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The theory sim (simulation) we currently recommend was originally made by XLII, now maintained by the sim team and can be accessed here.

For help on specific (active) strategies, Hackzzzzzz’s Theory Quick Purchase Testers can output when to buy variables. Take a look for help with difficult strategies.

▶︎ 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 Permalink: list-of-strategies

Official Theories Permalink: 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. T3ρ2C23d is an easier version being 10-15% slower.

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

T3Play2 — Very Active
T3Play — Very Active
T3SNAX2 — Active
T3SNAXdC12 — Active recovery, then Semi-Idle
T3SNAX — Semi-Idle
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 Permalink: theory-4-polynomials

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

T4C456dC12rcvMS — Active
T4C356dC12rcv — Active
T4C3dC12rcv — Active
T4C3d — Active
T4C3coast — Semi-Idle
T4C3 — Idle
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
T6C125d — Active
T6C125 — Idle
T6C5d — Active
T6C5 — Idle
T6C12d — Active
T6C12 — 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 Permalink: 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.

SLMSd — Very Active
SLMS — 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 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 cap increase from e100 to e150.

CSR2XL x.xx — VERY Active pre-e500, Active post-e500
CSR2XLPT — Active
CSR2d — Active
CSR2PT — Semi-Idle
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 contribution rate increase by x4.

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

▶︎ 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 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.

RZdBHRewind — EXTREMELY Active
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.

MFVariantdxdxdx — Very Active
MFd3 — Very Active
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 Permalink: t1solarxlii-xexxx

T1SolarXLII xexxx
	Below xexxx	Above xexxx
	When costlvl% cost and costlvl% cost and cost	❌
	when cost	❌
	See T1Ratio	❌
	See T1Ratio	❌
	See T1Ratio	❌
	✔️	❌

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

This means to begin coasting at .

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 Permalink: t1ratio

T1Ratio
	When cost
	When cost
	When ratio cost
	When ratio cost
	When ratio cost
	✔️

Do not buy or after e300.

For the Ratio:

LATEXDOLLARcLATEXUNDERSCORE2LATEXDOLLAR Ratio

For the Ratio:

Ratio
	1
	1.1
	2
	5
	10

Strategy Credits:

XLII

▶︎ T1C34 Permalink: t1c34

T1C34
	✔️
	✔️
	❌
	❌
	✔️
	✔️

▶︎ T1C4 Permalink: t1c4

T1C4
	✔️
	✔️
	❌
	❌
	❌
	✔️

▶︎ Theory 2: Differential Calculus

▶︎ T2MC Permalink: t2mc

T2MC
Pub. Mult.*
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
* 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 Permalink: t2mcalt2

T2MCAlt2
Pub. Mult.*
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
* 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 Permalink: t2mcalt3

T2MCAlt3
Pub. Mult.*
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
	✔️	✔️	✔️	✔️	❌
	✔️	✔️	✔️	❌	❌
	✔️	✔️	❌	❌	❌
	✔️	❌	❌	❌	❌
* 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 Permalink: t2ms

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

▶︎ T2QS Permalink: t2qs

T2QS
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

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 is at the end of your last publication:

Publication Multiplier
	10
	200
	600
	100
	25

▶︎ T2 Permalink: t2

T2
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Theory 3: Linear Algebra

▶︎ T3Play2 Permalink: t3play2

T3Play2
	Before from recovered*	from recovered to Pub. Mult.	Pub. Mult	Pub. Mult.**
	When of cost	❌	❌	❌
	When of cost	When of cost	When of cost	✔️
	When of cost	When of cost	When of cost	✔️
	❌	❌	❌	❌
	When of cost	When of cost	✔️	✔️
	❌	❌	❌	❌
	❌	❌	❌	❌
	When of cost	When of cost	When of cost	❌
	✔️	✔️	✔️	✔️
	✔️	❌	❌	❌
	✔️	✔️	When of cost	❌
	When of cost	When of cost	❌	❌
* An earlier version of the strategy did not buy any variables. This is only around 1% slower than the strategy shown above, which does buy and in early parts of the strategy. It’s up to you whether you think that a 1% improvement is worth it or not.
** Coasting Phase

Strategy Credits:

Playspout for creating this strategy.
Solarion for 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 Permalink: t3play

T3Play
Pub. Mult.*	(Recovery)		(Coasting)
	When of cost	When of cost	❌
	When of cost and of cost	When of cost and of cost	✔️
	When of cost and of cost	When of cost and of cost	When of cost and of cost
	❌	❌	❌
	✔️	✔️	✔️
	❌	❌	❌
	❌	❌	❌
	When of cost	When of cost	✔️
	✔️	✔️	✔️
	✔️	✔️	❌
	✔️	✔️	✔️
	When of cost	When of cost	When of cost
* Publication Multiplier

Strategy Credits:

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

▶︎ T3SNAX2 Permalink: t3snax2

T3SNAX2
	Recovery (pub mult )	Gain (pub mult )
	When cost is of	❌
	When cost is of	When cost is of
	When cost is of	When cost is of
	❌	❌
	When cost is of	✔️
	❌	❌
	❌	❌
	✔️	When cost is of
	✔️	✔️
	✔️	❌
	✔️	❌
	When cost is of	❌

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.

