Theory Strategies Explained
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The theory sim (simulation) we currently recommend was originally made by XLII, now maintained by the sim team and can be accessed here.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.
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T1SolarXLII xexxx — Very Active
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T1Ratio — Active
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T1C34 — Idle
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T1C4 — Idle
Theory 2: Differential Calculus #
T2 is the only theory without an active strategy after all milestones are bought, despite attempts.
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T2MC — Semi-Idle
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T2MCAlt2 — Semi-Idle
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T2MCAlt3 — Semi-Idle
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T2MS — Active
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T2QS — Semi-Idle
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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\(\rho\). T3ρ2C23d is an easier version being 10-15% slower.
T3SNAX is currently the best idle strategy above e200\(\rho\). T3SNAX2 is similar to T3SNAX but is designed to be QoL compatible.
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T3Play2 — Very Active
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T3Play — Very Active
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T3SNAX — Semi-Idle
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T3SNAXdC12 — Active recovery, then Semi-Idle
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T3SNAX2 — Active
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T3ρ2C23d — Active
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T3ρ2C23 — Idle
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T3ρ2C23C33d — Active
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T3ρ2C23C33 — Idle
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T3NoC11C13C21C33d — Active
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T3NoC11C13C21C33 — Idle
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T3NoC13C33d — Active
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T3NoC13C33 — Idle
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T3NoC11C13C33d — Active
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T3NoC11C13C33 — Idle
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T3NoC13C32C33d — Active
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T3NoC13C32C33 — Idle
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T3C11C12C21d — Active
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T3C11C12C21 — Idle
Theory 4: Polynomials #
T4 is the third-strongest theory in endgame, only behind T5 and T6.
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T4C3d66 — Active
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T4C3coast — Semi-Idle
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T4C3 — Idle
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T4C3dC12rcv — Active
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T4C356dC12rcv — Active
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T4C456dC12rcvMS — Active
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T4C123d — Active
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T4C123 — Idle
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T4C12d — Active
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T4C12 — Idle
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T4C56 — Idle
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T4C4 — Idle
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T4C5 — Idle
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T4 — Idle
Theory 5: Logistic Function #
T5 is the second-strongest theory in endgame, only behind T6.
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T5AI — Active
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T5Idle xexxx — Semi-Idle
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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.
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T6AI — Active
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T6SNAX x.xxexxx — Semi-Idle
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T6NoC34d — Active
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T6NoC34 — Idle
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T6NoC1234d — Active
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T6NoC1234 — Idle
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T6NoC345d — Active
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T6NoC345 — Idle
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T6C4d — Active
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T6C4 — Idle
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T6C3d — Active
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T6C3 — Idle
Theory 7: Numerical Methods #
T7 is the third-weakest theory in endgame, ahead of T2 and T8.
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T7PlaySpqceyX — Active
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T7C3d — Active
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T7C12d — Active
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T7C12 — Idle
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T7C123d — Active
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T7NoC12 — Idle
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T7NoC123 — Idle
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T7NoC124 — Idle
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T7NoC1234 — Idle
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T7 — Idle
Theory 8: Chaos Theory #
T8 is the weakest theory in endgame and has the most active strategy of any main theory (T8PlaySolarSwap).
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T8PlaySolarSwap — VERY Active
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T8Play — Active
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T8SNAX — Semi-Idle
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T8NoC35d — Active
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T8NoC35 — Idle
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T8NoC5d — Active
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T8NoC5 — Idle
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T8NoC3d — Active
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T8NoC3 — Idle
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T8d — Active
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T8 — Idle
Official Custom Theories #
In chronological order of release.
Custom Theory 1: Weierstraß Sine Product #
The first official custom theory, abbreviated WSP, was created by xelaroc and released on January 15, 2022.
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WSPdStopC1 — Active
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WSPStopC1 — Semi-Idle
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WSP — Idle
Custom Theory 2: Sequential Limits #
The second official custom theory, abbreviated SL, was created by ellipsis and released on January 22, 2022.
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 tau cap increase.
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 tau cap increase from e100 to e150.
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CSR2XL x.xx — VERY Active pre-e500\(\rho\), Active post-e500\(\rho\)
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CSR2d — Active
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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 tau contribution rate increase by x4.
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FId — Active
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FI — Idle
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FIMSd — Active
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FIMS — Active
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FIdPermaSwap — Active
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FIPermaSwap — Semi-Idle
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FIMSdPermaSwap — Active
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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 tau contribution rate increase by x4.
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FPmodBurstC1MS — Active
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FPdMS — Active
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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.
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RZdBH — Active
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RZBH — Idle
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RZSpiralSwap — EXTREMELY Active
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RZdMS — Active
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RZMS — Semi-Idle
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RZd — Active
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RZ — Idle
Theory 1: Recurrence Relations #
T1SolarXLII xexxx #
T1SolarXLII xexxx | ||
---|---|---|
Below xexxx | Above xexxx | |
q1 | When q1cost × (6 + lvl % 10) < q2 cost And q1 cost × (15 + lvl % 10) < c4 cost And ρ > 5 × cost |
❌ |
q2 | When ρ > 1.11 × cost | ❌ |
c1 | See T1Ratio | ❌ |
c2 | See T1Ratio | ❌ |
c3 | See T1Ratio | ❌ |
c4 | ✔️ | ❌ |
The “xexxx” is returned by the recommended theory simulator. For example, it could say “3e647”.
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 #
T1Ratio | |
---|---|
q1 | When ρ > 10 × cost |
q2 | When ρ > 1.11 × cost |
c1 | When ρ > 10 × c2ratio × cost |
c2 | When ρ > c2ratio × cost |
c3 | When ρ > c3ratio × cost |
c4 | ✔️ |
Do not buy \(c_1\) or \(c_2\) after e300\(\rho\).
