Don't bother with this guide until you've unlocked all the price ratios reduction paragon, unlocked Pawgan Rituals, completed the Atheism challenge, and you have a nice pile of time crystals and can afford to burn ~100 per run for a dozen or more runs. Maybe you've even unlocked a few event horizons and black obelisks. Your next step is growing a massive pile of paragon so you can push to afford 98 chronospheres.
I haven't checked the math in this. There are probably errors. Any improvements to this document are welcome.
The limit to how much paragon you can get per hour is set by the rate at which kittens arrive, and the amount of housing you can build in a game while still keeping up with the kittens showing up.
The equation for how quickly kittens arrive per second is
Kittens Per Second = 0.01 Kittens/Tick * (1 + VenusOfWillenFluff * 0.75 + PawganRituals * 1.5) * (5 Ticks/Second) * FestivalEffects
Where FestivalEffects is 1 if there is no festival, or 2 + 0.001 * # Breweries if there is a festival. The bonus from breweries is so small, that we can ignore it in these calculations (if we have 40 breweries, it only changes the overall kittens per second by 2%, and we're not going to build that many breweries in a short run).
Assuming that the first thing you do after a reset is unlock Festivals and build some starter housing, you can get 0.325 kittens per second, which is 19.5 kittens per minute. Therefore, you don't start accumulating any paragon 70 kittens, which takes 215 seconds (3 minutes 25 seconds).
100% efficiency would be if you were able to keep up with kittens showing up forever. You'd be getting about 1,170 paragon per hour. However, eventually, building extra huts requires more storage than you have, so you need to reset and start all over again. The optimal length of a run depends on how much housing you can build in a run, which is a function of your paragon. You'll find that when you have ~10k paragon and a +5000% solar revolution bonus, you can easily build housing for about 600 kittens in a half hour (assuming you buy everything in the right order and can click really fast), in which case you'll need wait for about 30 minutes for all the kittens to arrive. If you do resets faster than 30 minutes, then you're sub-optimal because you spend too much of your time (3 minutes 25 seconds per run) waiting for the first 70 kittens to show up. If you do resets longer than 60 minutes, you're likely sub optimal because you're waiting too long to save up for the next housing to stuff more kittens in. If you really want to grind paragon fast, the optimal time to reset is when you can no longer keep up with incoming kittens by building space stations, mansions, huts, and log houses to put them in.
If you could make it to 500 kittens, then you had to reset because you couldn't keep up with your incoming kittens, you would get 430 paragon out of 500 kittens in 0.42 hours, so 1006 paragon/hour (86% efficiency). To know what your efficiency is, it's (# kittens - 70) / (#number of kittens). If you made it to 1000 kittens, you would be running at 93% of the asymptotic perfect efficiency. The difference between 500-kitten resets and 1000-kitten resets is only 7% (only 82 paragon/hour).
Another way to write the efficiency is
(# kittens - 70) / # kittens ~= 1 - 70 / (# kittens)
With some calculus, and assuming lots of kittens, the change in efficiency with each additional kitten you reset with is about 70 * dK / (#number of kittens)2. The difference in efficiency between 500 kittens and 501 kittens is 70 / 5002 = 0.03%, or about .35 paragon/hour (virtually nothing). So for real, once you can't keep up with your incoming kittens anymore, finish the pre-reset checklist below, and reset. There's not much point waiting to get more storage for more kittens.
When you reset, you carry over many of your resources. In the late game, you want to carry over large amounts of resources, which requires large amounts of chronospheres, which requires large amounts of unobtainium.
Let's suppose you just completed a very long run, and you have lots of unobtainium. You can do a series of short runs, where you only build housing, build some chronospheres, and then reset. Let's say that you have just done a long run, maxed chronospheres, and you find yourself restarting the game with 10.29 M unobtainium. If you build only one chronosphere, you're left with 10.28 M unobtainium, and you can carry over 1.5% of your unobtainium bank, which leaves you with 154k unobtainium your next reset. If you max chronospheres, then you build 43 chronospheres and are left with 3.5k, and when you reset you only have 2.2k unobtainium. The trick is to find the right balance between investing enough unobtainium to get your reset percentage high enough, and also have a large bank left over.
If you have U unobtainium before you build any chronospheres, you can calculate the amount of chronospheres n that you need to buy to get the optimal amount of unobtainium R after you reset. The price ratio for chronospheres with all the price ratio reduction paragon is r = 1.163541882. We want to maximize the following equation.
