Note: this is a work in progress. Feel free to make additions, improvements or edits but be aware that they may be removed or undone. Please also include a summary of changes.
Think of the Order of the Sun as having 4 distinct levels:
Every level improves the one before it:
The fact that each level improves the one before it means that you should ALWAYS go from the higher level first, ie transcend -> faith reset -> praise the sun \o/
*Go from the top down, TAP: Transcend, Adore the galaxy, Praise the sun \o/ (Fun fact: Bloodrizer specifically picked the verb "Adore" to preserve the TAP acronym!)
This was a lot more confusing before 126.96.36.199, when worship was called "total faith" and epiphany wasn't named at all.
You can pretty much Praise the Sun whenever you want after buying Solar Revolution. Praising the sun will consume all your faith and increase your Solar Revolution production bonus. The Solar Revolution bonus is soft-capped. Early in the game (the first few runs) you may not be able to reach the cap. A few runs later, you may need to fill your faith and Praise the Sun many times to reach the cap. Later in the game you can reach the Solar Revolution cap by filling your faith and praising once.
You won't want to Praise when you are saving up your faith to buy Religion upgrades, or when you are trying to cap your faith so that you can Transcend or Adore.
You can always Adore just before you reset; the game will Adore for you if you don't, and you get a small 1% bonus if you remember to click on the button.
Otherwise, Adoring will remove your Solar Revolution bonus, and you can Adore and then Praise whenever you have enough faith to restore your Solar Revolution bonus back close to its cap.
Each transcend level costs a certain amount of your Praise Bonus as given in the table below. In the first few runs, when you can't reach your Solar Revolution cap, after you Transcend, you will immediately Adore. (And if you aren't about to reset, you will then Praise.) You want the Adore to restore your Praise Bonus. So you will need enough Worship, as give in the tables below, so that your Praise Bonus will be restored.
Once you can cap (or nearly cap) your Solar Revolution bonus by Praising your capped faith once, it's no longer useful to build up a large pool of Worship. Instead, the equivalent strategy is to Transcend after raising your Praise Bonus to 2x the level needed to Transcend. (The tables below suggest there are more optimal strategies. For example, when you have Black Obelisks, Transcending will increase your Solar Revolution cap allowing you to gain faith faster, so transcending sooner can be beneficial.)
Note: you should probably clone your game and do some tests to ensure that you can get your SR back to where it was fairly quickly after doing your faith resets
|Transcendence Tier||Minimum Praise bonus % needed||1.5 x Praise bonus||2 x Praise bonus||Break-even Praise bonus (0 Black Obelisks)||Break-even Praise bonus (10 Black Obelisks)||Break-even Praise bonus (50 Black Obelisks)||Break-even Praise bonus (many Black Obelisks)|
|To Transcendence Tier||Minimum Praise Bonus % needed||Worship needed to restore Praise Bonus|
|Tier 1||~1.97%||~ 2950|
|Tier 2||~5.90%||~ 5220|
|Tier 3||~17.38%||~ 14.9 K|
|Tier 4||~49.29%||~ 58.4 K|
|Tier 5||~136.45%||~277 K|
|Tier 6||~373.55%||~ 1.46M|
|Tier 7||~1.02K%||~ 8.17M|
|Tier 8||~2.77K%||~ 47.5 M|
|Tier 9||~7.53K%||~284 M|
|Tier 10||~20.48K%||~ 1.73G|
|Tier 11||~55.67K%||~ 10.7 G|
|Tier 12||~151.34K%||~ 67.6 G|
|Tier 13||~411.39K%||~431 G|
|Tier 14||~1.12M%||~ 2.77T|
|Tier 15||~3.04M%||~ 18.0 T|
|Tier 16||~8.26M%||~118 T|
|Tier 17||~22.46M%||~776 T|
|Tier 18||~61.06M%||~ 5.14P|
|Tier 19||~165.97M%||~ 34.3 P|
|Tier 20||~451.14M%||~230 P|
|Tier 21||~1.23G%||~ 1.55E|
|Tier 22||~3.33G%||~ 10.5 E|
|Tier 23||~9.06G%||~ 70.9 E|
|Tier 24||~24.63G%||~483 E|
|Tier 25||~66.96G%||~ 3.30Z|
|Tier 26||~182.00G%||~ 22.6 Z|
|Tier 27||~494.74G%||~155 Z|
|Tier 28||~1.34T%||~ 1.07Y|
|Tier 29||~3.66T%||~ 7.38Y|
|Tier 30||~9.94T%||~ 51.1 Y|
The remainder of this page discusses implementation details and the math used to derive these tables.