For the \(c_2\) Ratio:
For the \(c_3\) Ratio:
c3 Ratio | |
---|---|
ρ < e300 | 1 |
e300 < ρ < e450 | 1.1 |
e450 < ρ < e550 | 2 |
e550 < ρ < e655 | 5 |
ρ > e655 | 10 |
Strategy Credits:
- XLII
T1C34 #
T1C34 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ✔️ |
T1C4 #
T1C4 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ✔️ |
Theory 2: Differential Calculus #
T2MC #
T2MC | |||||
---|---|---|---|---|---|
Publication Multiplier below 1150 | Publication Multiplier 1150-2250 | Publication Multiplier 2250-2900 | Publication Multiplier 2900-4650 | Publication Multiplier above 4650 | |
q1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
q2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
q3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
q4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
r1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
r2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
r3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
r4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
Strategy Credits:
- rus9384#1864
- XLII, whose theory simulator was used to develop and test this strategy.
The “MC” in T2MC stands for MultivariableCoast.
T2MCAlt2 #
T2MCAlt2 | |||||
---|---|---|---|---|---|
Publication Multiplier below 550 | Publication Multiplier 550-2050 | Publication Multiplier 2050-2700 | Publication Multiplier 2700-3500 | Publication Multiplier above 3500 | |
q1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
q2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
q3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
q4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
r1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
r2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
r3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
r4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
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 #
T2MCAlt3 | |||||
---|---|---|---|---|---|
Publication Multiplier below 750 | Publication Multiplier 750-1700 | Publication Multiplier 1700-2650 | Publication Multiplier 2650-3700 | Publication Multiplier above 3700 | |
q1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
q2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
q3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
q4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
r1 | ✔️ | ✔️ | ✔️ | ✔️ | ❌ |
r2 | ✔️ | ✔️ | ✔️ | ❌ | ❌ |
r3 | ✔️ | ✔️ | ❌ | ❌ | ❌ |
r4 | ✔️ | ❌ | ❌ | ❌ | ❌ |
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 #
T2QS | |||||
---|---|---|---|---|---|
q1 | ✔️ | ||||
q2 | ✔️ | ||||
q3 | ✔️ | ||||
q4 | ✔️ | ||||
r1 | ✔️ | ||||
r2 | ✔️ | ||||
r3 | ✔️ | ||||
r4 | ✔️ |
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 \(\rho\) is \(\rho\) at the end of your last publication:
Publication Multiplier | |
---|---|
ρ < e75 | 10 |
e75 < ρ < e150 | 200 |
e150 < ρ < e200 | 600 |
e200 < ρ < e225 | 100 |
ρ > e225 | 25 |
T2 #
T2 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
q3 | ✔️ |
q4 | ✔️ |
r1 | ✔️ |
r2 | ✔️ |
r3 | ✔️ |
r4 | ✔️ |
Theory 3: Linear Algebra #
T3Play2 #
T3Play2 | ||||
---|---|---|---|---|
Recovery up until e1 away from recovered * | From e1 away from recovered until 1.2 Pub Mult | Publication Mult 1.2-2.4 | Coasting (pub mult > 2.4) | |
b1 | When ⅛ of c31 cost | ❌ | ❌ | ❌ |
b2 | When ⅕ of c32 cost | When ⅕ of c32 cost | When ⅛ of c12 cost | ✔️ |
b3 | When ⅛ of c23 cost | When ⅛ of c23 cost | When ⅛ of c23 cost | ✔️ |
c11 | ❌ | ❌ | ❌ | ❌ |
c12 | When 1/100 of c32 cost | When 1/100 of c32 cost | ✔️ | ✔️ |
c13 | ❌ | ❌ | ❌ | ❌ |
c21 | ❌ | ❌ | ❌ | ❌ |
c22 | When ⅖ of c32 cost | When ⅖ of c32 cost | When ⅛ of c12 cost | ❌ |
c23 | ✔️ | ✔️ | ✔️ | ✔️ |
c31 | ✔️ | ❌ | ❌ | ❌ |
c32 | ✔️ | ✔️ | When ⅛ of c12 cost | ❌ |
c33 | When 1/10 of c23 cost | When 1/10 of c23 cost | ❌ | ❌ |
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.
* 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.
T3Play #
T3Play | |||
---|---|---|---|
Recovery (pub mult < 1) | Publication Mult 1-2 | Coasting (pub mult > 2) | |
b1 | When cost is ⅛ of c31 cost | When cost is ⅛ of c31 cost | ❌ |
b2 | When cost is 2/9 of c12 cost, 4/9 of c22 cost | When cost is ¼ of c32, c12 cost, ½ of c22 cost | ✔️ |
b3 | When cost is ⅛ of c23 cost, 4/9 of c33 cost | When cost is ⅛ of c23 cost, ½ of c33 cost | When cost is ⅛ of c23 cost, ½ of c33 cost |
c11 | ❌ | ❌ | ❌ |
c12 | ✔️ | ✔️ | ✔️ |
c13 | ❌ | ❌ | ❌ |
c21 | ❌ | ❌ | ❌ |
c22 | When cost is ½ of c32, c12 cost | When cost is ½ of c32, c12 cost | ✔️ |
c23 | ✔️ | ✔️ | ✔️ |
c31 | ✔️ | ✔️ | ❌ |
c32 | ✔️ | ✔️ | ✔️ |
c33 | When cost is 9/32 of c23 cost | When cost is ¼ of c23 cost | When cost is ¼ of c23 cost |
Strategy Credits:
- Playspout for creating this strategy.
- xelaroc, whose sim was used to verify Playspout’s results
T3SNAX #
T3SNAX | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
b1 | ✔️ | ❌ |
b2 | ✔️ | ✔️ |
b3 | ✔️ | ✔️ |
c11 | ❌ | ❌ |
c12 | ✔️ | ✔️ |
c13 | ❌ | ❌ |
c21 | ❌ | ❌ |
c22 | ✔️ | ✔️ |
c23 | ✔️ | ✔️ |
c31 | ✔️ | ❌ |
c32 | ✔️ | ❌ |
c33 | ✔️ | ❌ |
Strategy Credits:
- Snaeky for the idea.