R = (U - 2500 * (1 - r ^ n) / (1 - r)) * 0.015 * n
After some boring calculus, we find that the solution is
n = round(W(e * (r - 1) * U / 2500 + e) - 1) / ln( r )
where W is the Lambert W function and e is Euler's constant (2.71828). We round the value to the nearest integer. Note that if you want to buy something like Flux Condensator or other upgrades with unobtainium, then the value of U is the amount of Unobtainium you have left after buying the upgrade
If you want to determine the amount of unobtainium you need before the nth chronosphere is worth it, you plug n into the following equation:
U = 2500 * ( 1 - r ^ n (1 + n ln ( r ) ) ) / (1 - r)
Note that the breakpoints are at half-integers (i.e., the breakpoint where 2 chronospheres get your more than 1 chronosphere is at n = 1.5, and U = 8.3k.
A reference table is shown below.
|unobtainium before building chronospheres (U)||optimal chronospheres (n)||unobtainium after building chronospheres||amount of resources carried over||unobtainium after reset (R)||optimal reset ROI||time crystal cost|
|2.5k - 8.3k||1||~2.7k||1.5%||~40.4||~0.8%||1.0|
|8.3k - 15.5k||2||~6.3k||3.0%||~188.1||~1.6%||2.2|
|15.5k - 24.5k||3||~10.9k||4.5%||~492.4||~2.5%||3.5|
|24.5k - 35.5k||4||~17.0k||6.0%||~1.0k||~3.4%||5.1|
|35.5k - 49.2k||5||~24.7k||7.5%||~1.9k||~4.4%||6.9|
|49.2k - 65.9k||6||~34.5k||9.0%||~3.1k||~5.4%||9.1|
|65.9k - 86.4k||7||~46.8k||10.5%||~4.9k||~6.5%||11.5|
|86.4k - 111.4k||8||~62.2k||12.0%||~7.5k||~7.6%||14.4|
|111.4k - 141.9k||9||~81.5k||13.5%||~11.0k||~8.7%||17.8|
|141.9k - 179.0k||10||~105.3k||15.0%||~15.8k||~9.9%||21.7|
|179.0k - 224.0k||11||~134.8k||16.5%||~22.2k||~11.1%||26.2|
|224.0k - 278.5k||12||~171.1k||18.0%||~30.8k||~12.3%||31.5|
|278.5k - 344.4k||13||~215.6k||19.5%||~42.1k||~13.6%||37.7|
|344.4k - 424.0k||14||~270.2k||21.0%||~56.7k||~14.8%||44.9|
|424.0k - 520.1k||15||~336.9k||22.5%||~75.8k||~16.1%||53.2|
|520.1k - 635.9k||16||~418.1k||24.0%||~100.3k||~17.4%||62.9|
|635.9k - 775.1k||17||~516.9k||25.5%||~131.8k||~18.8%||74.2|
|775.1k - 942.6k||18||~636.8k||27.0%||~171.9k||~20.1%||87.3|
|942.6k - 1.1M||19||~782.0k||28.5%||~222.9k||~21.5%||102.6|
|1.1M - 1.4M||20||~957.8k||30.0%||~287.4k||~22.8%||120.4|
|1.4M - 1.7M||21||~1.2M||31.5%||~368.6k||~24.2%||141.0|
|1.7M - 2.0M||22||~1.4M||33.0%||~470.7k||~25.6%||165.1|
|2.0M - 2.4M||23||~1.7M||34.5%||~598.6k||~27.0%||193.1|
|2.4M - 2.9M||24||~2.1M||36.0%||~758.4k||~28.4%||225.7|
|2.9M - 3.5M||25||~2.6M||37.5%||~957.5k||~29.8%||263.6|
|3.5M - 4.2M||26||~3.1M||39.0%||~1.2M||~31.2%||307.7|
|4.2M - 5.1M||27||~3.7M||40.5%||~1.5M||~32.7%||359.0|
|5.1M - 6.1M||28||~4.5M||42.0%||~1.9M||~34.1%||418.8|
|6.1M - 7.3M||29||~5.4M||43.5%||~2.4M||~35.5%||488.2|
|7.3M - 8.7M||30||~6.5M||45.0%||~2.9M||~37.0%||569.1|
|8.7M - 10.4M||31||~7.9M||46.5%||~3.7M||~38.4%||663.1|
|10.4M - 12.4M||32||~9.4M||48.0%||~4.5M||~39.8%||772.6|
|12.4M - 14.8M||33||~11.3M||49.5%||~5.6M||~41.3%||900.0|
|14.8M - 17.7M||34||~13.6M||51.0%||~6.9M||~42.7%||1.0k|
|17.7M - 21.1M||35||~16.3M||52.5%||~8.5M||~44.2%||1.2k|
|21.1M - 25.1M||36||~19.5M||54.0%||~10.5M||~45.7%||1.4k|
|25.1M - 29.9M||37||~23.3M||55.5%||~12.9M||~47.1%||1.7k|
|29.9M - 35.6M||38||~27.8M||57.0%||~15.8M||~48.6%||1.9k|