▶︎ T3SNAXdC12 Permalink: t3snaxdc12

T3SNAXdC12
	Recovery (pub mult )	Gain (pub mult )
	✔️	❌
	✔️	✔️
	✔️	✔️
	❌	❌
	When cost cost	✔️
	❌	❌
	❌	❌
	✔️	✔️
	✔️	✔️
	✔️	❌
	✔️	❌
	✔️	❌

Strategy Credits:

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

▶︎ T3SNAX Permalink: t3snax

T3SNAX
	Recovery (pub mult )	Gain (pub mult )
	✔️	❌
	✔️	✔️
	✔️	✔️
	❌	❌
	✔️	✔️
	❌	❌
	❌	❌
	✔️	✔️
	✔️	✔️
	✔️	❌
	✔️	❌
	✔️	❌

Strategy Credits:

Snaeky for the idea.
XLII for simulating the strategy

▶︎ T3ρ2C23d Permalink: t3r2c23d

T3ρ2C23d
	❌
	When cost is of cost
	When cost is of cost
	❌
	✔️
	❌
	❌
	✔️
	✔️
	❌
	✔️
	❌

▶︎ T3ρ2C23 Permalink: t3r2c23

T3ρ2C23
	❌
	✔️
	✔️
	❌
	✔️
	❌
	❌
	✔️
	✔️
	❌
	✔️
	❌

▶︎ T3ρ2C23C33d Permalink: t3r2c23c33d

T3ρ2C23C33d
	❌
	When cost is of cost
	When cost is of cost
	❌
	✔️
	❌
	❌
	✔️
	✔️
	❌
	✔️
	✔️

▶︎ T3ρ2C23C33 Permalink: t3r2c23c33

T3ρ2C23C33
	❌
	✔️
	✔️
	❌
	✔️
	❌
	❌
	✔️
	✔️
	❌
	✔️
	✔️

▶︎ T3NoC11C13C21C33d Permalink: t3noc11c13c21c33d

T3NoC11C13C21C33d
	When cost is of cost
	When cost is of cost
	When cost is of cost
	❌
	✔️
	❌
	❌
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC11C13C21C33 Permalink: t3noc11c13c21c33

T3NoC11C13C21C33
	✔️
	✔️
	✔️
	❌
	✔️
	❌
	❌
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC13C33d Permalink: t3noc13c33d

T3NoC13C33d
	When cost is of cost
	When cost is of cost
	When cost is of cost
	✔️
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC13C33 Permalink: t3noc13c33

T3NoC13C33
	✔️
	✔️
	✔️
	✔️
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC11C13C33d Permalink: t3noc11c13c33d

T3NoC11C13C33d
	When cost is of cost
	When cost is of cost
	When cost is of cost
	❌
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC11C13C33 Permalink: t3noc11c13c33

T3NoC11C13C33
	✔️
	✔️
	✔️
	❌
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T3NoC13C32C33d Permalink: t3noc13c32c33d

T3NoC13C32C33d
	When cost is of cost
	When cost is of cost
	When cost is of cost
	✔️
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	❌
	❌

▶︎ T3NoC13C32C33 Permalink: t3noc13c32c33

T3NoC13C32C33
	✔️
	✔️
	✔️
	✔️
	✔️
	❌
	✔️
	✔️
	✔️
	✔️
	❌
	❌

▶︎ T3C11C12C21d Permalink: t3c11c12c21d

T3C11C12C21d
	When cost is of cost
	When cost is of cost
	❌
	✔️
	✔️
	❌
	✔️
	❌
	❌
	❌
	❌
	❌

▶︎ T3C11C12C21 Permalink: t3c11c12c21

T3C11C12C21
	✔️
	✔️
	❌
	✔️
	✔️
	❌
	✔️
	❌
	❌
	❌
	❌
	❌

▶︎ Theory 4: Polynomials

▶︎ T4C456dC12rcvMS Permalink: t4c456dc12rcvms

T4C456dC12rcvMS
	Recovery (pub mult )	Gain (pub mult )
	When cost is of cost	❌
	✔️	❌
	❌	❌
	✔️	✔️
	✔️	✔️
	✔️	✔️
	When cost is of cost	When cost is of cost
	✔️	✔️

Milestone swapping strategy

During your recovery phase, set your milestones in the order 2→3→1
During the 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

