This is a math paper with the purpose of seeing how far we need to go, and how much time it takes to get there in terms of cultivation. Along the way, I will be setting up the idea that taking four actions cultivating with the last one doing a quest is the best way to reach the goals we wish to achieve. The math is set up to prove that, but the work is going to be useful to anyone who wishes to use the math to support other ideas.
Spiritual cultivation
120 to mid-yellow
240 to late yellow
480 to peak yellow
Total of 840
Physical cultivation
120 to mid-silver
240 to late silver
480 to Peak Silver
Total of 840
Qi cultivation
26 qi, 27 qi, 28 qi, 29 qi, 30 qi, 31 qi, 32 qi, 33 qi, 34 qi, 35 qi, 36 qi, 37 qi, 38 qi, 39 qi, 40 qi, 41qi, 42 qi, 43 qi, 44 qi, 45 qi, 46 qi, 47 qi, 48 qi, 49 qi, 50 qi, 51 qi
Total of 991 successes in order to get to 60+ qi
With Bear Marrow Elixir successes drop to 711.
Total number of success to get to Late yellow/late silver with 60 qi
2,671 successes
Divide by an average of 15 successes per action =
179 actions.
With three actions a week, that will be
59 weeks to reach that goal.
With four actions a week, that will be
45 weeks.
With five actions a week, that will be
36 weeks.
With Bear marrow elixir our needed successes and actions drop to
2391 successes
Which divided by 15 average success per action =
160 actions.
With three actions that means it will take
54 weeks.
With four actions that means it will take
40 weeks.
With Five actions, that means it will take
31 weeks.
This assumes 15 successes an action for a premise. The moment we change that to 16 or 17 successes a week, everything changes. Every additional success seems to reduce the weeks required by 3.5 (around never exact)
With the assumption of 16 successes
2391 divided by 16 =
149 actions
With three actions a week that becomes
50 weeks
With four actions a week that becomes
37 weeks.
With 5 actions a week that becomes
30 weeks.
However, the magic will happen when we get 17 successes a week.
2391 divided by 17 =
141 actions
With three actions a week that becomes
47 weeks.
With four actions a week that becomes
35 weeks
With five actions a week that becomes
28 weeks.
As we can see here, Bear Marrow elixir is absolutely essential in order to do this in the time required. If we are able to get a total of 17 successes per action per week, we will be able to get to peak yellow, and peak silver, and 60+ qi within 35 weeks. This would leave one week to do a breakthrough to either bronze or green depending on what we wanted to do before the 52 weeks were up.
You might be saying though, but how can we get to 17 successes for a spiritual, physical, and qi cultivation every single week? And where are the arts and meridians we need! Fear not, for with the notification that we have 5 major actions we are going to be able to do everything we need. The reason for that is that we will get much more than 17 successes a week, and, in all likelihood, we will be able to get 18 or 19 successes a week.
At the current level, without any pills or other modifications, we have
Talent + AS + Red stones + Yellow Stone + AS vent = ?? + 2 auto successes
6 + 6 + 5 + 5 + 8 = 30 dice being thrown at the problem.
With an average of 15 successes + 2 auto-successes, we have 17 successes on average for every action involving physical, spiritual, and Qi rolling.
With only spending 3 red spirit stones we are already getting on average 17 successes. Now we throw in the pills we can buy: Steady growth pill (SGP), Bear Marrow Elixir (BME), Argent Elixir (AE), and Flowing rivers pill (FRP). (Note: I will also start referring to Spiritual cultivation as SC and Physical cultivation as PC)
From most expensive to least we have
AE = 10 red spirit stones (4 additional die for physical cultivation)
SGP = 8 red spirit stones (4 additional die for PC, SC, Qi)
FRP = 6 red spirit stones (3 additional die for water arts and SC)
BME = 4 red spirit stones (3 additional die for PC, + Qi expansion)
With the three red spirit stones we normally use, that brings us up to 31 spirit stones used per week for cultivation. Now some of you will be wondering "Why is AE being used, it's primarily used for Argent Soul cultivation and not really anything else." The answer is, it depends on Yrsillar. If he allows the AE proc to occur, but the overflow goes to SC, then we should most definitely use it because it will help SC keep up with PC. However, if Yrsillar views that it is gaming the system too much and using a pill for something that it was not designed for, then we can switch that pill with White Heart pill, which is cheaper, but gives one less die, and also only triggers for training wind arts and PC.
Moving on to the math then! This is where it becomes trickier, because the pills begin to affect different things, and so different cultivations will get different results. However, if we are able to get a rough approximation of which action will get what number of successes, we can hopefully see a medium amount of successes from the actions
This is Physical cultivation
Talent + AS + 3 redstones + 1 Yellow stone + ASV + SGE + BME + AE = ?? + 2 auto
6 + 6 + 5 + 5 + 8 + 4 + 3 + 4 = 41 dice + 2 auto's
On average that would be around 22 successes an action
(The loss of AE where it is replaced with White Heart Elixir will not change this number)
This is SC
Talent + AS + 3 redstones + 1 yellow stone + ASV + SGE + FRP = ?? + 2 auto
6 + 6 + 5 + 5 + 8 + 4 + 3 = 37 dice + 2 auto's
This comes out to about 20 successes an action
This is Qi expansion
Talent + AS + 3 redstones + 1 yellow stone + ASV + SGE = ?? + 2 auto
6 + 6 + 5 + 5 + 8 + 4 = 34 + 2 auto
This comes out to about 19 successes an action.