|35.6M - 42.3M||39||~33.2M||58.5%||~19.4M||~50.1%||2.2k|
|42.3M - 50.3M||40||~39.6M||60.0%||~23.8M||~51.5%||2.6k|
|50.3M - 59.8M||41||~47.3M||61.5%||~29.1M||~53.0%||3.0k|
|59.8M - 71.0M||42||~56.3M||63.0%||~35.5M||~54.5%||3.5k|
|71.0M - 84.3M||43||~67.1M||64.5%||~43.3M||~55.9%||4.1k|
|84.3M - 100.1M||44||~79.9M||66.0%||~52.7M||~57.4%||4.8k|
|100.1M - 118.7M||45||~95.1M||67.5%||~64.2M||~58.9%||5.6k|
|118.7M - 140.8M||46||~113.1M||69.0%||~78.0M||~60.3%||6.5k|
|140.8M - 166.9M||47||~134.4M||70.5%||~94.8M||~61.8%||7.5k|
|166.9M - 197.8M||48||~159.7M||72.0%||~115.0M||~63.3%||8.8k|
|197.8M - 234.3M||49||~189.7M||73.5%||~139.4M||~64.8%||10.2k|
|234.3M - 277.5M||50||~225.3M||75.0%||~168.9M||~66.3%||11.9k|
|277.5M - 328.5M||51||~267.3M||76.5%||~204.5M||~67.7%||13.8k|
|328.5M - 388.8M||52||~317.2M||78.0%||~247.4M||~69.2%||16.1k|
|388.8M - 460.1M||53||~376.1M||79.5%||~299.0M||~70.7%||18.7k|
|460.1M - 544.2M||54||~445.9M||81.0%||~361.2M||~72.2%||21.8k|
|544.2M - 643.6M||55||~528.4M||82.5%||~435.9M||~73.7%||25.4k|
|643.6M - 760.9M||56||~626.0M||84.0%||~525.8M||~75.1%||29.5k|
|760.9M - 899.3M||57||~741.4M||85.5%||~633.9M||~76.6%||34.3k|
|899.3M - 1.1G||58||~877.8M||87.0%||~763.7M||~78.1%||40.0k|
|1.1G - 1.3G||59||~1.0G||88.5%||~919.4M||~79.6%||46.5k|
|1.3G - 1.5G||60||~1.2G||90.0%||~1.1G||~81.1%||54.1k|
|1.5G - 1.8G||61||~1.5G||91.5%||~1.3G||~82.6%||62.9k|
|1.8G - 2.1G||62||~1.7G||93.0%||~1.6G||~84.1%||73.2k|
|2.1G - 2.4G||63||~2.0G||94.5%||~1.9G||~85.5%||85.2k|
|2.4G - 2.9G||64||~2.4G||96.0%||~2.3G||~87.0%||99.2k|
|2.9G - 3.4G||65||~2.8G||97.5%||~2.8G||~88.5%||115.4k|
|3.4G - 4.0G||66||~3.4G||99.0%||~3.3G||~90.0%||134.3k|
|4.0G - 4.7G||67||~4.0G||100.5%||~4.0G||~91.5%||156.2k|
|4.7G - 5.6G||68||~4.7G||102.0%||~4.8G||~93.0%||181.8k|
|5.6G - 6.6G||69||~5.5G||103.5%||~5.7G||~94.5%||211.5k|
|6.6G - 7.7G||70||~6.5G||105.0%||~6.8G||~96.0%||246.1k|
|7.7G - 9.1G||71||~7.7G||106.5%||~8.2G||~97.4%||286.3k|
|9.1G - 10.8G||72||~9.1G||108.0%||~9.8G||~98.9%||333.1k|
|10.8G - 12.7G||73||~10.7G||109.5%||~11.7G||~100.4%||387.6k|
|12.7G - 14.9G||74||~12.6G||111.0%||~14.0G||~101.9%||451.0k|
|14.9G - 17.6G||75||~14.9G||112.5%||~16.8G||~103.4%||524.8k|
|17.6G - 20.7G||76||~17.6G||114.0%||~20.0G||~104.9%||610.6k|
|20.7G - 24.4G||77||~20.7G||115.5%||~23.9G||~106.4%||710.5k|
|24.4G - 28.7G||78||~24.4G||117.0%||~28.6G||~107.9%||826.6k|
|28.7G - 33.8G||79||~28.8G||118.5%||~34.1G||~109.4%||961.8k|
|33.8G - 39.8G||80||~33.9G||120.0%||~40.7G||~110.9%||1.1M|
|39.8G - 46.9G||81||~39.9G||121.5%||~48.5G||~112.3%||1.3M|
|46.9G - 55.1G||82||~47.0G||123.0%||~57.9G||~113.8%||1.5M|
|55.1G - 64.9G||83||~55.4G||124.5%||~69.0G||~115.3%||1.8M|
|64.9G - 76.3G||84||~65.2G||126.0%||~82.2G||~116.8%||2.1M|
|76.3G - 89.8G||85||~76.8G||127.5%||~97.9G||~118.3%||2.4M|
|89.8G - 105.6G||86||~90.4G||129.0%||~116.7G||~119.8%||2.8M|
|105.6G - 124.2G||87||~106.4G||130.5%||~138.9G||~121.3%||3.2M|
|124.2G - 146.0G||88||~125.3G||132.0%||~165.4G||~122.8%||3.8M|
|146.0G - 171.7G||89||~147.4G||133.5%||~196.8G||~124.3%||4.4M|
|171.7G - 201.9G||90||~173.5G||135.0%||~234.2G||~125.8%||5.1M|
|201.9G - 237.3G||91||~204.1G||136.5%||~278.6G||~127.3%||5.9M|
|237.3G - 278.9G||92||~240.1G||138.0%||~331.3G||~128.8%||6.9M|
|278.9G - 327.8G||93||~282.3G||139.5%||~393.9G||~130.3%||8.0M|