▶︎ T4C356dC12rcv Permalink: t4c356dc12rcv

T4C356dC12rcv
	Recovery (pub mult )	Gain (pub mult )
	When cost is of cost	❌
	✔️	❌
	✔️	✔️
	❌	❌
	✔️	✔️
	✔️	✔️
	When cost is of cost	When cost is of cost
	✔️	✔️

▶︎ T4C3dC12rcv Permalink: t4c3dc12rcv

T4C3dC12rcv
	Recovery (pub mult )	Gain (pub mult )
	When cost is of cost	❌
	✔️	❌
	✔️	✔️
	❌	❌
	❌	❌
	❌	❌
	When cost is of cost	When cost is of cost
	✔️	✔️

▶︎ T4C3d Permalink: t4c3d

T4C3d
	Recovery (pub mult )	Gain (pub mult )
	❌	❌
	❌	❌
	✔️	✔️
	❌	❌
	❌	❌
	❌	❌
	When cost lvl% cost	When cost lvl% cost
	✔️	When cost is of cost

When the theory simulator recommends this strategy, it will show something like: T4C3d : 377 : 252”. The levels it shows after and are the last levels you should buy them in this publication.

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

Previously known as T4C3d66

Strategy Credits:

XLII
rus9384#1864

▶︎ T4C3coast Permalink: t4c3coast

T4C3coast
	❌
	❌
	✔️
	❌
	❌
	❌
	✔️
	✔️

When the theory simulator recommends this strategy, it will show something like: T4C3coast : 377 : 252”. The levels it shows after and are the last levels you should buy them to in this publication.

▶︎ T4C3 Permalink: t4c3

T4C3
	❌
	❌
	✔️
	❌
	❌
	❌
	✔️
	✔️

▶︎ T4C123d Permalink: t4c123d

T4C123d
	When cost is of cost
	✔️
	✔️
	❌
	❌
	❌
	When cost is of cost
	✔️

This strategy is typically seen at lower and is eventually outpaced by T4C3d.

▶︎ T4C123 Permalink: t4c123

T4C123
	✔️
	✔️
	✔️
	❌
	❌
	❌
	✔️
	✔️

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

▶︎ T4C12d Permalink: t4c12d

T4C12d
	When cost is of cost
	✔️
	❌
	❌
	❌
	❌
	❌
	❌

▶︎ T4C12 Permalink: t4c12

T4C12
	✔️
	✔️
	❌
	❌
	❌
	❌
	❌
	❌

▶︎ T4C56 Permalink: t4c56

T4C56
	❌
	❌
	❌
	❌
	✔️
	✔️
	✔️
	✔️

▶︎ T4C4 Permalink: t4c4

T4C4
	❌
	❌
	❌
	✔️
	❌
	❌
	✔️
	✔️

▶︎ T4C5 Permalink: t4c5

T4C5
	❌
	❌
	❌
	❌
	✔️
	❌
	✔️
	✔️

▶︎ T4 Permalink: t4

T4
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Theory 5: Logistic Function

▶︎ T5AI Permalink: 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 Permalink: t5idle-xexxx

T5Idle xexxx
	Before xexxx	After xexxx
	✔️	✔️
	✔️	✔️
	✔️	❌
	✔️	✔️
	✔️	✔️

IMPORTANT:
Do active buying (buying when 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 .

Strategy Credit:

XLII

▶︎ T5 Permalink: t5

T5
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Theory 6: Integral Calculus

▶︎ T6AI Permalink: t6ai

T6AI
	When cost lvl% cost
	✔️
	When cost lvl% cost
	✔️
	When cost lvl% cost
	As the publication progresses, buy less (and ).
	❌
	❌
	✔️

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

How does purchasing works exactly?

In the sim, the ratio at which is bought to , , is defined as the term ratio between the term and the term, which equates to . If this ratio is 2, then the sim will buy when 2 times cheaper than , , .

▶︎ T6SNAX x.xxexxx Permalink: t6snax-xxxexxx

T6SNAX x.xxexxx
	Before x.xxexxx	After x.xxexxx
	✔️	✔️
	✔️	✔️
	✔️	✔️
	✔️	✔️
	✔️	❌
	✔️	❌
	❌	❌
	❌	❌
	✔️	✔️

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

This means to start coasting at .

Strategy Credits:

Snaeky
XLII

▶︎ T6C125d Permalink: t6c125d

T6C125d
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	❌
	❌
	✔️

▶︎ T6C125 Permalink: t6c125

T6C125
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	❌
	❌
	✔️

▶︎ T6C5d Permalink: t6c5d

T6C5d
	When cost lvl% cost
	✔️
	When cost cost
	✔️
	❌
	❌
	❌
	❌
	✔️

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

▶︎ T6C5 Permalink: t6c5

T6C5
	✔️
	✔️
	✔️
	✔️
	❌
	❌
	❌
	❌
	✔️

▶︎ T6C12d Permalink: t6c12d

T6C12d
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	❌
	❌
	❌

This strategy is sometimes seen at lower 's but not at higher 's.

