Ex­po­nen­tial Idle Guides

The­ory Strategies Ex­plained

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

This guide is cur­rently un­der­go­ing change. Keep in mind, strategies may change.

The the­ory sim we cur­rently re­com­mend was made by XLII 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 T1AI.

The­ory 2: Dif­fer­en­tial Cal­cu­lus

T2 is the only the­ory without an act­ive strategy, des­pite at­tempts.

The­ory 3: Lin­ear Al­gebra

T3 has the most vari­ables of any the­ory and has be­ne­fit­ted the most from player-cre­ated strategies. T3SNAX is cur­rently the best idle strategy above e200\(\rho\). T3SNAX2 is sim­ilar to T3SNAX but is de­signed to be QoL com­pat­ible.

The­ory 4: Poly­no­mi­als

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

The­ory 5: Lo­gistic Func­tion

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

The­ory 6: In­teg­ral Cal­cu­lus

T6 is the most power­ful the­ory in en­dgame, with sev­eral play­ers reach­ing well over e1100𝜏 on their main save, some even over e1200𝜏.

The­ory 7: Nu­mer­ical Meth­ods

T7 is the third-weak­est the­ory, ahead of T2 and T8. T7PlaySpqceyX is a slightly faster ver­sion of T7Play-25.

The­ory 8: Chaos The­ory

T8 is the weak­est the­ory in en­dgame and has the most act­ive strategy of any the­ory (T8PlaySo­l­arSwap) T8 also has the largest num­ber of strategies (20+ total), but only those I have seen re­com­men­ded by the sim are shown here.
Older the­ory sim­u­lat­ors may re­turn the at­tractor as part of the strategy name (Ex­ample: T8R in­stead of T8). As al­ways, we re­com­mend us­ing XLII’s sim. We have since de­cided to re­move the at­tractor let­ter from strategy names.

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.

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.

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
c2
c3 When ρ > 5 × cost
c4 ✔️
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 ⅔ of c3 cost

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:

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 ✔️


For the \(c_2\) Ra­tio:

 Ratio

For the \(c_3\) Ra­tio:

c3 Ra­tio
ρ < e300 1
e300 < ρ < e450 1.1
e450 < ρ < e550 2
e550 < ρ < e625 5
ρ > e625 10


Strategy Cred­its:

T1AI #

T1AI
q1 When ρ > 5 × cost
q2 When ρ > 1.15 × cost
c1
c2
c3 When ρ > 2 × cost
c4 ✔️

T1C34 #

T1C34
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:

The “MC” in T2MC stands for Mul­tivari­ableCoast.

T2Coast-X% #

T2­Coast-X%
Be­fore X% of T2’s Op­timal Mul­ti­plier After X% of T2’s Op­timal Mul­ti­plier
q1 ✔️
q2 ✔️
q3 ✔️
q4 ✔️
r1 ✔️
r2 ✔️
r3 ✔️
r4 ✔️

If the sim re­com­mends this, it will re­turn a per­cent­age in the box: T2Coast-☐%

We gen­er­ally re­com­mend us­ing T2MC in­stead of this strategy.

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:



* 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 ⅛ of c31 cost When ⅛ of c31 cost
b2 When 2/​9 of c12 cost, 4/​9 of c22 cost When ¼ of c32, c12 cost, ½ of c22 cost ✔️
b3 When ⅛ of c23 cost, 4/​9 of c33 cost When ⅛ of c23 cost, ½ of c33 cost When ⅛ of c23 cost, ½ of c33 cost
c11
c12 ✔️ ✔️ ✔️
c13
c21
c22 When ½ of c32, c12 cost When ½ of c32, c12 cost ✔️
c23 ✔️ ✔️ ✔️
c31 ✔️ ✔️
c32 ✔️ ✔️ ✔️
c33 When 9/​32 of c23 cost When ¼ of c23 cost When ¼ of c23 cost

Strategy Cred­its:

T3SNAX #

T3SNAX
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
b1 ✔️
b2 ✔️ ✔️
b3 ✔️ ✔️
c11
c12 When e2 be­low ρ2 (auto c12
also works, is a bit slower)
✔️
c13
c21
c22 ✔️ ✔️
c23 ✔️ ✔️
c31 ✔️
c32 ✔️
c33 ✔️

Strategy Cred­its:

T3SNAX2 #

T3SNAX2
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
b1 When 1/​10 of ρ1
b2 When ⅓ of ρ2 When ⅓ of ρ2
b3 When ⅕ of ρ3 When ⅕ of ρ3
c11
c12 When e2 be­low ρ2 ✔️
c13
c21
c22 ✔️ When ⅛ of ρ2
c23 ✔️ ✔️
c31 ✔️
c32 ✔️
c33 When 1/​10 of ρ3