|327.8G - 385.2G||94||~332.1G||141.0%||~468.2G||~131.7%||9.3M|
|385.2G - 452.7G||95||~390.5G||142.5%||~556.4G||~133.2%||10.9M|
|452.7G - 531.9G||96||~459.1G||144.0%||~661.1G||~134.7%||12.6M|
|531.9G - 624.8G||97||~539.8G||145.5%||~785.3G||~136.2%||14.7M|
|624.8G - 734.0G||98||~634.5G||147.0%||~932.7G||~137.7%||17.1M|
|734.0G - 862.2G||99||~745.8G||148.5%||~1.1T||~139.2%||19.9M|
|862.2G - 1.0T||100||~876.5G||150.0%||~1.3T||~140.7%||23.1M|
Note that you probably don't need to wait until you amass 10.8G unobtainium before you can start the infinite loop of resets. What you need is to have 10.8G unobtainium immediately after a reset in order to directly reset again with a net increase in unobtainium without having to mine anything from a lunar outpost. The conditions for resetting into a game with 10.8 unobtainium is to satisfy the equation
10.88 * 10 ^ 9 = 0.015 * n * U
where n is the number of Chronospheres you have, and U is your unobtainium cap (assuming you max before reset). Furthermore, the number of chronospheres that you can afford is related to your unobtainium cap by
n = floor(log(U / 2500))
, and plugging this into the previous equation
10.88 * 10 ^ 9 = 0.015 * U * floor(log(U / 2500) / log(r))
Which has solutions at U > 7.41G (resetting with 98 chronospheres).
Unobtainium production per second is a function of:
Unobtainium Per Second = (# Lunar Outposts) * (1 + Space Production Bonus) * ( 1 + .15 * Cosmological Libertarianism Policy) * ( 1 + .1 * BLS * Necrocacy Policy) * ( 1 + 0.5 * Tempus Fugit Is On) * ( 1 + .75 * Microwarp Reactors) * (Year and Festival Effects)
where Space Production Bonus (a value you can see if you hover over the Unobtainium per Second value in your game) is
Space Production Bonus = (1 + 0.01 * # Space Elevators + 0.02 * # Orbital Arrays) * (1 + 0.75*(0.05 + Factory Logistics Workshop * .01) * (1 + 0.05 * Full Industrialization Policy) * # Factories) - 1
Year and Festival Effects = 1 always if you don't have Numerology researched. If you have Numerology researched, then you get a -10% if you're in the Charon cycle,
a +20% if you're in a Redmoon cycle, and the effect of having half your space elevators if you're in the Kairo cycle. Furthermore, if you have Numeromancy researched, you get an extra factor of x2 in the Redmoon cycle, which is boosted by 1% for each Brewery that you have. It makes the most sense to spend most of your time in a Redmoon cycle. The first Redmoon cycle always starts at year 25, and lasts for five years (66.67 real minutes). If you're always in the Redmoon cycle, then
Year and Festival Effects = 2.4 * (1 + 0.01 * # Breweries)
Therefore, if you're going for a short run resetting with a lot of stuff from Chronospheres, you want to follow the following research tree:
In a typical reset, you are trying to accomodate several hundred kittens in houses as fast as they arrive. The things that will slow you down are the following bottlenecks. All of these can be prevented if you reset with sufficient chronospheres and flux condensators. If you're using scripts, make sure that you go through this before you enable your script. Also, go ahead and get your unobtainium enhancements listed above.