▶︎ T6C12 Permalink: t6c12

T6C12
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	❌
	❌
	❌

This strategy is sometimes seen at lower 's but not at higher 's.

▶︎ T6C4d Permalink: t6c4d

T6C4d
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	❌
	❌
	❌
	✔️
	❌

▶︎ T6C4 Permalink: t6c4

T6C4
	✔️
	✔️
	✔️
	✔️
	❌
	❌
	❌
	✔️
	❌

▶︎ T6C3d Permalink: t6c3d

T6C3d
	When cost is of cost
	✔️
	❌
	❌
	✔️
	❌
	❌

Both T6C3d and T6C3 don’t have or listed because the two strategies only appear on the sim below the milestones that give and .

▶︎ T6C3 Permalink: t6c3

T6C3
	✔️
	✔️
	❌
	❌
	✔️
	❌
	❌

Both T6C3d and T6C3 don’t have or listed because the two strategies only appear on the sim below the milestones that give and .

▶︎ Theory 7: Numerical Methods

▶︎ T7PlaySpqceyX Permalink: t7playspqceyx

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

T7PlaySpqcey
	When cost is of cost
	❌
	❌
	When cost is of cost
	When cost is of cost
	When cost is of cost
	✔️

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

T7PlaySpqceyX
	When cost is of cost
	When cost is of cost
	When X times cheaper than cost
	When cost is of cost
	When cost is of cost
	When cost is of cost
	✔️

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

Regardless of the “X” value, the buying condition remains “When cost is of cost”

The number after T7PlaySpqcey occurs more at lower values.

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

Strategy Credits:

Playspout for , , , buying strategy
spqcey for the addition of
Snaeky for number after T7PlaySpqcey for if and are bought, and if so, what ratio
XLII for simulating Snaeky’s idea

▶︎ T7C3d Permalink: t7c3d

T7C3d
	When cost is of cost
	❌
	❌
	✔️
	❌
	❌
	❌

▶︎ T7C12d Permalink: t7c12d

T7C12d
	When cost is of cost
	When cost is of cost
	✔️
	❌
	❌
	❌
	❌

▶︎ T7C12 Permalink: t7c12

T7C12
	✔️
	✔️
	✔️
	❌
	❌
	❌
	❌

▶︎ T7C123d Permalink: t7c123d

T7C123d
	When cost is of cost
	When cost is of cost
	✔️
	✔️
	❌
	❌
	❌

▶︎ T7NoC12 Permalink: t7noc12

T7NoC12
	✔️
	❌
	❌
	✔️
	✔️
	✔️
	✔️

▶︎ T7NoC123 Permalink: t7noc123

T7NoC123
	✔️
	❌
	❌
	❌
	✔️
	✔️
	✔️

▶︎ T7NoC124 Permalink: t7noc124

T7NoC124
	✔️
	❌
	❌
	✔️
	❌
	✔️
	✔️

▶︎ T7NoC1234 Permalink: t7noc1234

T7NoC1234
	✔️
	❌
	❌
	❌
	❌
	✔️
	✔️

▶︎ T7 Permalink: t7

T7
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Theory 8: Chaos Theory Permalink: theory-8-chaos-theory-1

▶︎ T8PlaySolarSwap Permalink: t8playsolarswap

T8PlaySolarSwap
	When cost lvl% cost
	✔️
	When cost is of cost
	✔️
	When cost is of 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 Permalink: t8play

T8Play
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	When cost is of cost

Strategy Credits:

Playspout

▶︎ T8SNAX Permalink: t8snax

T8SNAX
Pub. Mult.*
	✔️	❌	❌
	✔️	✔️	✔️
	✔️	✔️	❌
	✔️	✔️	✔️
	✔️	✔️	❌
* Publication Multiplier

Strategy Credits:

Snaeky
XLII

▶︎ T8NoC35d Permalink: t8noc35d

T8NoC35d
	When cost is of cost
	✔️
	❌
	✔️
	❌

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

▶︎ T8NoC35 Permalink: t8noc35

T8NoC35
	✔️
	✔️
	❌
	✔️
	❌

▶︎ T8NoC5d Permalink: t8noc5d

T8NoC5d
	When cost is of cost
	✔️
	✔️
	✔️
	❌

▶︎ T8NoC5 Permalink: t8noc5

T8NoC5
	✔️
	✔️
	✔️
	✔️
	❌

▶︎ T8NoC3d Permalink: t8noc3d

T8NoC3d
	When cost is of cost
	✔️
	❌
	✔️
	✔️

▶︎ T8NoC3 Permalink: t8noc3

T8NoC3
	✔️
	✔️
	❌
	✔️
	✔️

▶︎ T8d Permalink: t8d

T8d
	When cost is of cost
	✔️
	✔️
	✔️
	✔️

▶︎ T8 Permalink: t8

T8
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Weierstraß Sine Product Permalink: weierstrass-sine-product