Strategy Cred­its:

T3Noρ1C13rcvNoC12 #

T3Noρ1C13r­cvNoC12
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
b1
b2 ✔️ ✔️
b3 ✔️ ✔️
c11
c12 ✔️
c13
c21
c22 ✔️
c23 ✔️ ✔️
c31
c32 ✔️
c33 ✔️

Strategy Cred­its:

T3Noρ1C13rcv #

T3Noρ1C13r­cvNoC12
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
b1
b2 ✔️ ✔️
b3 ✔️ ✔️
c11
c12 ✔️ ✔️
c13
c21
c22 ✔️
c23 ✔️ ✔️
c31
c32 ✔️
c33 ✔️

Strategy Cred­its:

T3NoC11C13C21C33d #

T3NoC11C13C21C33d
b1 When 1/​8 of c31 cost
b2 When 1/​5 of other ρ2 vari­ables’ cost (c12, c22, c32)
b3 When 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 1/​10 of min(c21 cost, c31 cost)
b2 When ¼ of min(c12, c22, c32)
b3 When 1/​10 of c23 cost
c11 ✔️
c12 ✔️
c13
c21 ✔️
c22 ✔️
c23 ✔️
c31 ✔️
c32 ✔️
c33

T3NoC13C33 #

T3NoC13C33d
b1 ✔️
b2 ✔️
b3 ✔️
c11 ✔️
c12 ✔️
c13
c21 ✔️
c22 ✔️
c23 ✔️
c31 ✔️
c32 ✔️
c33

T3NoC11C13C33d #

T3NoC13C33d
b1 When 1/​10 of min(c21 cost, c31 cost)
b2 When ¼ of min(c12, c22, c32)
b3 When 1/​10 of c23 cost
c11
c12 ✔️
c13
c21 ✔️
c22 ✔️
c23 ✔️
c31 ✔️
c32 ✔️
c33

T3NoC11C13C33 #

T3NoC13C33d
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 ⅐ of min(c11 cost, c21 cost)
b2 When 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 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 to 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:

T4C3d #

T4C3d
c1
c2
c3 ✔️
c4
c5
c6
q1 When 1/​10 of q2 cost and c3 cost
q2 ✔️

T4SNAX #

T4SNAX
Pub­lic­a­tion Mul­ti­plier < 2.75 Pub­lic­a­tion Mul­ti­plier > 2.75
c1
c2
c3 ✔️ ✔️
c4
c5
c6
q1 ✔️
q2 ✔️ ✔️



Strategy Cred­its:

T4C3dC12rcv #

T4C3d­C12rcv
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
c1 When 1/​10 of c2 cost
c2 ✔️
c3 ✔️ ✔️
c4
c5
c6
q1 When 1/​10 of q2 cost When 1/​10 of q2 cost
q2 ✔️ ✔️

T4C3 #

T4C3
c1
c2
c3 ✔️
c4
c5
c6
q1 ✔️
q2 ✔️

T4C123d #

T4C123d
c1 When 1/​10 of c2 cost
c2 ✔️
c3 ✔️
c4
c5
c6
q1 When 1/​10 of q2 cost
q2 ✔️

This strategy is typ­ic­ally seen at lower \(\rho\) and is even­tu­ally out­paced by T4C3d.

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 1/​10 of c2 cost
c2 ✔️
c3
c4
c5
c6
q1
q2

T4C12 #

T4C12
c1 ✔️
c2 ✔️
c3
c4
c5
c6
q1
q2

T4C56d #

T4C56d
c1
c2
c3
c4
c5 ✔️
c6 ✔️
q1 When 1/​10 of q2 cost
q2 ✔️

T4C56 #

T4C56d
c1
c2
c3
c4
c5 ✔️
c6 ✔️
q1 ✔️
q2 ✔️

T4C4d #

T4C4d
c1
c2
c3
c4 ✔️
c5
c6
q1 When 1/​10 of q2 cost
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:

T5 #

T5
q1 ✔️
q2 ✔️
c1 ✔️
c2 ✔️
c3 ✔️

The­ory 6: In­teg­ral Cal­cu­lus #

T6AI #

T6AI
q1 When 7 + q1lvl % 10 times cheaper than q2
q2 ✔️
r1 When 5 + r1lvl % 10 times cheaper than r2
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.

