T2MS #

T2MS is the milestone swap strategy for T2, which can be found over here.

T2QS #

Class: strat; Caption: T2QS;


$q_{1}$	CHECK
$q_{2}$	CHECK
$q_{3}$	CHECK
$q_{4}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$r_{3}$	CHECK
$r_{4}$	CHECK

Start the publication with milestones in the 1→2→3→4 order.

When your publication multiplier reaches a certain point, switch your milestones to the 3→4→1→2 order.

The publication multiplier when you should switch is determined as follows, where $ρ$ is $ρ$ at the end of your last publication:

Class: strat; Caption: Publication Multiplier;


$ρ < e 75$	10
$e 75 \leq ρ < e 150$	200
$e 150 \leq ρ < e 200$	600
$e 200 \leq ρ < e 225$	100
$ρ > e 225$	25

T2 #

Class: strat; Caption: T2;


$q_{1}$	CHECK
$q_{2}$	CHECK
$q_{3}$	CHECK
$q_{4}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$r_{3}$	CHECK
$r_{4}$	CHECK

Theory 3: Linear Algebra #

T3Play2 #

Class: strat_separated; Caption: T3Play2;

INVIS	Before $e 1$ from recovered*	$e 1$ from recovered to $1.2$ Pub. Mult.	Pub. Mult $1.2 - 2.4$	Pub. Mult. $> 2.4$ **
$b_{1}$	When $\frac{1}{8}$ of $c_{31}$ cost	REDX	REDX	REDX
$b_{2}$	When $\frac{1}{5}$ of $c_{32}$ cost	When $\frac{1}{5}$ of $c_{32}$ cost	When $\frac{1}{8}$ of $c_{12}$ cost	CHECK
$b_{3}$	When $\frac{1}{8}$ of $c_{23}$ cost	When $\frac{1}{8}$ of $c_{23}$ cost	When $\frac{1}{8}$ of $c_{23}$ cost	CHECK
$c_{11}$	REDX	REDX	REDX	REDX
$c_{12}$	When $\frac{1}{100}$ of $c_{32}$ cost	When $\frac{1}{100}$ of $c_{32}$ cost	CHECK	CHECK
$c_{13}$	REDX	REDX	REDX	REDX
$c_{21}$	REDX	REDX	REDX	REDX
$c_{22}$	When $\frac{2}{5}$ of $c_{32}$ cost	When $\frac{2}{5}$ of $c_{32}$ cost	When $\frac{1}{8}$ of $c_{12}$ cost	REDX
$c_{23}$	CHECK	CHECK	CHECK	CHECK
$c_{31}$	CHECK	REDX	REDX	REDX
$c_{32}$	CHECK	CHECK	When $\frac{1}{8}$ of $c_{12}$ cost	REDX
$c_{33}$	When $\frac{1}{10}$ of $c_{23}$ cost	When $\frac{1}{10}$ of $c_{23}$ cost	REDX	REDX
				[FOOT;]* An earlier version of the strategy did not buy any $ρ_{1}$ variables. This is only around 1% slower than the strategy shown above, which does buy $c_{31}$ and $b_{1}$ in early parts of the strategy. It’s up to you whether you think that a 1% improvement is worth it or not.
				[FOOT;]** Coasting Phase

Strategy Credits:

Playspout for creating this strategy.
Solarion for $c_{12}$ overpush idea.
xelaroc, whose sim was used to verify Playspout’s results
rus9384#1864 for changing phase 3 start from pub mult 1 to pub mult 1.2, and changing phase 4 start from 2 to 2.4
XLII, whose sim was used by rus to test T3Play2 modifications, including the one stated above.

T3Play #

Class: strat_separated; Caption: T3Play;

Pub. Mult.*	$< 1$ (Recovery)	$1 - 2$	$> 2$ (Coasting)
$b_{1}$	When $\frac{1}{8}$ of $c_{31}$ cost	When $\frac{1}{8}$ of $c_{31}$ cost	REDX
$b_{2}$	When $\frac{2}{9}$ of $c_{12}$ cost and $\frac{4}{9}$ of $c_{22}$ cost	When $\frac{1}{4}$ of $c_{32}, c_{12}$ cost and $\frac{1}{2}$ of $c_{22}$ cost	CHECK
$b_{3}$	When $\frac{1}{8}$ of $c_{23}$ cost and $\frac{4}{9}$ of $c_{33}$ cost	When $\frac{1}{8}$ of $c_{23}$ cost and $\frac{1}{2}$ of $c_{33}$ cost	When $\frac{1}{8}$ of $c_{23}$ cost and $\frac{1}{2}$ of $c_{33}$ cost
$c_{11}$	REDX	REDX	REDX
$c_{12}$	CHECK	CHECK	CHECK
$c_{13}$	REDX	REDX	REDX
$c_{21}$	REDX	REDX	REDX
$c_{22}$	When $\frac{1}{2}$ of $c_{32}, c_{12}$ cost	When $\frac{1}{2}$ of $c_{32}, c_{12}$ cost	CHECK
$c_{23}$	CHECK	CHECK	CHECK
$c_{31}$	CHECK	CHECK	REDX
$c_{32}$	CHECK	CHECK	CHECK
$c_{33}$	When $\frac{9}{32}$ of $c_{23}$ cost	When $\frac{1}{4}$ of $c_{23}$ cost	When $\frac{1}{4}$ of $c_{23}$ cost
			[FOOT;]* Publication Multiplier

Strategy Credits:

Playspout for creating this strategy.
xelaroc, whose sim was used to verify Playspout’s results

T3SNAX #

Class: strat_separated; Caption: T3SNAX;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$b_{1}$	CHECK	REDX
$b_{2}$	CHECK	CHECK
$b_{3}$	CHECK	CHECK
$c_{11}$	REDX	REDX
$c_{12}$	CHECK	CHECK
$c_{13}$	REDX	REDX
$c_{21}$	REDX	REDX
$c_{22}$	CHECK	CHECK
$c_{23}$	CHECK	CHECK
$c_{31}$	CHECK	REDX
$c_{32}$	CHECK	REDX
$c_{33}$	CHECK	REDX

Strategy Credits:

Snaeky for the idea.
XLII for simulating the strategy

T3SNAXdC12 #

Class: strat_separated; Caption: T3SNAXdC12;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$b_{1}$	CHECK	REDX
$b_{2}$	CHECK	CHECK
$b_{3}$	CHECK	CHECK
$c_{11}$	REDX	REDX
$c_{12}$	When cost $\times 100 < c_{32}$ cost	CHECK
$c_{13}$	REDX	REDX
$c_{21}$	REDX	REDX
$c_{22}$	CHECK	CHECK
$c_{23}$	CHECK	CHECK
$c_{31}$	CHECK	REDX
$c_{32}$	CHECK	REDX
$c_{33}$	CHECK	REDX

Strategy Credits:

Snaeky for the idea.
XLII for simulating the strategy and finding optimal ratios.