▶︎ WSPdStopC1 Permalink: wspdstopc1

WSPdStopC1
	First 15sec of Publication	Rest of Publication
	When cost lvl% cost	When cost lvl% cost
	✔️	✔️
	✔️	✔️
	✔️	When cost is Ratio* of cost
	✔️	✔️

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

* The “Ratio” stated in is determined as follows, where is at the end of your last publication:

Ratio
	1




	Do not buy after 15sec into publication

Strategy Credits:

xelaroc for testing/creating the strategy
Snaeky for the stop idea
XLII for some modifications including adding modulus and changes

▶︎ WSPStopC1 Permalink: wspstopc1

WSPStopC1
	First 15sec of Publication	Rest of Publication
	✔️	✔️
	✔️	✔️
	✔️	✔️
	✔️	If , ✔️ If ,❌
	✔️	✔️

Strategy Credits:

xelaroc for simulating it/adding it to the sim
Snaeky for the stop idea
XLII for modification

▶︎ WSP Permalink: wsp

WSP
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Sequential Limits Permalink: sequential-limits

▶︎ SLMSd Permalink: slmsd

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

SLMSd
Pub. Mult.*
	If lvl%, then ✔️. If not, buy when costlvl% cost.	❌	❌
	✔️	❌	❌
	If lvl% or , then ✔️. If not, buy when costlvl% cost.	If lvl% or , then ✔️. If not, buy when costlvl% cost.	❌
	✔️	✔️	❌
* Publication Multiplier

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

Strategy Credit:

XLII

▶︎ SLMS Permalink: 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 term)

State 2: 2→1→4→3 (prioritizes boost for )

State 3: 1→2→4→3 (prioritizes boost for instantaneous gain, aka exponent)

This strategy swaps milestones depending on how far away the next or upgrade is.

The goal of this strategy is:

Buy /
Swap milestones into State 1 to fully utilize the boost from the new / 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 so we get more quicker.
When we are closer to the next / upgrade, swap to State 3 so we utilize the boost that we just got for . This will get us to the next / upgrade a lot quicker.
Repeat.

This may seem difficult to execute, but publications in SL are 1 to 1.5 hours long after e50-e300. This means there can be up to 5-10 minute gaps between / 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 boost before publishing.

As long as < 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: is lower than the ratio provided under the header:

Ratios for SLMS Swapping
	State 1	State 2	State 3
	Until 5x	Until 4x	Until upgrade is bought
	Until 7x	Until 6x	Until upgrade is bought
	Until 12x	Until 10x	Until upgrade is bought
	Until 20x	Until 15x	Until upgrade is bought
	Until 8x	Until 6x	Until upgrade is bought
	Until 1.5x	Until upgrade is bought	Skip
	Until 3x	Skip	Until upgrade is bought
	Until 2x	Skip	Until upgrade is bought
cost in the table refers to cost.

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

In the first phase,, you should have your milestones in State 1 until is of min( cost, cost).

Then, swap to State 2 until is 1/4 of min( cost, 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+ range, you only want to swap when close to next /. and e75-e150 you swap very early.

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

Variable Buying

SLMS
Pub. Mult.*
	✔️	❌	❌
	✔️	❌	❌
	✔️	✔️	❌
	✔️	✔️	❌
* Publication Multiplier

Strategy Credit:

XLII

▶︎ SLStopAd Permalink: slstopad

SLStopAd
Pub. Mult.*
	If lvl%, then ✔️. If not, buy when costlvl% cost.	❌	❌
	✔️	❌	❌
	If lvl% or , then ✔️. If not, buy when costlvl% cost.	If lvl% or , then ✔️. If not, buy when costlvl% cost.	❌
	✔️	✔️	❌
* Publication Multiplier

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

The boost from doublings ( to , to ) is rarely enough to justify choosing this strategy over the idle strategy SLStopA.