- XLII for simulating the strategy
T3SNAXdC12 #
T3SNAXdC12 | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
b1 | ✔️ | ❌ |
b2 | ✔️ | ✔️ |
b3 | ✔️ | ✔️ |
c11 | ❌ | ❌ |
c12 | When cost × 100 < c32 cost | ✔️ |
c13 | ❌ | ❌ |
c21 | ❌ | ❌ |
c22 | ✔️ | ✔️ |
c23 | ✔️ | ✔️ |
c31 | ✔️ | ❌ |
c32 | ✔️ | ❌ |
c33 | ✔️ | ❌ |
Strategy Credits:
- Snaeky for the idea.
- XLII for simulating the strategy and finding optimal ratios.
T3SNAX2 #
T3SNAX2 | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
b1 | When cost is 1/10 of ρ1 | ❌ |
b2 | When cost is ⅓ of ρ2 | When cost is ⅓ of ρ2 |
b3 | When cost is ⅕ of ρ3 | When cost is ⅕ of ρ3 |
c11 | ❌ | ❌ |
c12 | When cost is 1/100 of ρ2 | ✔️ |
c13 | ❌ | ❌ |
c21 | ❌ | ❌ |
c22 | ✔️ | When cost is ⅛ of ρ2 |
c23 | ✔️ | ✔️ |
c31 | ✔️ | ❌ |
c32 | ✔️ | ❌ |
c33 | When cost is 1/10 of ρ3 | ❌ |
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 #
T3ρ2C23d | |
---|---|
b1 | ❌ |
b2 | When cost is ⅓ of min(c12 cost, c22 cost, c32 cost) |
b3 | When cost is 1/9 of c23 cost |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ❌ |
c32 | ✔️ |
c33 | ❌ |
T3ρ2C23 #
T3ρ2C23 | |
---|---|
b1 | ❌ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ❌ |
c32 | ✔️ |
c33 | ❌ |
T3ρ2C23C33d #
T3ρ2C23C33d | |
---|---|
b1 | ❌ |
b2 | When cost is ⅓ of min(c12 cost, c22 cost, c32 cost) |
b3 | When cost is 1/9 of c23 cost |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ❌ |
c32 | ✔️ |
c33 | ✔️ |
T3ρ2C23C33 #
T3ρ2C23C33 | |
---|---|
b1 | ❌ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ❌ |
c32 | ✔️ |
c33 | ✔️ |
T3NoC11C13C21C33d #
T3NoC11C13C21C33d | |
---|---|
b1 | When cost is 1/8 of c31 cost |
b2 | When cost is 1/5 of other ρ2 variables’ cost (c12, c22, c32) |
b3 | When cost is 1/8 of c23 cost |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC11C13C21C33 #
T3NoC11C13C21C33 | |
---|---|
b1 | ✔️ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ❌ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC13C33d #
T3NoC13C33d | |
---|---|
b1 | When cost is 1/10 of min(c21 cost, c31 cost) |
b2 | When cost is ¼ of min(c12, c22, c32) |
b3 | When cost is 1/10 of c23 cost |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC13C33 #
T3NoC13C33 | |
---|---|
b1 | ✔️ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC11C13C33d #
T3NoC11C13C33d | |
---|---|
b1 | When cost is 1/10 of min(c21 cost, c31 cost) |
b2 | When cost is ¼ of min(c12, c22, c32) |
b3 | When cost is 1/10 of c23 cost |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC11C13C33 #
T3NoC11C13C33d | |
---|---|
b1 | ✔️ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ❌ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ✔️ |
c33 | ❌ |
T3NoC13C32C33d #
T3C13C32C33d | |
---|---|
b1 | When cost is ⅛ of min(c11 cost, c21 cost, c31 cost) |
b2 | When cost is ⅕ of min(c12 cost, c22 cost) |
b3 | When cost is ⅛ of c23 cost |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ❌ |
c33 | ❌ |
T3NoC13C32C33 #
T3C13C32C33 | |
---|---|
b1 | ✔️ |
b2 | ✔️ |
b3 | ✔️ |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ✔️ |
c23 | ✔️ |
c31 | ✔️ |
c32 | ❌ |
c33 | ❌ |
T3C11C12C21d #
T3C11C12C21d | |
---|---|
b1 | When cost is ⅐ of min(c11 cost, c21 cost) |
b2 | When cost is ⅐ of c12 cost |
b3 | ❌ |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ❌ |
c23 | ❌ |
c31 | ❌ |
c32 | ❌ |
c33 | ❌ |
T3C11C12C21 #
T3C11C12C21 | |
---|---|
b1 | ✔️ |
b2 | ✔️ |
b3 | ❌ |
c11 | ✔️ |
c12 | ✔️ |
c13 | ❌ |
c21 | ✔️ |
c22 | ❌ |
c23 | ❌ |
c31 | ❌ |
c32 | ❌ |
c33 | ❌ |
Theory 4: Polynomials #
T4C3d66 #
T4C3d66 | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
c1 | ❌ | ❌ |
c2 | ❌ | ❌ |
c3 | ✔️ | ✔️ |
c4 | ❌ | ❌ |
c5 | ❌ | ❌ |
c6 | ❌ | ❌ |
q1 | When 10 + q1lvl % 10 times cheaper than min(q2 cost, c3 cost) | When 10 + q1lvl % 10 times cheaper than min(q2 cost, c3 cost) |
q2 | ✔️ | When cost is ⅔ of c3 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 #
T4C3coast | ||
---|---|---|
c1 | ❌ | |
c2 | ❌ | |
c3 | ✔️ | |
c4 | ❌ | |
c5 | ❌ | |
c6 | ❌ | |
q1 | ✔️ | |
q2 | ✔️ |
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 #
T4C3 | |
---|---|
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
q1 | ✔️ |
q2 | ✔️ |
T4C3dC12rcv #
T4C3dC12rcv | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
c1 | When cost is 1/10 of c2 cost | ❌ |
c2 | ✔️ | ❌ |
c3 | ✔️ | ✔️ |
c4 | ❌ | ❌ |
c5 | ❌ | ❌ |
c6 | ❌ | ❌ |
q1 | When cost is 1/10 of q2 cost | When cost is 1/10 of q2 cost |
q2 | ✔️ | ✔️ |
T4C356dC12rcv #
T4C356dC12rcv | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
c1 | When cost is 1/10 of c2 cost | ❌ |
c2 | ✔️ | ❌ |
c3 | ✔️ | ✔️ |
c4 | ❌ | ❌ |
c5 | ✔️ | ✔️ |
c6 | ✔️ | ✔️ |
q1 | When cost is 1/10 of q2 cost | When cost is 1/10 of q2 cost |
q2 | ✔️ | ✔️ |
T4C456dC12rcvMS #
T4C456dC12rcvMS | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
c1 | When cost is 1/10 of c2 cost | ❌ |
c2 | ✔️ | ❌ |
c3 | ❌ | ❌ |
c4 | ✔️ | ✔️ |
c5 | ✔️ | ✔️ |
c6 | ✔️ | ✔️ |
q1 | When cost is 1/10 of q2 cost | When cost is 1/10 of q2 cost |
q2 | ✔️ | ✔️ |
Milestone swapping strategy
- During your recovery phase, set your milestones in the order 2→3→1
- During the tau 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 #
T4C123d | |
---|---|
c1 | When cost is 1/10 of c2 cost |
c2 | ✔️ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
q1 | When cost is 1/10 of q2 cost |
q2 | ✔️ |
This strategy is typically seen at lower \(\rho\) and is eventually outpaced by T4C3d66.