T3SNAX2 #

Class: strat_separated; Caption: T3SNAX2;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$b_{1}$	When cost is $\frac{1}{10}$ of $ρ_{1}$	REDX
$b_{2}$	When cost is $\frac{1}{3}$ of $ρ_{2}$	When cost is $\frac{1}{3}$ of $ρ_{2}$
$b_{3}$	When cost is $\frac{1}{5}$ of $ρ_{3}$	When cost is $\frac{1}{5}$ of $ρ_{3}$
$c_{11}$	REDX	REDX
$c_{12}$	When cost is $\frac{1}{100}$ of $ρ_{2}$	CHECK
$c_{13}$	REDX	REDX
$c_{21}$	REDX	REDX
$c_{22}$	CHECK	When cost is $\frac{1}{8}$ of $ρ_{2}$
$c_{23}$	CHECK	CHECK
$c_{31}$	CHECK	REDX
$c_{32}$	CHECK	REDX
$c_{33}$	When cost is $\frac{1}{100}$ of $ρ_{3}$	REDX

Strategy Credits:

Snaeky for the idea.
XLII for simulating the strategy and finding optimal ratios.

It is designed to be an easier version of current T3 strategies.

This is the only active SNAX strategy.

T3ρ2C23d #

Class: strat; Caption: T3ρ2C23d;


$b_{1}$	REDX
$b_{2}$	When cost is $\frac{1}{3}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{9}$ of $c_{23}$ cost
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	REDX
$c_{32}$	CHECK
$c_{33}$	REDX

T3ρ2C23 #

Class: strat; Caption: T3ρ2C23;


$b_{1}$	REDX
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	REDX
$c_{32}$	CHECK
$c_{33}$	REDX

T3ρ2C23C33d #

Class: strat; Caption: T3ρ2C23C33d;


$b_{1}$	REDX
$b_{2}$	When cost is $\frac{1}{3}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{9}$ of $c_{23}$ cost
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	REDX
$c_{32}$	CHECK
$c_{33}$	CHECK

T3ρ2C23C33 #

Class: strat; Caption: T3ρ2C23C33;


$b_{1}$	REDX
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	REDX
$c_{32}$	CHECK
$c_{33}$	CHECK

T3NoC11C13C21C33d #

Class: strat; Caption: T3NoC11C13C21C33d;


$b_{1}$	When cost is $\frac{1}{8}$ of $c_{31}$ cost
$b_{2}$	When cost is $\frac{1}{5}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{8}$ of $c_{23}$ cost
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC11C13C21C33 #

Class: strat; Caption: T3NoC11C13C21C33;


$b_{1}$	CHECK
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	REDX
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC13C33d #

Class: strat; Caption: T3NoC13C33d;


$b_{1}$	When cost is $\frac{1}{10}$ of $min (c_{21}, c_{31})$ cost
$b_{2}$	When cost is $\frac{1}{4}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{10}$ of $c_{23}$ cost
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC13C33 #

Class: strat; Caption: T3NoC13C33;


$b_{1}$	CHECK
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC11C13C33d #

Class: strat; Caption: T3NoC11C13C33d;


$b_{1}$	When cost is $\frac{1}{10}$ of $min (c_{21}, c_{31})$ cost
$b_{2}$	When cost is $\frac{1}{4}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{10}$ of $c_{23}$ cost
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC11C13C33 #

Class: strat; Caption: T3NoC11C13C33;


$b_{1}$	CHECK
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	REDX
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	CHECK
$c_{33}$	REDX

T3NoC13C32C33d #

Class: strat; Caption: T3NoC13C32C33d;


$b_{1}$	When cost is $\frac{1}{8}$ of $min (c_{11}, c_{21}, c_{31})$ cost
$b_{2}$	When cost is $\frac{1}{5}$ of $min (c_{12}, c_{22}, c_{32})$ cost
$b_{3}$	When cost is $\frac{1}{8}$ of $c_{23}$ cost
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	REDX
$c_{33}$	REDX

T3NoC13C32C33 #

Class: strat; Caption: T3NoC13C32C33;


$b_{1}$	CHECK
$b_{2}$	CHECK
$b_{3}$	CHECK
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	CHECK
$c_{23}$	CHECK
$c_{31}$	CHECK
$c_{32}$	REDX
$c_{33}$	REDX

T3C11C12C21d #

Class: strat; Caption: T3C11C12C21d;


$b_{1}$	When cost is $\frac{1}{7}$ of $min (c_{11}, c_{21})$ cost
$b_{2}$	When cost is $\frac{1}{5}$ of $c_{12}$ cost
$b_{3}$	REDX
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	REDX
$c_{23}$	REDX
$c_{31}$	REDX
$c_{32}$	REDX
$c_{33}$	REDX

T3C11C12C21 #

Class: strat; Caption: T3C11C12C21;


$b_{1}$	CHECK
$b_{2}$	CHECK
$b_{3}$	REDX
$c_{11}$	CHECK
$c_{12}$	CHECK
$c_{13}$	REDX
$c_{21}$	CHECK
$c_{22}$	REDX
$c_{23}$	REDX
$c_{31}$	REDX
$c_{32}$	REDX
$c_{33}$	REDX

Theory 4: Polynomials #

T4C3d66 #

Class: strat_separated; Caption: T4C3d66;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$c_{1}$	REDX	REDX
$c_{2}$	REDX	REDX
$c_{3}$	CHECK	CHECK
$c_{4}$	REDX	REDX
$c_{5}$	REDX	REDX
$c_{6}$	REDX	REDX
$q_{1}$	When cost $\times (10 +$ lvl% $10) <$ $min (q_{2}, c_{3})$ cost	When cost $\times (10 +$ lvl% $10) <$ $min (q_{2}, c_{3})$ cost
$q_{2}$	CHECK	When cost is $\frac{2}{3}$ of $c_{3}$ cost

When the theory simulator recommends this strategy, it will show something like: T4C3d66 $q_{1}$ : 377 $q_{2}$ : 252”.

The levels it shows after $q_{1}$ and $q_{2}$ are the last levels you should buy them in this publication.

If you are confused about the “%”, read about it here.

The “66” in the name T4C3d66 refers to the ⅔ ratio $q_{2}$ is bought at relative to $c_{3}$ .

Strategy Credits:

XLII
rus9384#1864

T4C3coast #

Class: strat; Caption: T4C3coast;


$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	CHECK
$q_{2}$	CHECK

When the theory simulator recommends this strategy, it will show something like: T4C3coast $q_{1}$ : 377 $q_{2}$ : 252”.

The levels it shows after $q_{1}$ and $q_{2}$ are the last levels you should buy them to in this publication.

T4C3 #

Class: strat; Caption: T4C3;


$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	CHECK
$q_{2}$	CHECK

T4C3dC12rcv #

Class: strat_separated; Caption: T4C3dC12rcv;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost	REDX
$c_{2}$	CHECK	REDX
$c_{3}$	CHECK	CHECK
$c_{4}$	REDX	REDX
$c_{5}$	REDX	REDX
$c_{6}$	REDX	REDX
$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK	CHECK

T4C356dC12rcv #

Class: strat_separated; Caption: T4C356dC12rcv;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost	REDX
$c_{2}$	CHECK	REDX
$c_{3}$	CHECK	CHECK
$c_{4}$	REDX	REDX
$c_{5}$	CHECK	CHECK
$c_{6}$	CHECK	CHECK
$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK	CHECK

T4C456dC12rcvMS #

Class: strat_separated; Caption: T4C456dC12rcvMS;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost	REDX
$c_{2}$	CHECK	REDX
$c_{3}$	REDX	REDX
$c_{4}$	CHECK	CHECK
$c_{5}$	CHECK	CHECK
$c_{6}$	CHECK	CHECK
$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK	CHECK

Milestone swapping strategy

During your recovery phase, set your milestones in the order 2→3→1
During the $τ$ gain phase, alternate between 1 minute with milestones in the order 1→3→2 and 1 minute with milestones in the order 3→1→2

T4C123d #

Class: strat; Caption: T4C123d;


$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK

This strategy is typically seen at lower $ρ$ and is eventually outpaced by T4C3d66.