Strategy Credits:

xelaroc
Playspout
rus9384#1864 for , coasting at 6 publication multiplier
XLII for buying ratios change and integration of modulus

▶︎ SLStopA Permalink: slstopa

SLStopA
Pub. Mult.*
	✔️	❌	❌
	✔️	❌	❌
	✔️	✔️	❌
	✔️	✔️	❌
* Publication Multiplier

Strategy Credits:

xelaroc
Playspout
rus9384#1864 for , coasting at 6 publication multiplier

▶︎ Euler’s Formula Permalink: eulers-formula

▶︎ EFAI Permalink: efai

EFAI
	Recovery (pub mult )	Gain (pub mult )
	✔️	✔️
	When costlvl% cost	When costlvl% cost
	✔️	✔️
	✔️	When of cost
	✔️	When of cost
	✔️	When of cost
	✔️	When of cost
	When cost cost	When cost cost
	✔️	✔️
	✔️	✔️

When the theory simulator recommends this strategy, it will show something like:
EFAI : 1223 : 144 : 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 Permalink: efsnax

EFSNAX
	Recovery (pub mult )	Gain (pub mult )
	✔️	✔️
	✔️	❌
	✔️	✔️
	✔️	❌
	✔️	❌
	✔️	❌
	✔️	❌
	✔️	✔️
	✔️	✔️
	✔️	✔️
If below , don’t autobuy after recovery.

When the theory simulator recommends this strategy, it will show something like:
EFSNAX : 1223 : 144 : 382

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

Strategy Credits:

Snaeky
XLII
Gaunter for buying after recovery when past e150 strategy

▶︎ EFd Permalink: efd

EFd
	Recovery (pub mult )	Gain (pub mult )
	✔️	✔️
	When cost is of cost
	✔️	✔️
	✔️	❌
	✔️	❌
	✔️	❌
	✔️	❌
	When cost is of cost
	✔️	✔️
	✔️	✔️

When the theory simulator recommends this strategy, it will show something like:
EFd : 1223 : 144 : 382

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

▶︎ EF Permalink: ef

EF
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Convergents to √2 Permalink: convergents-to-2

▶︎ CSR2XL x.xx Permalink: csr2xl-xxx

CSR2XL x.xx
	Before x.xx Pub Mult	After x.xxx Pub Mult
	When costlvl% cost	❌
	✔️*	❌
	When costlvl% cost	❌
	✔️**	❌
	✔️	❌
* If cost is similar to or cost, prioritize or respectively.
** If and have similar costs, prioritize .

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)

Start publication with milestones in / exponent.

Swap to exponent when one of these is true:

Ratio cost
cost
cost and publication multiplier > 1

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

The “Ratio” stated in the swap conditions is determined as follows, where is at the end of your last publication:

Ratio
	Swap when you are very close to the upgrade.*
	4
	8
	20
	40
* Couldn’t find any good ratio here, just swap when you are very close to the upgrade. - XLII

Strategy Credits:

XLII

▶︎ CSR2XLPT Permalink: csr2xlpt

CSR2XLPT
	When costlvl% cost
	✔️*
	When costlvl% cost
	✔️**
	✔️
* If cost is similar to or cost, prioritize or respectively.
** If and have similar costs, prioritize .

When the theory simulator recommends this strategy, it will show something like:
CSR2XLPT : 1147 : 381 : 661

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

The “PT” in CSR2XLPT stands for Publication Table, an algorithm used by the sim to calculate optimal publication points.

Strategy Credits:

XLII for the variable buying strategy
Mathis S. for the PT/coasting algorithm

▶︎ CSR2d Permalink: csr2d

CSR2d
	When cost is of cost
	✔️
	When cost is of cost
	✔️
	✔️

▶︎ CSR2PT Permalink: csr2pt

CSR2PT
	✔️
	✔️
	✔️
	✔️
	✔️

When the theory simulator recommends this strategy, it will show something like:
CSR2PT : 1147 : 381 : 661

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

The “PT” in CSR2PT stands for Publication Table, an algorithm used by the sim to calculate optimal publication points.

Strategy Credits:

Mathis S. for the PT/coasting algorithm

▶︎ CSR2 Permalink: csr2

CSR2
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Fractional Integration

▶︎ FIMSdPermaSwap Permalink: fimsdpermaswap

FIMSdPermaSwap
	When costlvl% cost
	✔️
	✔️
	✔️
	When costlvl% cost

Milestone swapping strategy

When buying a new level of , swap and milestones to exponent to build up .

Swap back to and when got multiplied by a ratio (since you started the swapping phase) depending on your lvl%:

Ratio based on lvl%
lvl%	Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

PermaSwap strategy

Before reaching in your publication, do not use the level of the milestone.

Upon reaching , switch a milestone point into the level of the milestone, at the cost of resetting .

Strategy Credits:

Playspout for the milestone swapping strategy

▶︎ FIMSPermaSwap Permalink: fimspermaswap

FIMSPermaSwap
	✔️
	✔️
	✔️
	✔️
	✔️

Milestone swapping strategy

When buying a new level of , swap and milestones to exponent to build up .

Swap back to and when got multiplied by a ratio (since you started the swapping phase) depending on your lvl%:

Ratio based on lvl%
lvl%	Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

PermaSwap strategy

Before reaching in your publication, do not use the level of the milestone.