Before Solar Revolution:
Disclaimer: Assumes your BLS is full, you've sacrificed all your alicorns, you're maxed out on temporal flux, etc... Not worrying about these things in a short run, but you don't want to waste this if you have it.
Disclaimer, I haven't checked the math. This is probably wrong
Buying Microwarp reactors costs 50 eludium, and gives you a +75% increase in unobtainium production. There are also two space structures that enhance unobtainium production that cost unobtainium:
As you buy more of these, each additional structure provides the same benefit at an increased cost. Furthermore, as time progresses, the time remaining to get a benefit out of these structures also decreases. So there comes a point where investing in more structures doens't make sense, and you should just let unobtainium accumulate without spending it.
Remember that the equation for unobtainium per second is (rearranged for convenience):
Unobtainium Per Second = 0.035 * ( 1 + .15 * Cosmological Libertarianism Policy) * ( 1 + .1 * BLS * Necrocacy Policy) * ( 1 + 0.5 * Tempus Fugit Is On) * ( 1 + .75 * Microwarp Reactors) * (Year and Festival Effects) * (1 + Space Production Bonus) * (# Lunar Outposts)
I'm going to make some general assumptions. Your mileage may vary, so if you want to fine-tune this, go ahead.
The space production bonus is the product of two terms. The contribution from factories, and the contribution from your elevators+arrays
(1 + 0.01 * # Space Elevators + 0.02 * # Orbital Arrays)) * (1 + 0.75*(0.05 + Factory Logistics Workshop * .01) * (1 + 0.05 * Full Industrialization Policy) * # Factories) - 1
If you have the right policies and workshop upgrades, the second line is
1 + 0.04725 * # Factories)
This all boils down to
Unobtainium per second = 0.035 * 1.15 * 2.4 * (1 + .20) * # Outposts * (1 + .04725 * # Factories * (.01 * # Elevators + 0.02 * # Arrays)) * (1 + Microwarp * .75) ~= 0.116 * # Outposts * (1 + .04725 * # Factories * (.01 * # Elevators + 0.02 * # Arrays)) * (1 + Microwarp * .75)
When you build your nth elevator, you spend 50 * 1.15 ^(n-1) unobtainium, and increase your unobtainium production by (.2 * .04725 * .01 * # Outposts * # Factories) unobtainium per second. When you build your nth array, you spend 100 * 1.15 ^(n-1) eludium, and increase your unobtainium production by (.2 * .04725 * .02 * # Outposts * # Factories) unobtainium per second. Immediately before you reset, you can sell back these structures at half the cost, so the real sacrifice is half this amount. Assuming you sell back before you reset, this is how you determine if the sacrifice is worth it
A microwarp reactor gives you 0.035 * 1.15 * 2.4 * (1 + .01 * # breweries) *(1 + .04725 * # Factories) * 0.75 * # Outposts unobtainium per second, or (assuming 20 breweries) 5.21 unobtainium / minute / outpost. The break-even is 5.21 * (1 + .04725 # factories) * # outposts * remaining minutes = 50 * 1000 / craftRatio. Refactored, you want minutesRemaining > ~10000 / (# outposts * craftRatio * (1 + .04725 # factories). So, if you have ~20 outposts, 100 factories, and a craft ratio of 16 (+1500% craft effectiveness), it makes sense to invest in microwarp reactors if you have at least 5 minutes remaining.
Example 1: You have 150 factories, and 25 outposts, and microwarp reactors. OF = 3750. You're 10 minutes into a run, and have 20 minutes to go. 20 * 3750 / 176 = 426 unobtainium. You have 18 elevators, so the next one costs 618.7 unobtainium. Half of 618.7 is 309 (That's the unobtainium you lose by buying it, then getting a refund before resetting). So you sacrifice 309 unobtainium to gain 426 unobtainium for a 117 unobtainium profit. You should buy the 19th elevator.