T4C123 #
T4C123 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
q1 | ✔️ |
q2 | ✔️ |
This strategy is typically seen at lower \(\rho\) and is eventually outpaced by T4C3.
T4C12d #
T4C12d | |
---|---|
c1 | When cost is 1/10 of c2 cost |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
q1 | ❌ |
q2 | ❌ |
T4C12 #
T4C12 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
q1 | ❌ |
q2 | ❌ |
T4C56 #
T4C56 | |
---|---|
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
c6 | ✔️ |
q1 | ✔️ |
q2 | ✔️ |
T4C4 #
T4C4 | |
---|---|
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ✔️ |
c5 | ❌ |
c6 | ❌ |
q1 | ✔️ |
q2 | ✔️ |
T4C5 #
T4C5 | |
---|---|
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
c6 | ❌ |
q1 | ✔️ |
q2 | ✔️ |
T4 #
T4 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ✔️ |
c6 | ✔️ |
q1 | ✔️ |
q2 | ✔️ |
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 #
T5Idle xexxx | ||
---|---|---|
Before xexxx ρ | After xexxx ρ | |
q1 | ✔️ | ✔️ |
q2 | ✔️ | ✔️ |
c1 | ✔️ | ❌ |
c2 | ✔️ | ✔️ |
c3 | ✔️ | ✔️ |
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 recommended theory simulator. For example, it could say “3e647”.
Strategy Credit:
- XLII
T5 #
T5 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
Theory 6: Integral Calculus #
T6AI #
T6AI | |
---|---|
q1 | When 7 + q1lvl % 10 times cheaper than min(q2, r2, c5) |
q2 | ✔️ |
r1 | When 5 + r1lvl % 10 times cheaper than min(q2, r2, c5) |
r2 | ✔️ |
c1 | When 8 + c1lvl % 10 times cheaper than c2 |
c2 | As the publication progresses, buy less and less c2 (and therefore less c1 too) |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
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 #
T6SNAX x.xxexxx | ||
---|---|---|
Before x.xxexxx | After x.xxexxx | |
q1 | ✔️ | ✔️ |
q2 | ✔️ | ✔️ |
r1 | ✔️ | ✔️ |
r2 | ✔️ | ✔️ |
c1 | ✔️ | ❌ |
c2 | ✔️ | ❌ |
c3 | ❌ | ❌ |
c4 | ❌ | ❌ |
c5 | ✔️ | ✔️ |
The “x.xxexxx” is returned by the recommended theory simulator. For example, it could say “3e647”.
Strategy Credits:
- Snaeky
- XLII
T6NoC34d #
T6NoC34d | |
---|---|
q1 | When cost is 1/10 of q2 cost |
q2 | ✔️ |
r1 | When cost is 1/10 of r2 cost |
r2 | ✔️ |
c1 | When cost is 1/10 of c2 cost |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
T6NoC34 #
T6NoC34 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
r2 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
T6NoC1234d #
T6NoC1234d | |
---|---|
q1 | When 7 + q1lvl % 10 times times cheaper than min(q2, r2, c5,) |
q2 | ✔️ |
r1 | When 5 times cheaper than min(q2, r2, c5,) |
r2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
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 #
T6NoC1234 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
r2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
T6NoC345d #
T6NoC345d | |
---|---|
q1 | When cost is 1/10 of q2 cost |
q2 | ✔️ |
r1 | When cost is 1/10 of r2 cost |
r2 | ✔️ |
c1 | When cost is 1/10 of c2 cost |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
This strategy is sometimes seen at lower taus but not at higher taus.
T6NoC345 #
T6NoC345 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
r2 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
This strategy is sometimes seen at lower taus but not at higher taus.