Upon reaching , switch a milestone point into the level of the milestone, at the cost of resetting .

Strategy Credits:

Playspout for the milestone swapping strategy

▶︎ FIdPermaSwap Permalink: fidpermaswap

FIdPermaSwap
	When costlvl% cost
	✔️
	✔️
	✔️
	When costlvl% cost

PermaSwap strategy

Before reaching in your publication, do not use the level of the milestone.

Upon reaching , switch a milestone point into the level of the milestone, at the cost of resetting .

▶︎ FIPermaSwap Permalink: fipermaswap

FIPermaSwap
	✔️
	✔️
	✔️
	✔️
	✔️

PermaSwap strategy

Before reaching in your publication, do not use the level of the milestone.

Upon reaching , switch a milestone point into the level of the milestone, at the cost of resetting .

▶︎ FIMSd Permalink: fimsd

FIMSd
	When costlvl% cost
	✔️
	✔️
	✔️
	When costlvl% cost

Milestone swapping strategy

When buying a new level of , swap and milestones to exponent to build up .

Swap back to and when got multiplied by a ratio (since you started the swapping phase) depending on your lvl%:

Ratio based on lvl%
lvl%	Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

Strategy Credits:

Playspout for the milestone swapping strategy

▶︎ FIMS Permalink: fims

FIMS
	✔️
	✔️
	✔️
	✔️
	✔️

Milestone swapping strategy

When buying a new level of , swap and milestones to exponent to build up .

Swap back to and when got multiplied by a ratio (since you started the swapping phase) depending on your lvl%:

Ratio based on lvl%
lvl%	Ratio
1-4	4
5-9	3
10-19	2.5
0, 20-22	2

Strategy Credits:

Playspout for the milestone swapping strategy

▶︎ FId Permalink: fid

FId
	When costlvl% cost
	✔️
	✔️
	✔️
	When costlvl% cost

Milestone routing information

This strategy does not use the level of the milestone until you unlock the last milestone point at .

▶︎ FI Permalink: fi

FI
	✔️
	✔️
	✔️
	✔️
	✔️

Milestone routing information

This strategy does not use the level of the milestone until you unlock the last milestone point at .

▶︎ Fractal Patterns Permalink: fractal-patterns

▶︎ FPmodBurstC1MS Permalink: fpmodburstc1ms

FPmodBurstC1MS
	✔️
	When costlvl% cost*
	✔️**
	When costlvl% cost
	✔️***
	✔️
	✔️
	✔️
* If you can afford the next lvl% before the next or lvl, then autobuy .
** If and have similar costs, prioritize .
*** If and have similar costs, prioritize .

Milestone swapping strategy (e700+)

After you unlock the milestone, you can perform milestone swapping until . Alternate between having the milestone on and off. When , keep the milestone on everytime. Milestone swapping is no longer required once you can reach 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 Permalink: fpdms

FPdMS
	✔️
	When costlvl% cost
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

Milestone swapping strategy (+)

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

▶︎ FP Permalink: fp

FP
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

▶︎ Riemann Zeta Function Permalink: riemann-zeta-function

▶︎ RZdBHRewind Permalink: rzdbhrewind

RZdBH
	When lvllvl
	✔️
	When cost is of cost
	✔️
	✔️
	✔️*
* Do not buy until .

When the theory simulator recommends this strategy, it will show something like:
RZdBH =4478.52 c1: 6561 c2: 1640 w1: 7428.

The value after is the value at which the black hole should be set.

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

BHRewind strategy

This strategy allows to pass multiple times over a time period with high for massive gains.
It is more effective the more levels you have.

Once reaches the set value, let the black hole lock at the previous zero
Once the black hole is locked at the zero, manually disable it
Repeat these two steps until you reach the level indicated in the sim result

This strategy is extremely active.

Strategy credits:

AbsoPerf (discovery)
d4Nf6Bg51-0 (refining)
Mathis S. for the implementation in the sim
prop for the variable buying strategy
Hotab & Blackseal for the coasting strategy

▶︎ RZdBH Permalink: rzdbh

RZdBH
	When lvllvl
	✔️
	When cost is of cost
	✔️
	✔️
	✔️*
* Do not buy until .

When the theory simulator recommends this strategy, it will show something like:
RZdBH =388.85 : 3091 : 773.

The value after is the 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 and 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 Permalink: rzbh

RZBH
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

When the theory simulator recommends this strategy, it will show something like:
RZdBH =388.85 : 3091 : 773.

The value after is the 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 and 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 Permalink: rzspiralswap

RZSpiralSwap
	When lvllvl
	✔️
	When cost is of cost
	✔️
	✔️
	✔️*
* Do not buy until .

SpiralSwap

To perform SpiralSwap, switch milestones to prioritize exponent when is close to zero (when the graph is close to the origin) and to prioritize when .