T4C123 #

Class: strat; Caption: T4C123;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	CHECK
$q_{2}$	CHECK

This strategy is typically seen at lower $ρ$ and is eventually outpaced by T4C3.

T4C12d #

Class: strat; Caption: T4C12d;


$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	REDX
$q_{2}$	REDX

T4C12 #

Class: strat; Caption: T4C12;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	REDX
$q_{2}$	REDX

T4C56 #

Class: strat; Caption: T4C56;


$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK
$c_{6}$	CHECK
$q_{1}$	CHECK
$q_{2}$	CHECK

T4C4 #

Class: strat; Caption: T4C4;


$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	REDX
$c_{6}$	REDX
$q_{1}$	CHECK
$q_{2}$	CHECK

T4C5 #

Class: strat; Caption: T4C5;


$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK
$c_{6}$	REDX
$q_{1}$	CHECK
$q_{2}$	CHECK

T4 #

Class: strat; Caption: T4;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK
$q_{1}$	CHECK
$q_{2}$	CHECK

Theory 5: Logistic Function #

T5AI #

This active strategy does not work well with this method of showing theory strategies. Please visit this guide page to learn how to perform T5AI.

T5Idle xexxx #

Class: strat_separated; Caption: T5Idle xexxx;

INVIS	Before xexxx $ρ$	After xexxx $ρ$
$q_{1}$	CHECK	CHECK
$q_{2}$	CHECK	CHECK
$c_{1}$	CHECK	REDX
$c_{2}$	CHECK	CHECK
$c_{3}$	CHECK	CHECK

IMPORTANT: Do active $c_{2}$ buying (buying $c_{2}$ when $q$ isn’t increasing, and x10 for the first few seconds of the publication) for the first few minutes of the publication.

The “xexxx” is returned by the theory simulator. For example, it could say:
T1Idle 3e647.

This means to start coasting at $3 e 647 ρ$ .

Strategy Credit:

XLII

T5 #

Class: strat; Caption: T5;


$q_{1}$	CHECK
$q_{2}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK

Theory 6: Integral Calculus #

T6AI #

Class: strat; Caption: T6AI;


$q_{1}$	When cost $\times (7 +$ lvl% $10) <$ $min (q_{2}, r_{2}, c_{5})$ cost
$q_{2}$	CHECK
$r_{1}$	When cost $\times (5 +$ lvl% $10) <$ $min (q_{2}, r_{2}, c_{5})$ cost
$r_{2}$	CHECK
$c_{1}$	When cost $\times (7 +$ lvl% $10) < c_{2}$ cost
$c_{2}$	As the publication progresses, buy less $c_{2}$ (and $c_{1}$ ).
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK

If you are confused about the “%”, read about it here.

How does $c_{2}$ purchasing works exactly?

In the sim, the ratio at which $c_{2}$ is bought to $min (q_{2}$ , $r_{2}$ , $c_{5})$ is defined as the term ratio between the $c_{5}$ term and the ${c_{1}}^{1.15} c_{2}$ term, which equates to $c_{5} r / {c_{1}}^{1.15} c_{2}$ . If this ratio is 2, then the sim will buy $c_{2}$ when 2 times cheaper than $min (q_{2}$ , $r_{2}$ , $c_{5})$ .

T6SNAX x.xxexxx #

Class: strat_separated; Caption: T6SNAX x.xxexxx;

INVIS	Before x.xxexxx $ρ$	After x.xxexxx $ρ$
$q_{1}$	CHECK	CHECK
$q_{2}$	CHECK	CHECK
$r_{1}$	CHECK	CHECK
$r_{2}$	CHECK	CHECK
$c_{1}$	CHECK	REDX
$c_{2}$	CHECK	REDX
$c_{3}$	REDX	REDX
$c_{4}$	REDX	REDX
$c_{5}$	CHECK	CHECK

The “x.xxexxx” is returned by the recommended theory simulator. For example, it could say:
T6SNAX 4.52e760.

This means to start coasting at $4.52 e 760 ρ$ .

Strategy Credits:

Snaeky
XLII

T6NoC34d #

Class: strat; Caption: T6NoC34d;


$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK
$r_{1}$	When cost is $\frac{1}{10}$ of $r_{2}$ cost
$r_{2}$	CHECK
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK

T6NoC34 #

Class: strat; Caption: T6NoC34;


$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK

T6NoC1234d #

Class: strat; Caption: T6NoC1234d;


$q_{1}$	When cost $\times (7 +$ lvl% $10) <$ $min (q_{2}, r_{2}, c_{5})$ cost
$q_{2}$	CHECK
$r_{1}$	When $5 \times$ cost $<$ $min (q_{2}, r_{2}, c_{5})$ cost
$r_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK

Note: If you need to, you can idle recovery by autobuying $q_{1}$ and $r_{1}$ until the theory has passed its previous publication point. This will reduce your rates by only ~1% relative to buying $q_{1}$ and $r_{1}$ at e1 ratio the entire publication.

T6NoC1234 #

Class: strat; Caption: T6NoC1234;


$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK

T6NoC345d #

Class: strat; Caption: T6NoC34d;


$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK
$r_{1}$	When cost is $\frac{1}{10}$ of $r_{2}$ cost
$r_{2}$	CHECK
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX

This strategy is sometimes seen at lower $τ$ ’s but not at higher $τ$ ’s.

T6NoC345 #

Class: strat; Caption: T6NoC345;


$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX

This strategy is sometimes seen at lower $τ$ ’s but not at higher $τ$ ’s.

T6C4d #

Class: strat; Caption: T6C4d;


$q_{1}$	When cost is $\frac{1}{5}$ of $min (q_{2}, r_{2}, c_{4})$ cost
$q_{2}$	CHECK
$r_{1}$	When cost is $\frac{1}{5}$ of $min (q_{2}, r_{2}, c_{4})$ cost
$r_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	REDX

T6C4 #

Class: strat; Caption: T6C4;


$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$r_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	REDX

T6C3d #

Class: strat; Caption: T6C3d;


$q_{1}$	When cost is $\frac{1}{5}$ of $min (q_{2}, c_{3})$ cost
$q_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX

Both T6C3d and T6C3 don’t have $r_{1}$ or $r_{2}$ listed because the two strategies only appear on the sim below the milestones that give $r_{1}$ and $r_{2}$ .

T6C3 #

Class: strat; Caption: T6C3;


$q_{1}$	CHECK
$q_{2}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX

Both T6C3d and T6C3 don’t have $r_{1}$ or $r_{2}$ listed because the two strategies only appear on the sim below the milestones that give $r_{1}$ and $r_{2}$ .