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:

T6NoC34d #

T6NoC34d
q1 When 1/​10 of q2 cost
q2 ✔️
r1 When 1/​10 of r2 cost
r2 ✔️
c1 When 1/​10 of c2 cost
c2 ✔️
c3
c4
c5 ✔️

T6NoC34 #

T6NoC34
q1 ✔️
q2 ✔️
r1 ✔️
r2 ✔️
c1 ✔️
c2 ✔️
c3
c4
c5 ✔️

T6NoC1234d #

T6NoC1234d
q1 When 1/​10 of q2 cost
q2 ✔️
r1 When 1/​10 of r2 cost
r2 ✔️
c1
c2
c3
c4
c5 ✔️

T6NoC1234 #

T6NoC1234
q1 ✔️
q2 ✔️
r1 ✔️
r2 ✔️
c1
c2
c3
c4
c5 ✔️

T6NoC345d #

T6NoC345d
q1 When 1/​10 of q2 cost
q2 ✔️
r1 When 1/​10 of r2 cost
r2 ✔️
c1 When 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 ⅕ of min(c4 cost, q2 cost, r2 cost)
q2 ✔️
r1 When 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 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 ¼ of c6 cost
c1
c2
c3 When 1/​10 of c6 cost
c4 When 1/​10 of c6 cost
c5 When ¼ of c6 cost
c6 ✔️

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

T7­PlaySpqceyX
q1 When ¼ of c6 cost
c1 When 10 + c1lvl % 10 times cheaper than c2 cost
c2 When X times cheaper than c6 cost
c3 When 1/​10 of c6 cost
c4 When 1/​10 of c6 cost
c5 When ¼ of c6 cost
c6 ✔️



The num­ber after T7PlaySpqcey oc­curs more at lower \(\tau\) val­ues.

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

Strategy Cred­its:

T7Play-25 #

T7­Play-25
q1 When ¼ of c6 cost
c1
c2
c3
c4 When 1/​10 of c6 cost
c5 When ¼ of c6 cost
c6 ✔️

T7Play-25 has a “25” due to the two 25% (¼) ra­tios

Strategy Cred­its:

T7C3d #

T7C3d
q1 When 1/​10 of c3 cost
c1
c2
c3 ✔️
c4
c5
c6

T7C12d #

T7C12d
q1 When 1/​10 of c2 cost
c1 When ⅛ of c2 cost
c2 ✔️
c3
c4
c5
c6

T7C12 #

T7C12
q1 ✔️
c1 ✔️
c2 ✔️
c3
c4
c5
c6

T7C123d #

T7C123d
q1 When 1/​10 of min(c2 cost, c3 cost)
c1 When 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 ⅖ of min(c2 cost, c4 cost)
c4 ✔️
c5 When cost 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:

T8Play #

T8­Play
c1 When cost ⅛ of min(c2 cost, c4 cost)
c2 ✔️
c3 When cost ⅖ of min(c2 cost, c4 cost)
c4 ✔️
c5 When cost ¼ of min(c2 cost, c4 cost)

If you ever see a “C” or an “L” in­stead of the “R”, use the Chen or Lorentz at­tract­ors in­stead of the Rössler at­tractor.

Strategy Cred­its:

T8SNAX #

T8SNAX
Pub­lic­a­tion Mul­ti­plier < 1.6 Pub­lic­a­tion Mul­ti­plier 1.6-2.3 Pub­lic­a­tion Mul­ti­plier > 2.3
c1 ✔️
c2 ✔️ ✔️ ✔️
c3 ✔️ ✔️
c4 ✔️ ✔️ ✔️
c5 ✔️ ✔️



Strategy Cred­its:

T8NoC35d #

T8NoC35d
c1 When 10 + c1lvl % 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 1/​10 of min(c2 cost, c4 cost)
c2 ✔️
c3 ✔️
c4 ✔️
c5

T8NoC5/T834 #

T8NoC5/​T834
c1 ✔️
c2 ✔️
c3 ✔️
c4 ✔️
c5

T8NoC3d #

T8NoC3d
c1 When 1/​10 of min(c2 cost, c4 cost)
c2 ✔️
c3
c4 ✔️
c5 ✔️

T8NoC3 #

T8NoC3
c1 ✔️
c2 ✔️
c3
c4 ✔️
c5 ✔️

T8d #

T8d
c1 When 1/​10 of c2 cost
c2 ✔️
c3 ✔️
c4 ✔️
c5 ✔️

T8 #

T8
c1 ✔️
c2 ✔️
c3 ✔️
c4 ✔️
c5 ✔️

Of­fi­cial Cus­tom The­or­ies #

Wei­er­straß Sine Product #

WSPAI #

WSPAI
q1 When cost 1/​10 of q2 cost
q2 ✔️(Auto­buy when not sav­ing up for n)
n ✔️ Save up for n when ρ > cost/​4
c1 Stop buy­ing a few seconds into a
pub­lic­a­tion (or do e5 dif­fer­ence at lower ρ)
c2 ✔️ (Auto­buy when not sav­ing up for n)