Example 2: You now have 19 elevators, 160 factories, and 26 outposts, and microwarp reactors. OF = 4,160. You're now 15 minutes into the run, and have 12 minutes to go. 12 * 4160 / 176 = 283 (the gain). You are figuring out if you should buy the 20th elevator (costs 711.6). Half of 711.6 is 355 (the sacrifice). The sacrifice is greater than the gain, so that's a net loss of -72 Unobtainium. Don't buy the 20th elevator.
You have to account the workshop ratio into the eludium calculation. When you craft eludium, you consume 1000 unobtainium, and get 1 + craftRatio eludium. For this, we're going to treat the eludium we spend as a total loss. Even though we can sell the arrays to get our eludium back, the flux condensator only preserves the square root of the total eludium, and we can't use eludium to buy chronospheres. So the lost unobtainium to buy the nth orbital array is 100 * 1.15 ^ (n - 1) * 1000 / (1 + craftRatio).
Example 4: You have 130 factories, 20 outposts. OF = 2600. You're 5 minutes into a run so you have 25 minutes left. 2 * 25 * 2600 / 176 = 738 unobtainium. You have 0 arrays, so the first one costs 100 eludium. You have a crafting ratio of 17.50 (+1650% Craft Effectiveness), which means it will cost 100 * 1000 / 17.50 = 5714 unobtainium. There is no way that the array is worth it (spending 5714 to get 738 doesn't make sense).
Keep in mind that Orbital Arrays require the same resource that Microwarp reactors require: Eludium. Microwarp is a cheaper investment that gives a bigger benefit, and should be gotten every run that lasts longer than 5 minutes (which is pretty much all of them). Orbital arrays only should be gotten in runs that last longer than a half hour (or maybe even an hour).
Eludium huts cost 125 eludium, which is kind of a lot. Huts have a base price ratio of 2.5, which you can reduce by 50% with ironwood, 30% with concrete, 25% with unobtainium, 10% with eludium, and then 8.6458% with all the other paragon upgrades. Before eludium huts, they have a price ratio of r_unobtainium=1.36388. Afterwards, it comes down to r_eludium=1.289079. (You can always check in the console with game.bld.getPriceRatio('hut')). So assuming you're maxing out huts, and you have H_unobtainium huts before eludium huts, that means your max wood is around 5 * r_unobtainium ^ (H_unobtainium). Afterwards, you'll be able to afford 5 * r_eludium ^ (H_eludium) huts. So solving this gives.
H_eludium = H_unobtainium log(r_unobtainium) / log(r_eludium) = 1.231 H_unobtainium
With the extra huts, it takes a little longer to hit your kitten max (e.g., if you had 50 huts before eludium huts, then you could get 61 huts afterwards, for a total of 22 extra kittens, which takes an extra 67 seconds before you max out). If you are maxing out at 500 kittens without eludium huts, and you can get 522 kittens with eludium huts, your paragon-per-hour efficiency goes from 86% to 86.6%. So is it worth it, meh. ¯_(ツ)_/¯
Another consideration, if you sell an array, that can count towards the eludium you have at the beginning of the next run.
You get 1.5 * sqrt(eludium) * number of chronospheres eludium on reset, and you want to bring 50 eludium in order to get microwarp reactors early in your next run. That works out to 1111 / (# chronospheres)2. So if you go for 1 chronosphere, you need 1111 eludium to buy microwarp right off the bat. If you out 3 chronospheres, you only need 124 eludium (a little more than you get by buying two arrays, then selling them back). With five chronospheres, you need 44, which is what you get from buying and selling one array.
On a tangent, what is more efficient way to send eludium to the past? Crafting it before resetting, or crafting it after resetting?
Crafting before resetting: Eludium after reset = (# chronospheres) * 1.5 * sqrt( unobtainium * preResetCraftRatio / 1000 ).
Crafting after resetting: Eludium after reset = (# chronospheres) * 0.015 * unobtainium * (postResetCraftRatio / 1000).
Solving this for the breakpoint reveals that unless you're crafting huge amounts of unobtainium into eludium, it's more efficient to do the crafting before the reset than after. The point at which waiting until after resetting makes more sense is when you have more unobtainium than the following expression:
10 M * preResetCraftRatio / PostResetCraftRatio^2
Example: If you have a crafting ratio of 20 before resetting, and a crafting ratio of 10 after resetting, then you would need to intend to craft more than 2 million unobtainium waiting to craft eludium after resetting to be worthwhile.