Theory 7: Numerical Methods #

T7PlaySpqceyX #

If there is no number after T7PlaySpqcey, then use this table:

Class: strat; Caption: T7PlaySpqcey;


$q_{1}$	When cost is $\frac{1}{4}$ of $c_{6}$ cost
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	When cost is $\frac{1}{10}$ of $c_{6}$ cost
$c_{4}$	When cost is $\frac{1}{10}$ of $c_{6}$ cost
$c_{5}$	When cost is $\frac{1}{4}$ of $c_{6}$ cost
$c_{6}$	CHECK

If there is a number after T7PlaySpqcey (Example: T7PlaySpqcey10 or T7PlaySpqcey100), then use this table:

Class: strat; Caption: T7PlaySpqceyX;


$q_{1}$	When cost is $\frac{1}{4}$ of $c_{6}$ cost
$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	When X times cheaper than $c_{6}$ cost
$c_{3}$	When cost is $\frac{1}{10}$ of $c_{6}$ cost
$c_{4}$	When cost is $\frac{1}{10}$ of $c_{6}$ cost
$c_{5}$	When cost is $\frac{1}{4}$ of $c_{6}$ cost
$c_{6}$	CHECK

While the “X” is only directly in the $c_{2}$ buying condition, because the $c_{1}$ buying condition is based on the cost of $c_{2}$ , the “X” also indirectly affects how much $c_{1}$ is bought.

Regardless of the “X” value, the $c_{1}$ buying condition remains “When cost is $\frac{1}{10}$ of $c_{2}$ cost”

The number after T7PlaySpqcey occurs more at lower $τ$ values.

If you are confused about the “%”, read about it here.

Strategy Credits:

Playspout for $q_{1}$ , $c_{4}$ , $c_{5}$ , $c_{6}$ buying strategy
spqcey for the addition of $c_{3}$
Snaeky for number after T7PlaySpqcey for if $c_{2}$ and $c_{1}$ are bought, and if so, what ratio
XLII for simulating Snaeky’s idea

T7C3d #

Class: strat; Caption: T7C3d;


$q_{1}$	When cost is $\frac{1}{10}$ of $c_{3}$ cost
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX

T7C12d #

Class: strat; Caption: T7C12d;


$q_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{1}$	When cost is $\frac{1}{8}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX

T7C12 #

Class: strat; Caption: T7C12;


$q_{1}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX

T7C123d #

Class: strat; Caption: T7C123d;


$q_{1}$	When cost is $\frac{1}{10}$ of $min (c_{2}, c_{3})$ cost
$c_{1}$	When cost is $\frac{1}{8}$ of $min (c_{2}, c_{3})$ cost
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	REDX
$c_{6}$	REDX

T7NoC12 #

Class: strat; Caption: T7NoC12;


$q_{1}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK

T7NoC123 #

Class: strat; Caption: T7NoC123;


$q_{1}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK

T7NoC124 #

Class: strat; Caption: T7NoC124;


$q_{1}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	CHECK
$c_{4}$	REDX
$c_{5}$	CHECK
$c_{6}$	CHECK

T7NoC1234 #

Class: strat; Caption: T7NoC1234;


$q_{1}$	CHECK
$c_{1}$	REDX
$c_{2}$	REDX
$c_{3}$	REDX
$c_{4}$	REDX
$c_{5}$	CHECK
$c_{6}$	CHECK

T7 #

Class: strat; Caption: T7;


$q_{1}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK

Theory 8: Chaos Theory #

T8PlaySolarSwap #

Class: strat; Caption: T8PlaySolarSwap;


$c_{1}$	When cost $\times (5 +$ lvl% $10) <$ $min (c_{2}, c_{4})$ cost
$c_{2}$	CHECK
$c_{3}$	When cost is $\frac{2}{5}$ of $min (c_{2}, c_{4})$ cost
$c_{4}$	CHECK
$c_{5}$	When cost is $\frac{2}{5}$ of $min (c_{2}, c_{4})$ cost

Milestone Swap:

Every 34 seconds, remove one level from the first milestone then immediately add the level back.

If you are confused about the “%”, read about it here.

Strategy Credits:

Playspout for the variable buying strategy
Solarion for the milestone swap idea

T8Play #

Class: strat; Caption: T8Play;


$c_{1}$	When cost is $\frac{1}{8}$ of $min (c_{2}, c_{4})$ cost
$c_{2}$	CHECK
$c_{3}$	When cost is $\frac{2}{5}$ of $min (c_{2}, c_{4})$ cost
$c_{4}$	CHECK
$c_{5}$	When cost is $\frac{1}{4}$ of $min (c_{2}, c_{4})$ cost

Strategy Credits:

Playspout

T8SNAX #

Class: strat_separated; Caption: T8SNAX;

Pub. Mult.*	$< 1.6$	$1.6 - 2.3$	$> 2.3$
$c_{1}$	CHECK	REDX	REDX
$c_{2}$	CHECK	CHECK	CHECK
$c_{3}$	CHECK	CHECK	REDX
$c_{4}$	CHECK	CHECK	CHECK
$c_{5}$	CHECK	CHECK	REDX
			[FOOT;]* Publication Multiplier

Strategy Credits:

Snaeky
XLII

T8NoC35d #

Class: strat; Caption: T8NoC35d;


$c_{1}$	When cost is $\frac{1}{10}$ of $min (c_{2}, c_{4})$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	REDX

If you are confused about the “%”, read about it here.

T8NoC35 #

Class: strat; Caption: T8NoC35;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	REDX

T8NoC5d #

Class: strat; Caption: T8NoC5d;


$c_{1}$	When cost is $\frac{1}{10}$ of $min (c_{2}, c_{4})$ cost
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	REDX

T8NoC5 #

Class: strat; Caption: T8NoC5;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	REDX

T8NoC3d #

Class: strat; Caption: T8NoC3d;


$c_{1}$	When cost is $\frac{1}{10}$ of $min (c_{2}, c_{4})$ cost
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	CHECK

T8NoC3 #

Class: strat; Caption: T8NoC3;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	REDX
$c_{4}$	CHECK
$c_{5}$	CHECK

T8d #

Class: strat; Caption: T8d;


$c_{1}$	When cost is $\frac{1}{10}$ of $c_{2}$ cost
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK

T8 #

Class: strat; Caption: T8;


$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK

Weierstraß Sine Product #

WSPdStopC1 #

Class: strat_separated; Caption: WSPdStopC1;

INVIS	First 15sec of Publication	Rest of Publication
$q_{1}$	When cost $\times (8 +$ lvl% $10) <$ $min (q_{2}, n, c_{2})$ cost	When cost $\times (8 +$ lvl% $10) <$ $min (q_{2}, n, c_{2})$ cost
$q_{2}$	CHECK	CHECK
$n$	CHECK	CHECK
$c_{1}$	CHECK	When cost is Ratio* of $min (q_{2}, n, c_{2})$ cost
$c_{2}$	CHECK	CHECK

If you are confused about the “%”, read about it here.

* The “Ratio” stated in $c_{1}$ is determined as follows, where $ρ$ is $ρ$ at the end of your last publication:

Class: strat; Caption: $c_{1}$ Ratio;


$ρ < e 25$	1
$e 25 \leq ρ < e 40$	$\frac{1}{3}$
$e 40 \leq ρ < e 200$	$\frac{1}{10}$
$e 200 \leq ρ < e 400$	$\frac{1}{50}$
$e 400 \leq ρ < e 700$	$\frac{1}{1, 000}$
$ρ > e 700$	Do not buy $c_{1}$ after 15sec into publication

Strategy Credits:

xelaroc for testing/creating the strategy
Snaeky for the stop $c_{1}$ idea
XLII for some modifications including adding modulus and $c_{1}$ changes

WSPStopC1 #

Class: strat_separated; Caption: WSPStopC1;

INVIS	First 15sec of Publication	Rest of Publication
$q_{1}$	CHECK	CHECK
$q_{2}$	CHECK	CHECK
$n$	CHECK	CHECK
$c_{1}$	CHECK	If $ρ < e 450$ , ✔️ If $ρ > e 450$ ,❌
$c_{2}$	CHECK	CHECK

Strategy Credits:

xelaroc for simulating it/adding it to the sim
Snaeky for the stop $c_{1}$ idea
XLII for $c_{1}$ modification

WSP #

Class: strat; Caption: WSP;


$q_{1}$	CHECK
$q_{2}$	CHECK
$n$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK

Sequential Limits #

SLMS #

Milestone Swap

The milestone state will be described with four numbers. These describe the priority of the milestone. For example, 4→3→1→2 means you should prioritize buying fourth milestone levels first, then after the fourth milestone is maxed, then you buy third milestone levels, and then first milestone, then second milestone.