Strategy Cred­its:

WSPdStopC1 #

WSP­dStopC1
First 15 Seconds of Pub­lic­a­tion Rest of Pub­lic­a­tion
q1 When cost is 8 + q1lvl % 10 times cheaper than min(q2 cost, n cost, c2 cost) When cost is 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:

WSPd #

WSPd
q1 When cost 1/​10 of q2 cost
q2 ✔️
n ✔️
c1 When 1/​10 of c2 cost
(re­com­men­ded to stop buy­ing be­fore this)
c2 ✔️


Strategy Cred­its:

WSPStopC1 #

WSP­StopC1
First 15 Seconds of Pub­lic­a­tion Rest of Pub­lic­a­tion
q1 ✔️ ✔️
q2 ✔️ ✔️
n ✔️ ✔️
c1 ✔️ If ρ < e450, ✔️
If ρ > e450, ❌
c2 ✔️ ✔️


Strategy Cred­its:

Se­quen­tial Lim­its #

SLMS #


Mile­stone Swap:

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:

  1. Buy \(b_1\)/\(​b_2\)
  2. Swap mile­stones into State 1 to fully util­ize the boost from the new \(b_1\)/\(​b_2\) up­grade.
  3. 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.
  4. 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.
  5. 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


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:

SLMSd #


**For the mile­stone swap­ping de­tails, read the above strategy, [SLMS](ht­tps://​ex­po­nen­tial-idle-guides.net­lify.app/​guides/​the­ory-strategies/#​slms). This strategy only mod­i­fies the vari­able buy­ing strategies.**
SLMSd
Pub­lic­a­tion Mult < 4 Pub­lic­a­tion Mult 4-7.5 Pub­lic­a­tion Mult > 7.5
a1 When 2 × (a1lvl % 3) times cheaper than a2 cost
a2 ✔️
b1 When b1lvl % 4 times cheaper than b2 cost When b1lvl % 4 times cheaper than b2 cost
b2 ✔️ ✔️


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

Strategy Credit:

SLStopAd #

SLSto­pAd
Pub­lic­a­tion Mult < 4.5 Pub­lic­a­tion Mult 4.5-6 Pub­lic­a­tion Mult > 6
a1 When cost is 1/​10 of a2 cost
a2 ✔️
b1 When cost is 1/​10 of b2 cost When cost is 1/​10 of b2 cost
b2 ✔️ ✔️

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:

SLStopA #

SLStopA
Pub­lic­a­tion Mult < 4.5 Pub­lic­a­tion Mult 4.5-6 Pub­lic­a­tion Mult > 6
a1 ✔️
a2 ✔️
b1 ✔️ ✔️
b2 ✔️ ✔️


Strategy Cred­its:

Euler’s For­mula #

EFAI (post-e50ρ) #

EFAI
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
✔️ ✔️
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:

EFSNAX #

EF­SNAX
Re­cov­ery (pub mult < 1) Tau Gain (pub mult > 1)
✔️ ✔️
q1 ✔️
q2 ✔️ ✔️
b1 ✔️
b2 ✔️
c1 ✔️
c2 ✔️
a1 ✔️ ✔️
a2 ✔️ ✔️
a3 ✔️ ✔️


Strategy Cred­its:

EFd #

EFd
✔️
q1 Buy when 1/​10 of q2 cost
q2 ✔️
b1 ✔️
b2 ✔️
c1 ✔️
c2 ✔️
a1 Buy when ¼ of q2 cost
a2 ✔️
a3 ✔️

EF #

EF
✔️
q1 ✔️
q2 ✔️
b1 ✔️
b2 ✔️
c1 ✔️
c2 ✔️
a1 ✔️
a2 ✔️
a3 ✔️

Con­ver­gents to √2 #

CSR2XLx.xx #

CSR2XLx.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 “CSR2XL2.85”, 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:

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:

CSR2d #

CSR2d
q1 When cost × 10 < min(q2c, nc, c2c), where c = cost
q2 ✔️
c1 When cost × 10 < min(q2c, nc, c2c), where c = cost
n ✔️
c2 ✔️

CSR2 #

CSR2
q1 ✔️
q2 ✔️
c1 ✔️
n ✔️
c2 ✔️