T6C4d #
T6C4d | |
---|---|
q1 | When cost is ⅕ of min(c4 cost, q2 cost, r2 cost) |
q2 | ✔️ |
r1 | When cost is ⅕ of min(c4 cost, q2 cost, r2 cost) |
r2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ✔️ |
c5 | ❌ |
T6C4 #
T6C4 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
r2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ✔️ |
c5 | ❌ |
T6C3d #
T6C3d | |
---|---|
q1 | When cost is ⅓ of min(q2 cost, c3 cost) |
q2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
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 #
T6C3 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
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:
T7PlaySpqcey | |
---|---|
q1 | When cost is ¼ of c6 cost |
c1 | ❌ |
c2 | ❌ |
c3 | When cost is 1/10 of c6 cost |
c4 | When cost is 1/10 of c6 cost |
c5 | When cost is ¼ of c6 cost |
c6 | ✔️ |
If there is a number after T7PlaySpqcey (Example: T7PlaySpqcey10 or T7PlaySpqcey100), then use this table:
T7PlaySpqceyX | |
---|---|
q1 | When cost is ¼ of c6 cost |
c1 | When cost is 1/10 of c2 cost |
c2 | When X times cheaper than c6 cost |
c3 | When cost is 1/10 of c6 cost |
c4 | When cost is 1/10 of c6 cost |
c5 | When cost is ¼ of c6 cost |
c6 | ✔️ |
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 1/10 of \(c_2\) cost”
The number after T7PlaySpqcey occurs more at lower \(\tau\) 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 #
T7C3d | |
---|---|
q1 | When cost is 1/10 of c3 cost |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
T7C12d #
T7C12d | |
---|---|
q1 | When cost is 1/10 of c2 cost |
c1 | When cost is ⅛ of c2 cost |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
T7C12 #
T7C12 | |
---|---|
q1 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
T7C123d #
T7C123d | |
---|---|
q1 | When cost is 1/10 of min(c2 cost, c3 cost) |
c1 | When cost is ⅛ of min(c2 cost, c3 cost) |
c2 | ✔️ |
c3 | ✔️ |
c4 | ❌ |
c5 | ❌ |
c6 | ❌ |
T7NoC12 #
T7NoC12 | |
---|---|
q1 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ✔️ |
c6 | ✔️ |
T7NoC123 #
T7NoC123 | |
---|---|
q1 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ✔️ |
c5 | ✔️ |
c6 | ✔️ |
T7NoC124 #
T7NoC124 | |
---|---|
q1 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ✔️ |
c4 | ❌ |
c5 | ✔️ |
c6 | ✔️ |
T7NoC1234 #
T7NoC1234 | |
---|---|
q1 | ✔️ |
c1 | ❌ |
c2 | ❌ |
c3 | ❌ |
c4 | ❌ |
c5 | ✔️ |
c6 | ✔️ |
T7 #
T7 | |
---|---|
q1 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ✔️ |
c6 | ✔️ |
Theory 8: Chaos Theory #
T8PlaySolarSwap #
T8PlaySolarSwap | |
---|---|
c1 | When 5 + c1lvl % 10 times cheaper than min(c2 cost, c4 cost) |
c2 | ✔️ |
c3 | When cost is ⅖ of min(c2 cost, c4 cost) |
c4 | ✔️ |
c5 | When cost is ⅖ of min(c2 cost, c4 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 #
T8Play | |
---|---|
c1 | When cost is ⅛ of min(c2 cost, c4 cost) |
c2 | ✔️ |
c3 | When cost is ⅖ of min(c2 cost, c4 cost) |
c4 | ✔️ |
c5 | When cost is ¼ of min(c2 cost, c4 cost) |
Strategy Credits:
- Playspout
T8SNAX #
T8SNAX | |||
---|---|---|---|
Publication Multiplier < 1.6 | Publication Multiplier 1.6-2.3 | Publication Multiplier > 2.3 | |
c1 | ✔️ | ❌ | ❌ |
c2 | ✔️ | ✔️ | ✔️ |
c3 | ✔️ | ✔️ | ❌ |
c4 | ✔️ | ✔️ | ✔️ |
c5 | ✔️ | ✔️ | ❌ |
Strategy Credits:
- Snaeky
- XLII
T8NoC35d #
T8NoC35d | |
---|---|
c1 | When 10 times cheaper than min(c2 cost, c4 cost) |
c2 | ✔️ |
c3 | ❌ |
c4 | ✔️ |
c5 | ❌ |
If you are confused about the “%”, read about it here.
T8NoC35 #
T8NoC35 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ✔️ |
c5 | ❌ |
T8NoC5d #
T8NoC5d | |
---|---|
c1 | When cost is 1/10 of min(c2 cost, c4 cost) |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ❌ |
T8NoC5 #
T8NoC5 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ❌ |
T8NoC3d #
T8NoC3d | |
---|---|
c1 | When cost is 1/10 of min(c2 cost, c4 cost) |
c2 | ✔️ |
c3 | ❌ |
c4 | ✔️ |
c5 | ✔️ |
T8NoC3 #
T8NoC3 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ❌ |
c4 | ✔️ |
c5 | ✔️ |
T8d #
T8d | |
---|---|
c1 | When cost is 1/10 of c2 cost |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ✔️ |
T8 #
T8 | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
c3 | ✔️ |
c4 | ✔️ |
c5 | ✔️ |
Weierstraß Sine Product #
WSPdStopC1 #
WSPdStopC1 | ||
---|---|---|
First 15 Seconds of Publication | Rest of Publication | |
q1 | When 8 + q1lvl % 10 times cheaper than min(q2 cost, n cost, c2 cost) | When 8 + q1lvl % 10 times cheaper than min(q2 cost, n cost, c2 cost) |
q2 | ✔️ | ✔️ |
n | ✔️ | ✔️ |
c1 | ✔️ | When cost 1/Ratio of min(q2 cost, n cost, c2 cost) |
c2 | ✔️ | ✔️ |
If you are confused about the “%”, read about it here.