There are 3 milestone states:

State 1: 4→3→1→2 (prioritizes boost for the $e - γ$ term)

State 2: 2→1→4→3 (prioritizes boost for ${\dot{ρ}}_{2}$ )

State 3: 1→2→4→3 (prioritizes boost for instantaneous $ρ$ gain, aka $ρ_{2}$ exponent)

This strategy swaps milestones depending on how far away the next $b_{1}$ or $b_{2}$ upgrade is.

The goal of this strategy is:

Buy $b_{1}$ / $b_{2}$
Swap milestones into State 1 to fully utilize the boost from the new $b_{1}$ / $b_{2}$ upgrade.
After some time (the exact amount of time will be described later in the strategy), we want to swap to State 2. This way we boost ${\dot{ρ}}_{2}$ so we get more $ρ_{2}$ quicker.
When we are closer to the next $b_{1}$ / $b_{2}$ upgrade, swap to State 3 so we utilize the boost that we just got for $ρ_{2}$ . This will get us to the next $b_{1}$ / $b_{2}$ upgrade a lot quicker.
Repeat.

This may seem difficult to execute, but publications in SL are 1 to 1.5 hours long after e50 $ρ$ -e300 $ρ$ . This means there can be up to 5-10 minute gaps between $b_{1}$ / $b_{2}$ upgrades later in the publication. You will also get used to the swapping ratios and duration quickly because of the consistent publication lengths. At the very end of publications, you will also not have to milestone swap, as we will use State 3 only, to get the last $ρ$ boost before publishing.

As long as $ρ$ < e175, we will swap between the three states, after that its just the first two states.

Note: NEVER swap into State 2 after 4.5 publication multiplier. Do State 3 instead for that time.

The ratios for swapping are as follows, where you enter the next state when the ratio: $\frac{m i n (b_{1} c o s t, b_{2} c o s t)}{ρ}$ is lower than the ratio provided under the header:

Class: strat_separated; Caption: Ratios for SLMS Swapping;

INVIS	State 1	State 2	State 3
$e 25 \leq ρ < e 50$	Until 5x $\frac{cost}{ρ}$	Until 4x $\frac{cost}{ρ}$	Until upgrade is bought
$e 50 \leq ρ < e 75$	Until 7x $\frac{cost}{ρ}$	Until 6x $\frac{cost}{ρ}$	Until upgrade is bought
$e 75 \leq ρ < e 100$	Until 12x $\frac{cost}{ρ}$	Until 10x $\frac{cost}{ρ}$	Until upgrade is bought
$e 100 \leq ρ < e 150$	Until 20x $\frac{cost}{ρ}$	Until 15x $\frac{cost}{ρ}$	Until upgrade is bought
$e 150 \leq ρ < e 175$	Until 8x $\frac{cost}{ρ}$	Until 6x $\frac{cost}{ρ}$	Until upgrade is bought
$e 175 \leq ρ < e 200$	Until 1.5x $\frac{cost}{ρ}$	Until upgrade is bought	Skip
$e 200 \leq ρ < e 275$	Until 3x $\frac{cost}{ρ}$	Skip	Until upgrade is bought
$e 275 \leq ρ < e 300$	Until 2x $\frac{cost}{ρ}$	Skip	Until upgrade is bought
			[FOOT;]cost in the table refers to $min (b_{1}, b_{2})$ cost.

This may seem confusing, but let’s take the first row as an example.

In the first phase, $e 25 ρ - e 50 ρ$ , you should have your milestones in State 1 until $ρ$ is $\frac{1}{5}$ of min( $b_{1}$ cost, $b_{2}$ cost).

Then, swap to State 2 until $ρ$ is 1/4 of min( $b_{1}$ cost, $b_{2}$ cost).

After that, swap to State 3 until you get the upgrade.

Note: You do not have to follow those ratios exactly. It does not make much difference if you do it slightly differently.

The numbers are just important to give the idea for around where you want to swap.

e.g. in e200 $ρ$ + range, you only want to swap when close to next $b_{1}$ / $b_{2}$ . and e75-e150 $ρ$ you swap very early.

These numbers also tell you that you never want to be in State 2 for a long time.

Variable Buying

Class: strat_separated; Caption: SLMS;

Pub. Mult.*	$< 4$	$4 - 7.5$	$> 7.5$
$a_{1}$	CHECK	REDX	REDX
$a_{2}$	CHECK	REDX	REDX
$b_{1}$	CHECK	CHECK	REDX
$b_{2}$	CHECK	CHECK	REDX
			[FOOT;]* Publication Multiplier

Strategy Credit:

XLII

SLMSd #

For the milestone swapping details, read the above strategy, SLMS. This strategy only modifies the variable buying strategies.

Class: strat_separated; Caption: SLMSd;

Pub. Mult.*	$< 4$	$4 - 7.5$	$> 7.5$
$a_{1}$	If lvl% $3 = 0$ , then ✔️. If not, buy when cost $\times 2 \times ($ lvl% $3) < a_{2}$ cost.	REDX	REDX
$a_{2}$	CHECK	REDX	REDX
$b_{1}$	If lvl% $4 = 0$ or $1$ , then ✔️. If not, buy when cost $\times ($ lvl% $4) < b_{2}$ cost.	If lvl% $4 = 0$ or $1$ , then ✔️. If not, buy when cost $\times ($ lvl% $4) < b_{2}$ cost.	REDX
$b_{2}$	CHECK	CHECK	REDX
			[FOOT;]* Publication Multiplier

If you are confused about the “%”, read about it here.

Strategy Credit:

XLII

SLStopAd #

Class: strat_separated; Caption: SLStopAd;

Pub. Mult.*	$< 4.5$	$4.5 - 6$	$> 6$
$a_{1}$	If lvl% $3 = 0$ , then ✔️. If not, buy when cost $\times 2 \times ($ lvl% $3) < a_{2}$ cost.	REDX	REDX
$a_{2}$	CHECK	REDX	REDX
$b_{1}$	If lvl% $4 = 0$ or $1$ , then ✔️. If not, buy when cost $\times ($ lvl% $4) < b_{2}$ cost.	If lvl% $4 = 0$ or $1$ , then ✔️. If not, buy when cost $\times ($ lvl% $4) < b_{2}$ cost.	REDX
$b_{2}$	CHECK	CHECK	REDX
			[FOOT;]* Publication Multiplier

If you are confused about the “%”, read about it here.

The boost from doublings ( $a_{1}$ to $a_{2}$ , $b_{1}$ to $b_{2}$ ) is rarely enough to justify choosing this strategy over the idle strategy SLStopA.