As you can see, PC will be moving at a bit of a faster clip than SC, but will also be helping Qi along as well. I'm not counting the addition to Qi right here because that addition was already calculated at the beginning in order to come up with the initial targets to hit. Now that we have this out of the way, we can work on what 20 successes a turn would look like with the previous numbers
With the BME the number of successes to hit is around
2391
To get the number of actions required to meet that number I have been dividing it based on the number of successes that I predict we will need to hit in order to determine that number of weeks it will take. However, I have decided that while that worked for the above hypothesis that it was possible to get to Peak yellow/silver it would be prudent to work in more detail in order to establish the growth rate of each level. This is because the medicines have messed with the numbers as well as to determine the exact number of actions we need for each specific area.
PC was a total of
840
Divide that number by the number of average successes we expect per turn, and we should have the number of independent actions it will take to get to peak yellow.
840 / 22 = 38 independent actions
SC was a total of
840
Divide that number by the number of average successes we expect per turn, and we should have the number of independent actions it will take to get to peak yellow.
840 / 20 = 42 Independent actions
Qi expansion (with Bear Marrow) was
711
Divide that number by the number of average successes we expect per turn, and we should have the number of independent actions it will take to get to peak yellow.
711 / 19 = 37 independent actions.
So, to get these numbers it will require us to take in about 29-31 spirit stones a week. With our current supply of spirit stones, we will be out within two to three weeks. In order to fuel this massive drug engine, it becomes imperative that we take a quest from the Job board every single week, preferably the Hard Gathering Mission. This mission will net us 8 sect points, and various components that can be sold for spirit stones. Should 6 of those sect points be given in exchange for 5 Spirit stones each, we will have 30 spirit stones to play with. The difference can be made up by selling the spirit beast parts we would have acquired through killing the spirit beasts that guard the areas. The left over sect points can accumulate to let us get a reward. Taking other missions, especially the 10 point ones, will allow us to gather points faster, but are not needed for this system to work.
So there are some hard numbers on the number of actions it will take for each category to be at the minimum level we want them to be in. They can be depressing as it appears to be a lofty goal to have everything ready and still break Green Bronze by the time of the Thunderdome 2. However, fret not! There are things I have not included in these calculations because A) I do not know their value, or B) I'm not going to do 36 separate calculations to determine when we hit mid yellow/silver in order to calculate the boost that having a second yellow stone will give.
We don't know what AS 5 does nor do we know what EPC does, nor do we know what beast cores do. All of these are valuable resources that can greatly speed up our cultivation if we know about them. Also, I haven't even considered what benefits friends will give us, or the possibility of tutoring (Tutor Spiritual cultivation, we need more dice). All of these will give us large boosts to the speed and efficiency that we can cultivate. Consider also the tokens that we have received, something which gives a bonus action to a specific cultivation. This is most likely going to be SC as well as Qi expansion and that gives us 3 actions in each section that should not be ignored.
There will be cries though, we don't have the time by your calculations to cultivate EPC, or Meridians, or combat arts! Fear not, I say! For I have only calculated for a total of 3 actions, PC, SC, and Qi. That leaves the fourth action to be used for EPC, Meridians, or combat arts as the situation demands it! There is also the possibility of closed-door training to be considered as well, and the speed at which we will increase cultivating once we reach EPC and Mid yellow/silver can not be ignored either.
There are no social actions either in this plan! You're right, there isn't. With the new system that Yrsillar developed, I could focus my pure unadulterated attention on the mathematical portion of cultivation without a care to the social side. Because of this division, I don't need to calculate if becoming a social pariah is needed in order to reach our goals. We can have a strong thriving social network as well as becoming the number one cultivator in the sect. Because make no mistake, that is my goal. To stand as the last one among the tourney goers and say "I have made it this far by reaching out to my friend while reaching for the stars at the same time. I have decided to try for everything and I have yet to fail."
It may be arrogant of me to believe that this is possible, but it is still my belief that I can bake a cake and eat it as well.
This math has not been combed through thoroughly for errors, and there may be some. Please be jubilant in pointing them out so that we may all profit from them. Ideas are welcomed for condensing our actions to better fit the format that Yrsillar has provided as well as getting the most out of each action, as well as ideas on how to make up actions that have been lost in the pursuit of other noble goals. This is a document specifically espousing the need and desire to have a quest from the Job board every single week in order to fuel the engine of cultivation we will require. The math is used to support that idea, but feel free to take the math for yourself and create long-term goals from it.
While we do not know the values of mid yellow or late yellow, I have taken Arkeus's recognition of the pattern in red and have based my assumptions on that.
Edit: I have not included the rerolls for one, mainly so that my math can have some leeway, as well as to give us a nice boost the longer the route goes on.