The “Ratio” stated in \(c_1\) is determined as follows, where \(\rho\) is \(\rho\) at the end of your last publication:
c1 Ratio | |
---|---|
ρ < e25 | 1 |
e25 < ρ < e40 | 3 |
e40 < ρ < e200 | 10 |
e200 < ρ < e400 | 50 |
e400 < ρ < e700 | 1000 |
ρ > e700 | Do not buy c1 after 15 seconds 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 #
WSPStopC1 | ||
---|---|---|
First 15 Seconds of Publication | Rest of Publication | |
q1 | ✔️ | ✔️ |
q2 | ✔️ | ✔️ |
n | ✔️ | ✔️ |
c1 | ✔️ | If ρ < e450, ✔️ If ρ > e450, ❌ |
c2 | ✔️ | ✔️ |
Strategy Credits:
- xelaroc for simulating it/adding it to the sim
- Snaeky for the stop \(c_1\) idea
- XLII for \(c_1\) modification
WSP #
WSP | ||
---|---|---|
q1 | ✔️ | |
q2 | ✔️ | |
n | ✔️ | |
c1 | ✔️ | |
c2 | ✔️ |
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 \(e-\gamma\) term)
State 2: 2→1→4→3 (prioritizes boost for \(\dot\rho_2\))
State 3: 1→2→4→3 (prioritizes boost for instantaneous \(\rho\) gain, aka \(\rho_2\) 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 \(\dot\rho_2\) so we get more \(\rho_2\) 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 \(\rho_2\). 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\(\rho\)-e300\(\rho\). 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 \(\rho\) boost before publishing.
As long as \(\rho\) < 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: \(\frac{min(b_1 cost, b_2 cost)}{\rho}\) is lower than the ratio provided under the header:
Ratios for Swapping | |||
---|---|---|---|
State 1 | State 2 | State 3 | |
e25ρ-e50ρ | Until 5x cost/ρ Ratio | Until 4x cost/ρ Ratio | Until upgrade is bought |
e50ρ-e75ρ | Until 7x cost/ρ Ratio | Until 6x cost/ρ Ratio | Until upgrade is bought |
e75ρ-e100ρ | Until 12x cost/ρ Ratio | Until 10x cost/ρ Ratio | Until upgrade is bought |
e100ρ-e150ρ | Until 20x cost/ρ Ratio | Until 15x cost/ρ Ratio | Until upgrade is bought |
e150ρ-e175ρ | Until 8x cost/ρ Ratio | Until 6x cost/ρ Ratio | Until upgrade is bought |
e175ρ-e200ρ | Until 1.5x cost/ρ Ratio | Until upgrade is bought | Skip |
e200ρ-e275ρ | Until 3x cost/ρ Ratio | Skip | Until upgrade is bought |
e275ρ-e300ρ | Until 2x cost/ρ Ratio | Skip | Until upgrade is bought |
cost in the table refers to minimum(\(b_1\) cost, \(b_2\) cost)
This may seem confusing, but let’s take the first row as an example.
In the first phase (e25\(\rho\) - e50\(\rho\)) you should have your milestones in State 1 until \(\rho\) is 1/5 of min(\(b_1\) cost, \(b_2\) cost).
Then, swap to State 2 until \(\rho\) 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\(\rho\)+ range, you only want to swap when close to next \(b_1\)/\(b_2\). and e75-e150\(\rho\) 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 | |||
---|---|---|---|
Publication Mult < 4 | Publication Mult 4-7.5 | Publication Mult > 7.5 | |
a1 | ✔️ | ❌ | ❌ |
a2 | ✔️ | ❌ | ❌ |
b1 | ✔️ | ✔️ | ❌ |
b2 | ✔️ | ✔️ | ❌ |
Strategy Credit:
- XLII
SLMSd #
For the milestone swapping details, read the above strategy, SLMS. This strategy only modifies the variable buying strategies.
SLMSd | |||
---|---|---|---|
Publication Mult < 4 | Publication Mult 4-7.5 | Publication Mult > 7.5 | |
a1 | If a1lvl % 3 = 0, then ✔️ If not, buy when 2 × (a1lvl % 3) times cheaper than a2 cost |
❌ | ❌ |
a2 | ✔️ | ❌ | ❌ |
b1 | If b1lvl % 4 = 0 or 1, then ✔️ If not, buy when b1lvl % 4 times cheaper than b2 cost |
If b1lvl % 4 = 0 or 1, then ✔️ If not, buy when b1lvl % 4 times cheaper than b2 cost |
❌ |
b2 | ✔️ | ✔️ | ❌ |
If you are confused about the “%”, read about it here.
Strategy Credit:
- XLII
SLStopAd #
SLStopAd | |||
---|---|---|---|
Publication Mult < 4.5 | Publication Mult 4.5-6 | Publication Mult > 6 | |
a1 | If a1lvl % 3 = 0, then ✔️ If not, buy when 2 × (a1lvl % 3) times cheaper than a2 cost |
❌ | ❌ |
a2 | ✔️ | ❌ | ❌ |
b1 | If b1lvl % 4 = 0 or 1, then ✔️ If not, buy when b1lvl % 4 times cheaper than b2 cost |
If b1lvl % 4 = 0 or 1, then ✔️ If not, buy when b1lvl % 4 times cheaper than b2 cost |
❌ |
b2 | ✔️ | ✔️ | ❌ |
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 #
SLStopA | |||
---|---|---|---|
Publication Mult < 4.5 | Publication Mult 4.5-6 | Publication Mult > 6 | |
a1 | ✔️ | ❌ | ❌ |
a2 | ✔️ | ❌ | ❌ |
b1 | ✔️ | ✔️ | ❌ |
b2 | ✔️ | ✔️ | ❌ |
Strategy Credits:
- xelaroc
- Playspout
- rus9384#1864 for \(b_1\), \(b_2\) coasting at 6 publication multiplier
Euler’s Formula #
EFAI #
EFAI | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
ṫ | ✔️ | ✔️ |
q1 | When cost × (10 + lvl % 10) < q2 cost | When cost × (10 + lvl % 10) < q2 cost |
q2 | ✔️ | ✔️ |
b1 | ✔️ | When ⅕ of a2 cost |
b2 | ✔️ | When ⅕ of a2 cost |
c1 | ✔️ | When ⅕ of a3 cost |
c2 | ✔️ | When ⅕ of a3 cost |
a1 | When cost × (4 + (lvl % 10)/2) < q2 cost | When cost × (4 + (lvl % 10)/2) < q2 cost |
a2 | ✔️ | ✔️ |
a3 | ✔️ | ✔️ |
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 #
EFSNAX | ||
---|---|---|
Recovery (pub mult < 1) | Tau Gain (pub mult > 1) | |
ṫ | ✔️ | ✔️ |
q1 | ✔️ | ❌ |
q2 | ✔️ | ✔️ |
b1 | ✔️ | ❌ |
b2 | ✔️ | ❌ |
c1 | ✔️ | ❌ |
c2 | ✔️ | ❌ |
a1 | ✔️ | ✔️ |
a2 | ✔️ | ✔️ |
a3 | ✔️ | ✔️ |
Strategy Credits:
- Snaeky
- XLII
- Gaunter for buying \(a_1\) after recovery when past e150\(\rho\) strategy
* If below e150\(\rho\), don’t autobuy \(a_1\) after recovery.