Strategy Credits:

xelaroc
Playspout
rus9384#1864 for $b_{1}$ , $b_{2}$ coasting at 6 publication multiplier
XLII for buying ratios change and integration of modulus

SLStopA #

Class: strat_separated; Caption: SLStopA;

Pub. Mult.*	$< 4.5$	$4.5 - 6$	$> 6$
$a_{1}$	CHECK	REDX	REDX
$a_{2}$	CHECK	REDX	REDX
$b_{1}$	CHECK	CHECK	REDX
$b_{2}$	CHECK	CHECK	REDX
			[FOOT;]* Publication Multiplier

Strategy Credits:

xelaroc
Playspout
rus9384#1864 for $b_{1}$ , $b_{2}$ coasting at 6 publication multiplier

Euler’s Formula #

EFAI #

Class: strat_separated; Caption: EFAI;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$\dot{t}$	CHECK	CHECK
$q_{1}$	When cost $\times (10 +$ lvl% $10) < q_{2}$ cost	When cost $\times (10 +$ lvl% $10) < q_{2}$ cost
$q_{2}$	CHECK	CHECK
$b_{1}$	CHECK	When $\frac{1}{5}$ of $a_{2}$ cost
$b_{2}$	CHECK	When $\frac{1}{5}$ of $a_{2}$ cost
$c_{1}$	CHECK	When $\frac{1}{5}$ of $a_{3}$ cost
$c_{2}$	CHECK	When $\frac{1}{5}$ of $a_{3}$ cost
$a_{1}$	When cost $\times (4 + \frac{lvl % 10}{2}) < q_{2}$ cost	When cost $\times (4 + \frac{lvl % 10}{2}) < q_{2}$ cost
$a_{2}$	CHECK	CHECK
$a_{3}$	CHECK	CHECK

When the theory simulator recommends this strategy, it will show something like:
EFAI $q_{1}$ : 1223 $q_{2}$ : 144 $a_{1}$ : 382

The levels it shows after each variable are the last levels you should buy them to in this publication.

If you are confused about the “%”, read about it here.

Strategy Credits:

The Amazing Community (EFAI is a product of a bunch of ideas from various players)

EFSNAX #

Class: strat_separated; Caption: EFSNAX;

INVIS	Recovery (pub mult $< 1$ )	$τ$ Gain (pub mult $> 1$ )
$\dot{t}$	CHECK	CHECK
$q_{1}$	CHECK	REDX
$q_{2}$	CHECK	CHECK
$b_{1}$	CHECK	REDX
$b_{2}$	CHECK	REDX
$c_{1}$	CHECK	REDX
$c_{2}$	CHECK	REDX
$a_{1}$	CHECK	CHECK
$a_{2}$	CHECK	CHECK
$a_{3}$	CHECK	CHECK
		[FOOT;]If below $e 150 ρ$ , don’t autobuy $a_{1}$ after recovery.

Strategy Credits:

Snaeky
XLII
Gaunter for buying $a_{1}$ after recovery when past e150 $ρ$ strategy

EFd #

Class: strat; Caption: EFd;


$\dot{t}$	CHECK
$q_{1}$	When cost is $\frac{1}{10}$ of $q_{2}$ cost
$q_{2}$	CHECK
$b_{1}$	CHECK
$b_{2}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$a_{1}$	When cost is $\frac{1}{4}$ of $q_{2}$ cost
$a_{2}$	CHECK
$a_{3}$	CHECK

EF #

Class: strat; Caption: EF;


$\dot{t}$	CHECK
$q_{1}$	CHECK
$q_{2}$	CHECK
$b_{1}$	CHECK
$b_{2}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$a_{1}$	CHECK
$a_{2}$	CHECK
$a_{3}$	CHECK

Convergents to √2 #

CSR2XL x.xx #

Class: strat_separated; Caption: CSR2XL x.xx;

INVIS	Before x.xx Pub Mult	After x.xxx Pub Mult
$q_{1}$	When cost is $\frac{1}{10}$ of $min (q_{2}, n, c_{2})$ cost	REDX
$q_{2}$	✔️*	REDX
$c_{1}$	When cost is $\frac{1}{10}$ of $min (q_{2}, n, c_{2})$ cost	REDX
$n$	✔️**	REDX
$c_{2}$	CHECK	REDX
		[FOOT;]* If $q_{2}$ cost is similar to $n$ or $c_{2}$ cost, prioritize $n$ or $c_{2}$ respectively.
		[FOOT;]** If $n$ and $c_{2}$ have similar costs, prioritize $c_{2}$ .

The “x.xx” is returned by the theory simulator. For example, it could say:
CSR2XL 2.85.

This means turn off autobuy on all variables at 2.85 publication multiplier.

Milestone Swap (pre e500 $ρ$ )

Start publication with milestones in $c_{2}$ / $c_{2}$ exponent.

Swap to $q_{1}$ exponent when one of these is true:

$ρ \times$ Ratio $> c_{2}$ cost
$ρ \times \frac{Ratio}{2} > n$ cost
$ρ \times 2 > q_{2}$ cost and publication multiplier > 1

Follow the sim’s advice for when to start coasting.

The “Ratio” stated in the $q_{1}$ swap conditions is determined as follows, where $ρ$ is $ρ$ at the end of your last publication:

Class: strat; Caption: Ratio;


$ρ < e 45$	Swap when you are very close to the upgrade.*
$e 45 \leq ρ < e 80$	4
$e 80 \leq ρ < e 115$	8
$e 115 \leq ρ < e 220$	20
$ρ > e 220$	40
	[FOOT;]* Couldn’t find any good ratio here, just swap when you are very close to the upgrade. - XLII

Strategy Credits:

XLII

CSR2d #

Class: strat; Caption: CSR2d;


$q_{1}$	When cost is $\frac{1}{10}$ of $min (q_{2}, n, c_{2})$ cost
$q_{2}$	CHECK
$c_{1}$	When cost is $\frac{1}{10}$ of $min (q_{2}, n, c_{2})$ cost
$n$	CHECK
$c_{2}$	CHECK

CSR2 #

Class: strat; Caption: CSR2;


$q_{1}$	CHECK
$q_{2}$	CHECK
$c_{1}$	CHECK
$n$	CHECK
$c_{2}$	CHECK

Fractional Integration #

FId #

Class: strat; Caption: FId;


$q_{1}$	When cost $\times (1 +$ lvl% $23) <$ $min (q_{2}, K)$ cost
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	When cost $\times (1 +$ lvl% $11) <$ $min (q_{2}, K, m)$ cost

Milestone routing information

This strategy does not use the $3^{rd}$ level of the $g (x)$ milestone until you unlock the last milestone point at $e 1150 ρ$ .

FI #

Class: strat; Caption: FI;


$q_{1}$	CHECK
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	CHECK

Milestone routing information

This strategy does not use the $3^{rd}$ level of the $g (x)$ milestone until you unlock the last milestone point at $e 1150 ρ$ .

FIMSd #

Class: strat; Caption: FIMSd;


$q_{1}$	When cost $\times (1 +$ lvl% $23) <$ $min (q_{2}, K)$ cost
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	When cost $\times (1 +$ lvl% $11) <$ $min (q_{2}, K, m)$ cost

Milestone swapping strategy

When buying a new level of $q_{2}$ , swap $n$ and $m$ milestones to $q_{1}$ exponent to build up $q$ .

Swap back to $m$ and $n$ when $q$ got multiplied by a ratio (since you started the swapping phase) depending on your $q_{1}$ lvl% $23$ :

Class: strat; Caption: $q$ Ratio based on $q_{1}$ lvl% $23$ ;

$q_{1}$ lvl% $23$	$q$ Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

Strategy Credits:

Playspout for the milestone swapping strategy

FIMS #

Class: strat; Caption: FIMS;


$q_{1}$	CHECK
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	CHECK

Milestone swapping strategy

When buying a new level of $q_{2}$ , swap $n$ and $m$ milestones to $q_{1}$ exponent to build up $q$ .