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 : 953 : 238.

The levels it shows after and 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 Permalink: rzdms

RZdMS
	When lvllvl
	✔️
	When cost is of cost
	✔️
	✔️
	✔️*
* Do not buy until .

When the theory simulator recommends this strategy, it will show something like:
RZdMS swap: 197 : 953 : 238.

Start the publication with the milestone on. The value after swap is the value were you should switch it to exponent.

The levels it shows after and 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 Permalink: rzms

RZMS
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

When the theory simulator recommends this strategy, it will show something like:
RZdMS swap: 197 : 953 : 238.

Start the publication with the milestone on. The value after swap is the value were you should switch it to exponent.

The levels it shows after and 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 Permalink: rzd

RZd
	When lvllvl*
	✔️
	When cost is of cost
	✔️
	✔️
	✔️**
* If you don’t have exponent milestones, use instead.
** Do not buy until .

When the theory simulator recommends this strategy, it will show something like:
RZd : 953 : 238.

The levels it shows after and 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 Permalink: rz

RZ
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

When the theory simulator recommends this strategy, it will show something like:
RZ : 953 : 238.

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

Strategy credits:

Hotab & Blackseal for the coasting strategy

▶︎ Magnetic Fields Permalink: magnetic-fields

MFRC Permalink: mfrc

You may see at the end of a strategy RC (ex: MFd2RC). This stands for Reset Coast. To perform MFRC

stop buying if cost > 50% total reset cost, and
stop buying if cost > 10% total reset cost

where total reset cost = total cost of buying all + + + levels needed for a reset.

▶︎ MFVariantdxdxdx Permalink: mfvariantdxdxdx

This strategy is often referred to as MFVariant.

This strategy name will be broken down into multiple parts. What they mean are detailed below:

Description of Each Strat Name Section (in order)
MFVariant	Strat Name
dx (first)	buying strategy Either d1 or d2.
dx (second)	buying strategy Either d1 or d2.
dx (third)	buying strategy Either d1, d2, or d3.
RC	Reset Coast (see MFRC) This may not always be present.
Coast Depth x c1: xxx	Depth x is the depth used in sim. xxx is final level purchased.

MFVariant visual breakdown

d1, d2, and d3 means to follow the MFd, MFd2, MFd3 strategies for the corresponding variable.

For example, it could say MFVariantd1d2d2RCCoast Depth: 0 c1: 803.
This means to follow:

buying strategy from MFd
buying strategy from MFd2
buying strategy from MFd2
Reset Coast as detailed in MFRC

where

depth 0 was used during simulation (no bruteforcing), and
the last lvl purchased is lvl 803.

A full summary of the strategies can be found below, but may be hard to read.

d1	d2	d3
When cost is of cost	When costlvl% cost	When cost is of cost
✔️	✔️	✔️
When or cost is of cost	When or and cost is of cost	When or and cost is of
✔️	✔️	✔️
✔️	When cost is of cost	When cost is of cost and of cost
Only buy right before a reset
Only buy right before a reset
Only buy right before a reset
Only buy right before a reset

Strategy Credits:

Hackzzzzzz for the Variant idea and implementation (see reddit post)
BlackSeal for the initial implementation of resets in the sim
Maimai for the new rules
Mathis S. for the new reset algorithm

▶︎ MFd3 Permalink: mfd3

MFd3
	When cost is of cost
	✔️
	When or and cost is of
	✔️
	When cost is of cost and of cost
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset

Strategy Credits:

BlackSeal for the initial implementation of resets in the sim
Maimai for the new rules
Mathis S. for the new reset algorithm

▶︎ MFd2 Permalink: mfd2

MFd2
	When costlvl% cost
	✔️
	When or and cost is of cost
	✔️
	When cost is of cost
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset

Strategy Credits:

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

▶︎ MFd Permalink: mfd

MFd
	When cost is of cost
	✔️
	When or cost is of cost
	✔️
	✔️
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset

Strategy Credits:

BlackSeal for the implementation of resets in the sim

▶︎ MF Permalink: mf

MF
	✔️
	✔️
	✔️
	✔️
	✔️
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset
	Only buy right before a reset

Strategy Credits:

BlackSeal for the implementation of resets in the sim

▶︎ Basel Problem Permalink: basel-problem

▶︎ BaPAI Permalink: bapai

BaPAI
	✔️
	If cumulative cost to lvl% is x cheapest other purchase, buy until lvl%. When saving for lvl%, ✔️. Otherwise, buy at lvl% ratio to other variables.
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

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

Strategy credits:

Mathis S.

▶︎ BaPAIMS Permalink: 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 Permalink: bapcoast

BaPcoast
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

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

Strategy credits:

Mathis S.

▶︎ BaP Permalink: bap

BaP
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️
	✔️

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