For that reason, ideally you should make up your mind how much eludium you want to start your next run with. 50 eludium is what you need for microwarp reactors, and you need 1111 eludium pre-reset with one chronosphere to get it. That's probably all you need. Orbital arrays aren't worth it for short runs, and eludium huts only get you about two dozen extra kittens which only speeds up your paragon-per-hour efficiency by 1%.
Stock up on time crystals, and then do ~30 minute runs.
Start each run by doing the following
Speed up unobtainium production:
Unlock the hut price ratio reductions:
Buy housing (log houses, mansions, space stations, and huts) and storage (harbors, accelerators) for as long as you can keep up with the incoming kittens. Max workshops, factories.
Prioritize using unobtainium for buying space elevators, and ignore orbital arrays and moon bases. Use the derivations above to determine when you should stop buying space elevators. (You can use a script for this, just don't waste unobtainium on stuff you won't use in the next 30 minutes).
When you can't keep up with incoming kittens, do the following.
Alright, so I'm assuming you've farmed all the paragon you want, built a bunch of Event Horizons, and pushed really hard to build 98 chronospheres and remax on unobtainium. Congratulations, you now have enough unobtainium to reset indefinitely without ever having to mine any more unobtainium. You can at this point exponentially grow your resources just by getting enough blueprints and science to build 73(+) chronospheres each run, and reset. The next question is what is the optimum number of Chronospheres to build to be economical with your time crystals, given that these are one of the few resources that don't build up each run.
With 67 Chronospheres, you get 100.5% of your resources back at the cost of 156.2k time crystals. So that's 0.5% growth for the cost of 156.2k time crystals, or 3.2%/1M TCs. If you build 68 Chronospheres, you get 2% growth for the cost of 181.8k time crystals, or 11%/1M TCs, so it's more economical with TCs to buy 68 chronospheres instead of 67. At some point, the exponential growth in TC cost catches up with the linear growth in profit. The crossover point happens at 73 Chronospheres, where you get 9.5% growth for 387.6k TCs, or 24.53%/1M TCs. 73 Chronospheres is also the minimum number of Chronospheres to get a profit on Unobtainium as well as the other resources. I'm not sure if bloodrizer did this intentionally, or whether she just got lucky, but 73 is the magic number for both TC efficiency and unobtainium break-even.
Resetting with 73 Chronospheres means you double all your non-unobtainium resources every 8 resets for a total of 3.1M TCs (Compare, for example, to resetting with 94 Chronospheres, which doubles every 2 resets at the total cost of 18.6M TCs).
By far, the fastest way to get time crystals in the late game is through trades with the leviathans (roughly by a factor of ~30x faster than accumulating alicorns). To do this, you want to get your base unobtainium production as high as possible, which has already been covered in this guide. In summary:
With all of this put together, you should be getting hundreds of unobtainium per second
Next, you want to max the number of time crystals you get per trade. In order to do this
Your TCs per 5000-unobtainium trade is this equation:
TCs / trade = 0.245 * (1 + energy / 50) * (1 + 0.015*tradeposts + IsMerchantLeader? * 0.03*(1 + ((sqrt(1 + 8*burntParagon/500)-1)/2)) )
In the late game, you should be able to get 5-10 time crystals per trade.
So if you get 500 unobtainium/second in a redmoon cycle, and 5 time crystals per trade, you get about 1800 TCs per hour without resource retrieval (only skipping 45 seasons every 66 minutes (44 minutes with Chronosurge) to stay in a redmoon cycle).
This can be greatly enhanced by purchasing Resource Retrieval levels and Chronofurnaces. Each level of Resource Retrieval gets you 1% of your annual production (your per-second rate divided by 800, or divided by 533 if you have Chronosurge). You can increase each level by buying Blazars. However, you're limited to how often you can do a Time Skip because shattering generates 10 units of heat (5 if you do the 1000 year challenge, which is quite easy to achieve).
The cooldown in seconds between skips in seconds is 50 / (chronofurnaces + 1). So with 24 furnaces, you can skip every 2 seconds, or 1800 times per hour. Or, you get 72 skips per hour per chronofurnace.
So your total rate of TC production is this equation here:
If you're doing a run for a certain number of hours, your total profit is
Profit = (Base * RR - shatter cost) * 72 * (CF + 1) * hours - CF cost - RR cost
where base is your (unobtainium / year / 800) * (1 + blazars / 50) * (TC per trade / 5000), and is somewhere between 2-4 depending on how late game you are. This ignores alicorns, but the alicorn contribution is small. The shatter cost is about 1 (which increases slowly with time, but so does your Leviatahan energy), and you can ignore this if you're doing stuff by hand. It also ignores the bonus TCs you get when you let your chronofurnaces automate before you finish your run. An easy way to figure out "base" if you have at least one RR is to make as many TCs as possible, do 45 time skips, then make as many TC as possible, and divide by (45 * RR), where RR is the number of resource retrievals you have.