Swap back to $m$ and $n$ when $q$ got multiplied by a ratio (since you started the swapping phase) depending on your $q_{1}$ lvl% $23$ :

Class: strat; Caption: $q$ Ratio based on $q_{1}$ lvl% $23$ ;

$q_{1}$ lvl% $23$	$q$ Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

Strategy Credits:

Playspout for the milestone swapping strategy

FIdPermaSwap #

Class: strat; Caption: FIdPermaSwap;


$q_{1}$	When cost $\times (1 +$ lvl% $23) <$ $min (q_{2}, K)$ cost
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	When cost $\times (1 +$ lvl% $11) <$ $min (q_{2}, K, m)$ cost

PermaSwap strategy

Before reaching $e 1076 ρ$ in your publication, do not use the $3^{rd}$ level of the $g (x)$ milestone.

Upon reaching $e 1076 ρ$ , switch a milestone point into the $3^{rd}$ level of the $g (x)$ milestone, at the cost of resetting $q$ .

FIPermaSwap #

Class: strat; Caption: FIPermaSwap;


$q_{1}$	CHECK
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	CHECK

PermaSwap strategy

Before reaching $e 1076 ρ$ in your publication, do not use the $3^{rd}$ level of the $g (x)$ milestone.

Upon reaching $e 1076 ρ$ , switch a milestone point into the $3^{rd}$ level of the $g (x)$ milestone, at the cost of resetting $q$ .

FIMSdPermaSwap #

Class: strat; Caption: FIMSdPermaSwap;


$q_{1}$	When cost $\times (1 +$ lvl% $23) <$ $min (q_{2}, K)$ cost
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	When cost $\times (1 +$ lvl% $11) <$ $min (q_{2}, K, m)$ cost

Milestone swapping strategy

When buying a new level of $q_{2}$ , swap $n$ and $m$ milestones to $q_{1}$ exponent to build up $q$ .

Swap back to $m$ and $n$ when $q$ got multiplied by a ratio (since you started the swapping phase) depending on your $q_{1}$ lvl% $23$ :

Class: strat; Caption: $q$ Ratio based on $q_{1}$ lvl% $23$ ;

$q_{1}$ lvl% $23$	$q$ Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

PermaSwap strategy

Before reaching $e 1076 ρ$ in your publication, do not use the $3^{rd}$ level of the $g (x)$ milestone.

Upon reaching $e 1076 ρ$ , switch a milestone point into the $3^{rd}$ level of the $g (x)$ milestone, at the cost of resetting $q$ .

Strategy Credits:

Playspout for the milestone swapping strategy

FIMSPermaSwap #

Class: strat; Caption: FIMSPermaSwap;


$q_{1}$	CHECK
$q_{2}$	CHECK
$K$	CHECK
$m$	CHECK
$n$	CHECK

Milestone swapping strategy

When buying a new level of $q_{2}$ , swap $n$ and $m$ milestones to $q_{1}$ exponent to build up $q$ .

Swap back to $m$ and $n$ when $q$ got multiplied by a ratio (since you started the swapping phase) depending on your $q_{1}$ lvl% $23$ :

Class: strat; Caption: $q$ Ratio based on $q_{1}$ lvl% $23$ ;

$q_{1}$ lvl% $23$	$q$ Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

PermaSwap strategy

Before reaching $e 1076 ρ$ in your publication, do not use the $3^{rd}$ level of the $g (x)$ milestone.

Upon reaching $e 1076 ρ$ , switch a milestone point into the $3^{rd}$ level of the $g (x)$ milestone, at the cost of resetting $q$ .

Strategy Credits:

Playspout for the milestone swapping strategy

Fractal Patterns #

FPmodBurstC1MS #

Class: strat; Caption: FPmodBurstC1MS;


$\dot{t}$	CHECK
$c_{1}$	When cost $\times (1 +$ lvl% $100) <$ $min (c_{2}, s)$ cost*
$c_{2}$	✔️**
$q_{1}$	When cost $\times (1 +$ lvl% $10) <$ $min (q_{2}, s)$ cost
$q_{2}$	✔️***
$r_{1}$	CHECK
$n$	CHECK
$s$	CHECK
	[FOOT;]* If you can afford the next $c_{1}$ lvl% $100 = 1$ before the next $c_{2}$ or $s$ lvl, then autobuy $c_{1}$ .
	[FOOT;]** If $c_{2}$ and $s$ have similar costs, prioritize $s$ .
	[FOOT;]*** If $q_{2}$ and $s$ have similar costs, prioritize $s$ .

Milestone swapping strategy (e700ρ+)

After you unlock the $s$ milestone, you can perform milestone swapping until $s > 2$ . Alternate between having the $s$ milestone on and off. When $s > 2$ , keep the milestone on everytime. Milestone swapping is no longer required once you can reach $s > 2$ quickly.

For more information about the FP milestone swapping strategy, check here.

Strategy Credits:

Hotab for implementing this strategy into the sim and adjusting it

FPdMS #

Class: strat; Caption: FPdMS;


$\dot{t}$	CHECK
$c_{1}$	When cost $\times (1 +$ lvl% $100) < c_{2}$ cost
$c_{2}$	CHECK
$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$n$	CHECK
$s$	CHECK

Milestone swapping strategy (e700ρ+)

For more information about the FP milestone swapping strategy, check here.

FP #

Class: strat; Caption: FP;


$\dot{t}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$q_{1}$	CHECK
$q_{2}$	CHECK
$r_{1}$	CHECK
$n$	CHECK
$s$	CHECK

Riemann Zeta Function #

RZdBH #

Class: strat; Caption: RZdBH;


$c_{1}$	When $c_{1}$ lvl $< 4 \times c_{2}$ lvl $+ 2$
$c_{2}$	CHECK
$w_{1}$	When cost is $f r a c 15$ of $min (w_{2}, w_{3})$ cost
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	✔️*
	[FOOT;]* Do not buy $b$ until $t > 16$ .

When the theory simulator recommends this strategy, it will show something like:
RZdBH $t$ =388.85 $c_{1}$ : 3091 $c_{2}$ : 773.

The value after $t$ is the $t$ value at which the black hole should be set. We recommend putting the threshold 0.01 above this value to avoid precision issues.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

Hotab, Blackseal, Mathis S. for the implementation in the sim
Hotab, Blackseal, LE★Baldy for the running simulations to set up the list of good zeros the final sim uses
prop for the variable buying strategy
Hotab & Blackseal for the coasting strategy

RZBH #

Class: strat; Caption: RZBH;


$c_{1}$	CHECK
$c_{2}$	CHECK
$w_{1}$	CHECK
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	CHECK

When the theory simulator recommends this strategy, it will show something like:
RZdBH $t$ =388.85 $c_{1}$ : 3091 $c_{2}$ : 773.

The value after $t$ is the $t$ value at which the black hole should be set. We recommend putting the threshold 0.01 above this value to avoid precision issues.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

Hotab, Blackseal, Mathis S. for the implementation in the sim
Hotab, Blackseal, LE★Baldy for the running simulations to set up the list of good zeros the final sim uses
Hotab & Blackseal for the coasting strategy

RZSpiralSwap #

Class: strat; Caption: RZSpiralSwap;


$c_{1}$	When $c_{1}$ lvl $< 4 \times c_{2}$ lvl $+ 2$
$c_{2}$	CHECK
$w_{1}$	When cost is $\frac{1}{5}$ of $w_{2}$ cost
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	✔️*
	[FOOT;]* Do not buy $b$ until $t > 16$ .