Functions and variables:
Prior to 188.8.131.52, epiphany was actually stored as a hidden resource, colloquially known as 'apocrypha points'. It still works the same, but it's a lot clearer now.
How epiphany is calculated:
(worship / 1000000) * bonusRatio
sum of faith resets - (((e^TT)/5+1)^2-1)/80
This is the math behind the Transcend from Worship table above. This mostly restates How the Code Works above, but in somewhat different words. For those who really want to dig into the math, having two slightly different wordings to compare might help understand some of the details better. If you don't really care about the math, you should skip this.
Faith is displayed along with other visible resources. By clicking on the gear icon for resources, one can get a "show hidden resources" checkbox. Clicking on that will cause Worship and Epiphany to be displayed.
Clicking on "Praise the Sun" in the Religion tab will convert Faith to Worship.
faith * (1 + (sqrt(1+80*epiphany)-1) / 20)
faith * 0.45 * sqrt(epiphany).)
Clicking on "Adore the Galaxy" will convert Worship to Epiphany.
(1 + TT)^2where TT is the current Transcendence Tier.
(worship / 1000000) * (1 + TT)^2
Clicking on the Transcend button will spend Epiphany to raise my Transcendence Tier.
((e^(2*TT+2))/10 + e^(TT+1) - (e^(2*TT))/10 - e^(TT)) / 200
e^(2*TT) * (e^2 - 1) / 2000
I'd expect that whenever we transcend, we want at least enough Worship so that we can restore our Praise Bonus.
If we transcend mid-tier, since Solar Revolution is capped, it seems like we can restore most of our Solar Revolution bonus reasonably quickly.
To replace spent Epiphany with Worship when transcending from level TT, we need
worship / 1000000 * (2 + TT)^2 > (2.718^(2*TT)) * 0.003194
worship > (2.718^(2*TT)) * 3194 / (2 + TT)^2
(2.718^16)*3194/100or somewhere over 283M worship.
Experimental work in progress:
What we must want to optimize is the rate of generation of epiphany (or Praise bonus) while maintaining a high Solar Revolution bonus. Epiphany is generated as roughly
worship*TT^2. Where worship is generated as roughly
faith*sqrt(epiphany). A nice circular generation function.
E' = F*sqrt(E)*TT^2. And the rate of increase in F depends on the Solar Revolution cap which is a function of
E' = TT*obelisks*sqrt(E)*TT^2. To keep the rate of generation constant across a Transcend, obelisks shouldn't be important; that should just be a constant multiplier before and after. Say we will spend
S epiphany, and before we transcend we have some multiple
k of that amount, then we want
TT^3*sqrt(k*S) <= (TT+1)^3 * sqrt((k-1)*s)
sqrt(k/(k-1)) <= ((TT+1)/TT)^3
k/(k-1) <= ((TT+1)/TT)^6
k <= c * (k-1)
k <= ck - c
c <= (c-1)*k
c/(c-1) <= k
(c-1)/c >= 1/k
1 - 1/c >= 1/k
1/k <= 1 - (TT/(TT+1))^6
The above equation is only used when there are some obelisks.
This suggests waiting longer before transcending. For example, when transcending from level 20, the TT-cubed bonuses will increase production by about 30%. Implying should reduce the Praise Bonus only by about 30% and not cut it in half as is suggested by the tables.
A more accurate equation than the above is
TT*sqrt(k*S)*(TT+1)^2 <= (TT+1)*sqrt((k-1)*S)*(TT+2)^2
sqrt(k/(k-1)) <= (TT+1)*(TT+2)*(TT+2)/(TT*(TT+1)*(TT+1))
k/k-1 <= ((TT+2)^2)/(TT*(TT+1))
That doesn't give hugely different results.