EFd #
EFd | |
---|---|
ṫ | ✔️ |
q1 | When cost is 1/10 of q2 cost |
q2 | ✔️ |
b1 | ✔️ |
b2 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
a1 | When cost is ¼ of q2 cost |
a2 | ✔️ |
a3 | ✔️ |
EF #
EF | |
---|---|
ṫ | ✔️ |
q1 | ✔️ |
q2 | ✔️ |
b1 | ✔️ |
b2 | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
a1 | ✔️ |
a2 | ✔️ |
a3 | ✔️ |
Convergents to √2 #
CSR2XL x.xx #
CSR2XL x.xx | ||
---|---|---|
Before x.xx Publication Multiplier | After x.xx Publication Multiplier | |
q1 | When cost × 10 < min(q2c, nc, c2c), where c = cost | ❌ |
q2 | ✔️(if q2 has a similar cost to either n or c2, prioritize the other variable over q2) |
❌ |
c1 | When cost × 10 < min (q2c, nc, c2c) | ❌ |
n | ✔️(if n and c2 have similar costs, prioritize c2) | ❌ |
c2 | ✔️ | ❌ |
The “x.xx” is returned by the recommended theory simulator. For example, it could say “CSR2XL 2.85”, which would mean turn off autobuy on all variables at 2.85 publication multiplier.
Milestone Swap (pre e500\(\rho\))
Start publication with milestones in \(c_2\)/\(c_2\) exponent.
Swap to \(q_1\) exponent when one of these is true:
- \(\rho\) × Ratio > \(c_2\) cost
- \(\rho\) × \(\frac{Ratio}{2}\) > \(n\) cost
- \(\rho\) × 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 \(\rho\) is \(\rho\) at the end of your last publication:
Ratio | |
---|---|
ρ < e45 | Couldn't find any good ratio here, just swap when you are very close to the upgrade. - XLII |
e45 < ρ < e80 | 4 |
e80 < ρ < e115 | 8 |
e115 < ρ < e220 | 20 |
ρ > e220 | 40 |
Strategy Credits:
- XLII
CSR2d #
CSR2d | |
---|---|
q1 | When cost × 10 < min(q2, n, c2), where c = cost |
q2 | ✔️ |
c1 | When cost × 10 < min(q2, n, c2), where c = cost |
n | ✔️ |
c2 | ✔️ |
CSR2 #
CSR2 | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
c1 | ✔️ |
n | ✔️ |
c2 | ✔️ |
Fractional Integration #
FId #
FId | |
---|---|
q1 | When cost × (1 + lvl % 23) < min(q2 cost, K cost) |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | When cost × (1 + lvl % 11) < min(q2 cost, K cost, m cost) |
Milestone routing information
This strategy does not use the 3rd level of the g(x) milestone until you unlock the last milestone point at e1150ρ.
FI #
FI | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | ✔️ |
Milestone routing information
This strategy does not use the 3rd level of the g(x) milestone until you unlock the last milestone point at e1150ρ.
FIMSd #
FIMSd | |
---|---|
q1 | When cost × (1 + lvl % 23) < min(q2 cost, K cost) |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | When cost × (1 + lvl % 11) < min(q2 cost, K cost, m cost) |
Milestone swapping strategy
When buying a new level of q2, swap n and m milestones to q1 exponent to build up q.
Swap back to m and n when your q got multiplied by a ratio (since you started the swapping phase) depending on your q1 lvl % 23:
q1 lvl % 23 | q ratio |
---|---|
1-4 | 4 |
5-9 | 3 |
10-19 | 2.5 |
20+ | 2 |
Strategy Credits:
- Playspout for the milestone swapping strategy
FIMS #
FIMS | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | ✔️ |
Milestone swapping strategy
When buying a new level of q2, swap n and m milestones to q1 exponent to build up q.
Swap back to m and n when your q got multiplied by a ratio (since you started the swapping phase) depending on your q1 lvl % 23:
q1 lvl % 23 | q ratio |
---|---|
1-4 | 4 |
5-9 | 3 |
10-19 | 2.5 |
20+ | 2 |
Strategy Credits:
- Playspout for the milestone swapping strategy
FIdPermaSwap #
FIdPermaSwap | |
---|---|
q1 | When cost × (1 + lvl % 23) < min(q2 cost, K cost) |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | When cost × (1 + lvl % 11) < min(q2 cost, K cost, m cost) |
PermaSwap strategy
Before reaching e1076ρ in your publication, do not use the 3rd level of the g(x) milestone.
Upon reaching e1076ρ, switch a milestone point into the 3rd level of the g(x) milestone, at the cost of resetting q.
FIPermaSwap #
FIPermaSwap | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | ✔️ |
PermaSwap strategy
Before reaching e1076ρ in your publication, do not use the 3rd level of the g(x) milestone.
Upon reaching e1076ρ, switch a milestone point into the 3rd level of the g(x) milestone, at the cost of resetting q.
FIMSdPermaSwap #
FIMSdPermaSwap | |
---|---|
q1 | When cost × (1 + lvl % 23) < min(q2 cost, K cost) |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | When cost × (1 + lvl % 11) < min(q2 cost, K cost, m cost) |
Milestone swapping strategy
When buying a new level of q2, swap n and m milestones to q1 exponent to build up q.