SpiralSwap

To perform SpiralSwap, switch milestones to prioritize $c_{1}$ exponent when $ζ$ is close to zero (when the graph is close to the origin) and to prioritize $w_{2}$ when $| ζ | > 1$ .

This strategy is extremely active. Using RZdMS is much easier and doesn’t lose that much time compared to RZSpiralSwap.

When the theory simulator recommends this strategy, it will show something like:
RZSpiralSwap $c_{1}$ : 953 $c_{2}$ : 238.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

prop for the milestone swapping and variable buying strategy
Hotab & Blackseal for the coasting strategy

RZdMS #

Class: strat; Caption: RZdMS;


$c_{1}$	When $c_{1}$ lvl $< 4 \times c_{2}$ lvl $+ 2$
$c_{2}$	CHECK
$w_{1}$	When cost is $\frac{1}{5}$ of $w_{2}$ cost
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	✔️*
	[FOOT;]* Do not buy $b$ until $t > 16$ .

When the theory simulator recommends this strategy, it will show something like:
RZdMS swap: 197 $c_{1}$ : 953 $c_{2}$ : 238.

Start the publication with the $w_{2}$ milestone on. The value after swap is the $ρ$ value were you should switch it to $c_{1}$ exponent.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

prop for the variable buying strategy
Hotab for the dynamic swap implementation
Hotab & Blackseal for the coasting strategy

RZMS #

Class: strat; Caption: RZMS;


$c_{1}$	CHECK
$c_{2}$	CHECK
$w_{1}$	CHECK
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	CHECK

When the theory simulator recommends this strategy, it will show something like:
RZdMS swap: 197 $c_{1}$ : 953 $c_{2}$ : 238.

Start the publication with the $w_{2}$ milestone on. The value after swap is the $ρ$ value were you should switch it to $c_{1}$ exponent.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

prop for the variable buying strategy
Hotab for the dynamic swap implementation
Hotab & Blackseal for the coasting strategy

RZd #

Class: strat; Caption: RZd;


$c_{1}$	When $c_{1}$ lvl $< 4 \times c_{2}$ lvl $+ 2$ *
$c_{2}$	CHECK
$w_{1}$	When cost is $\frac{1}{5}$ of $min (w_{2}, w_{3})$ cost
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	✔️**
	[FOOT;]* If you don’t have $c_{1}$ exponent milestones, use 4\times c_2$lvl + 1 instead.
	[FOOT;]** Do not buy $b$ until $t > 16$ .

When the theory simulator recommends this strategy, it will show something like:
RZd $c_{1}$ : 953 $1_{2}$ : 238.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

prop for the variable buying strategy
Hotab & Blackseal for the coasting strategy

RZ #

Class: strat; Caption: RZ;


$c_{1}$	CHECK
$c_{2}$	CHECK
$w_{1}$	CHECK
$w_{2}$	CHECK
$w_{3}$	CHECK
$b$	CHECK

When the theory simulator recommends this strategy, it will show something like:
RZ $c_{1}$ : 953 $c_{2}$ : 238.

The levels it shows after $c_{1}$ and $c_{2}$ are the last levels you should buy them to in this publication.

Strategy credits:

Hotab & Blackseal for the coasting strategy

Magnetic Fields #

MFd2 #

Class: strat; Caption: MFd2;


$c_{1}$	When cost $\times 8 + ($ lvl% $7) <$ $min (2 \times c_{2}, a_{2}, 3 \times δ)$ cost
$c_{2}$	CHECK
$a_{1}$	When $I \times 1.2 < I_{cap}$ or $I < I_{cap}$ and cost is $\frac{1}{20}$ of $min (c_{2}, a_{2}, δ)$ cost
$a_{2}$	CHECK
$δ$	When cost is $\frac{1}{3}$ of $min (2 \times c_{2}, a_{2})$ cost
$v_{1}$	Only buy right before a reset
$v_{2}$	Only buy right before a reset
$v_{3}$	Only buy right before a reset
$v_{4}$	Only buy right before a reset

Strategy Credits:

Gnarwhals for the variable buying strategy
BlackSeal for the implementation of resets in the sim

MFd #

Class: strat; Caption: MFd;


$c_{1}$	When cost is $\frac{1}{10}$ of $min (c_{2}, a_{2}, δ)$ cost
$c_{2}$	CHECK
$a_{1}$	When $I < \frac{1}{2} I_{cap}$ or cost is $\frac{1}{10}$ of $min (c_{2}, a_{2}, δ)$ cost
$a_{2}$	CHECK
$δ$	CHECK
$v_{1}$	Only buy right before a reset
$v_{2}$	Only buy right before a reset
$v_{3}$	Only buy right before a reset
$v_{4}$	Only buy right before a reset

Strategy Credits:

BlackSeal for the implementation of resets in the sim

MF #

Class: strat; Caption: MF;


$c_{1}$	CHECK
$c_{2}$	CHECK
$a_{1}$	CHECK
$a_{2}$	CHECK
$δ$	CHECK
$v_{1}$	Only buy right before a reset
$v_{2}$	Only buy right before a reset
$v_{3}$	Only buy right before a reset
$v_{4}$	Only buy right before a reset

Strategy Credits:

BlackSeal for the implementation of resets in the sim

Basel Problem #

BaPAI #

Class: strat; Caption: BaPAI;


$\dot{t}$	CHECK
$c_{1}$	If cumulative cost to $c_{1}$ lvl% $64 = 1$ is $< 2$ x cheapest other purchase, buy until $c_{1}$ lvl% $64 = 1$ . When saving for $c_{1}$ lvl% $64 = 1$ , ✔️. Otherwise, buy at $\frac{1}{2} (c_{1}$ lvl% $64)$ ratio to other variables.
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK
$c_{7}$	CHECK
$c_{8}$	CHECK
$c_{9}$	CHECK
$c_{10}$	CHECK
$n$	CHECK

Start coasting when x25 away from the next publication mark or next milestone.

Strategy credits:

Mathis S.

BaPAIMS #

BaPAIMS is the milestone swapping strategy for BaP.

For how to perform the milestone swapping strategy, check here.

For the variable buying strategy, check BaPAI.

BaPcoast #

Class: strat; Caption: BaPcoast;


$\dot{t}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK
$c_{7}$	CHECK
$c_{8}$	CHECK
$c_{9}$	CHECK
$c_{10}$	CHECK
$n$	CHECK

Start coasting when x25 away from the next publication mark or next milestone.

Strategy credits:

Mathis S.

BaP #

Class: strat; Caption: BaP;


$\dot{t}$	CHECK
$c_{1}$	CHECK
$c_{2}$	CHECK
$c_{3}$	CHECK
$c_{4}$	CHECK
$c_{5}$	CHECK
$c_{6}$	CHECK
$c_{7}$	CHECK
$c_{8}$	CHECK
$c_{9}$	CHECK
$c_{10}$	CHECK
$n$	CHECK

Table of Con­tents

Table of Con­tents

Guides

Guides

Re­sources

Re­sources

Guide Ex­ten­sions

Guide Ex­ten­sions

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Table of Con­tents ⓧ

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