The total cost is
Cost = 1000 * (1-1.3^RR)/(1-1.3) + 25 * (1 - 1.3^CF)/(1-1.3)
You can maximize profit using a spreadsheet, or you can use some rules of thumb. If you're doing a short run, you don't want to invest too much into a shatter engine, so your cost is small, but your total income is going to be small as well. For about 8 hours, the optimum income to cost ratio is about 2. For 24-hour runs, its closer to 3, and for week-long runs, it's closer to 4. Naturally, the longer the run, the more efficient your shatter engine becomes. But some good guidelines are:
|Base||hours to play||optimum RR||optimum CF||cost||profit||profit/h|
|2||(2 days) 48||22||39||~1.6M||~4.2M||~87.5k/h|
|3||(2 days) 48||24||42||~2.9M||~7.5M||~156k/h|
|4||(2 days) 48||25||43||~3.8M||~11.2M||~233k/h|
|3||(1 week) 168||29||48||~11.2M||~39M||~232k/h|
|4||(1 week) 168||30||50||~15.7M||~57.6M||~342k/h|
|4||(1 month) 750||36||57||~75.56M||~372M||~496k/h|
|5||(1 month) 750||37||58||~96.5M||~489M||~652k/h|
It usually takes some time get get your TC/skip high enough (unobtainium production high enough, enough leviathan energy, etc...).
If you reset with more than 73 CS, you grow the amount of unobtainium that you have. Eventually, you get a big enough unobtainium bank to start using your spare unobtainium to do fast trades with Leviathans (instead of using a shatter engine). Rather than using time crystals from your long shatter-engine run, you're building chronospheres with unobtainium + unobtainium quickly traded for time crystals. The equation for the optimum number of CS to build is now:
n = round(W(e * (r - 1) * U / (2500 + 5000/TCperTrade + e) - 1) / ln( r )
where r is the CS price ratio of r = 1.163541882, and W is the Lambert function, andn TCperTrade is the number of time crystals you get per trade. Assuming it's a short run, you'll only have a few energy. Assuming one energy, a Merchant leader, 300 tradeposts, and 250k burnt paragon, you'll get about 1.615 TC per trade (this goes up to 1.9 by the time you have 10 energy, so you might like waiting a little bit to get the enhancement, up to you). With a TCperTrade of 1.615, the magic number is 29G unobtainium and 70 CS. If you wait until TCperTrade is 2, the magic number is 26G unobtainium with 70 CS. Doing a long run to get several hundred Leviathan energy can get you a TCperTrade well above 10. At 10, you need 15G unobtainium and 72 CS to break even.
At some point, you can just start doing extremely fast resets where you buy ~70 CS (trading the Leviathans to get 246k time crystals), and resetting. The only thing you need to wait for is either trading or crafting blueprints for that many Chronospheres.
Normally, when you reset, you have 0 kittens, and you have to wait a few minutes before you have 70 kittens to start getting additional paragon.
However, if you have an exponentially growing void, you can afford to spend it on fixing cryochambers. Fixing cryochambers is a flat cost of 100 time crystals, 500 void, and 3000 temporal flux. Time crystal cost at this point is negligible, and by this point you should have stupidly large amounts of void. The 3000 temporal flux can be easily generated once you have the Chronosurge update (costs 9500 flux for Chronocontrol and Chronosurge unlock).
Assuming you have 71 Chronospheres, you can have up to 71 Cryochambers. It's the most economical to build these one chamber at a time in each run. Buy a chamber first, then start fixing your used ones, and you should never have to spend more than 1 karma per chamber. With 71 Chryochambers, you need 6500 + 3000 + 71 * 3000 = 12.5k flux. With 71 chronospheres, you need 176 skips to generate this much flux, which is quite affordable, compared to the huge TC investment for 71 Chronospheres.
The benefit of having 71 kittens at the beginning of a reset is that you get 1 paragon without having to wait for 71 kittens to arrive. They walk into cryochambers, take a nap while the world around them disintegrate, walk out of the cryochambers, build 71 chronospheres, have a shatter party, fix their cyrochambers, walk back into them, and take another nap. This cycle is very fast and generates paragon without kittens needing to be reborn.