Swap back to m and n when your q got multiplied by a ratio (since you started the swapping phase) depending on your q1 lvl % 23:
q1 lvl % 23 | q ratio |
---|---|
1-4 | 4 |
5-9 | 3 |
10-19 | 2.5 |
20+ | 2 |
PermaSwap strategy
Before reaching e1076ρ in your publication, do not use the 3rd level of the g(x) milestone.
Upon reaching e1076ρ, switch a milestone point into the 3rd level of the g(x) milestone, at the cost of resetting q.
Strategy Credits:
- Playspout for the milestone swapping strategy
FIMSPermaSwap #
FIMSPermaSwap | |
---|---|
q1 | ✔️ |
q2 | ✔️ |
K | ✔️ |
m | ✔️ |
n | ✔️ |
Milestone swapping strategy
When buying a new level of q2, swap n and m milestones to q1 exponent to build up q.
Swap back to m and n when your q got multiplied by a ratio (since you started the swapping phase) depending on your q1 lvl % 23:
q1 lvl % 23 | q ratio |
---|---|
1-4 | 4 |
5-9 | 3 |
10-19 | 2.5 |
20+ | 2 |
PermaSwap strategy
Before reaching e1076ρ in your publication, do not use the 3rd level of the g(x) milestone.
Upon reaching e1076ρ, switch a milestone point into the 3rd level of the g(x) milestone, at the cost of resetting q.
Strategy Credits:
- Playspout for the milestone swapping strategy
Fractal Patterns #
FPmodBurstC1MS #
FPmodBurstC1MS | |
---|---|
ṫ | ✔️ |
c | When cost × (1 + lvl % 100) < min(c2 cost, s cost) (Autobuy if you can afford the next lvl%100=1 before the next c2 or s) |
c2 | ✔️(if c2 and s have similar costs, prioritize s) |
q1 | When cost × (1 + lvl % 10) < min(q2 cost, s cost) |
q2 | ✔️(if q2 and s have similar costs, prioritize s) |
r1 | ✔️ |
n | ✔️ |
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 #
FPdMS | |
---|---|
ṫ | ✔️ |
c | When cost × (1 + lvl % 100) < c2 cost |
c2 | ✔️ |
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
n | ✔️ |
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.
FP #
FP | |
---|---|
ṫ | ✔️ |
c1 | ✔️ |
c2 | ✔️ |
q1 | ✔️ |
q2 | ✔️ |
r1 | ✔️ |
n | ✔️ |
s | ✔️ |
Riemann Zeta Function #
RZdBH #
RZdBH | |
---|---|
c1 | When c1lvl < 4 × c2lvl + 2 |
c2 | ✔️ |
w1 | When cost × 5 < min(w2 cost, w3 cost) |
w2 | ✔️ |
w3 | ✔️ |
b | ✔️(Don't buy until t>16) |
When the theory simulator recommends this strategy, it will show something like:
RZdBH t=388.85 c1: 3091 c2: 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 c1 and c2 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 #
RZBH | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
w1 | ✔️ |
w2 | ✔️ |
w3 | ✔️ |
b | ✔️ |
When the theory simulator recommends this strategy, it will show something like:
RZBH t=462.07 c1: 3091 c2: 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 c1 and c2 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 #
RZSpiralSwap | |
---|---|
c1 | When c1lvl < 4 × c2lvl + 2 |
c2 | ✔️ |
w1 | When cost × 5 < w2 cost |
w2 | ✔️ |
b | ✔️(Don't buy until t>16) |
SpiralSwap
To perform SpiralSwap, switch milestones to prioritize c1 exponent when ζ is close to zero (when the graph is close to the origin) and to prioritize w2 when |ζ| is > 1.
This strategy is extremely active. Using RZdMS is much easier and doesn’t lose that much time compared to spiralswap.
When the theory simulator recommends this strategy, it will show something like:
RZSpiralSwap c1: 953 c2: 238.
The levels it shows after c1 and c2 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 #
RZdMS | |
---|---|
c1 | When c1lvl < 4 × c2lvl + 2 |
c2 | ✔️ |
w1 | When cost × 5 < w2 cost |
w2 | ✔️ |
b | ✔️(Don't buy until t>16) |
When the theory simulator recommends this strategy, it will show something like:
RZdMS swap:197 c1: 953 c2: 238.
Start the publication with the w2 milestone on. The value after swap is the ρ value were you should switch it to c1 exponent.
The levels it shows after c1 and c2 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 #
RZMS | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
w1 | ✔️ |
w2 | ✔️ |
b | ✔️ |
When the theory simulator recommends this strategy, it will show something like:
RZMS swap:196 c1: 952 c2: 238.
Start the publication with the w2 milestone on. The value after swap is the ρ value were you should switch it to c1 exponent.
The levels it shows after c1 and c2 are the last levels you should buy them to in this publication.
Strategy credits:
- Hotab for the dynamic swap implementation
- Hotab & Blackseal for the coasting strategy
RZd #
RZd | |
---|---|
c1 | When c1lvl < 4 × c2lvl + 2* |
c2 | ✔️ |
w1 | When cost × 5 < min(w2 cost, w3 cost) |
w2 | ✔️ |
w3 | ✔️ |
b | ✔️(Don't buy until t>16) |
* If you don’t have \(c_1\) exponent milestones, use 4×\(c_2\)lvl + 1 instead.
When the theory simulator recommends this strategy, it will show something like:
RZd c1: 953 c2: 238.
The levels it shows after c1 and c2 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 #
RZ | |
---|---|
c1 | ✔️ |
c2 | ✔️ |
w1 | ✔️ |
w2 | ✔️ |
w3 | ✔️ |
b | ✔️ |
When the theory simulator recommends this strategy, it will show something like:
RZ c1: 953 c2: 238.
The levels it shows after c1 and c2 are the last levels you should buy them to in this publication.
Strategy credits:
- Hotab & Blackseal for the coasting strategy