Hello! This guide serves to determine whether you should spend your coins on Vials of Adeptal Speed. I will be simplifying the math as much as possible for easier understanding. TL;DR is at the bottom 🙂
Players have the option to buy up to 5 potions everyday to speed up their crafting at the cost of 10 coins each. Buying potions will let you place more furniture, increasing your Adeptal Energy and the number of coins you earn per hour. However, the coins spent could have been used to buy blueprints to increase your trust rank.
The main goal will be to maximize the rate of Trust Rank EXP you get. I will be using coins as a measure of efficiency since coins should only be spent on endeavors that will increase your trust rank.
This post is purely for players who want to min-max their Trust Rank. Please enjoy the housing system however you see fit 🙂
Approach (feel free to skim)
My method centers around the idea that buying vials will shorten the time taken to hit the next earning rank.
Consider 2 players:
Player A that spends all his coins on new recipes. Accumulating adeptal energy as fast as crafting lets him.
Player B that spends 50 coins a day on vials. He is able to place down 5 more furniture than player A, accumulating more adeptal energy.
Player B will reach the next earning rank faster than Player A. There will be a period of time where Player B earns more coins/hour compared to Player A. However, once Player A hits the next earning rank, Player B’s earning advantage is gone.
Therefore, we have to calculate the earning advantage B has during that period of time. We have to see if B’s extra earnings were able to justify spending 50 coins/day when he was at the same rank as A. (we will assume B stops buying vials once he reaches the next earning rank)
Now consider the 2 possible outcomes:
B’s extra earnings is greater than his expenditure on vials. He was able to make up for his expenses and now has more coins to spend on new recipes compared to A. (yay)
B’s extra earnings is less than his expenditure on vials. Despite earning more coins, he was not able to break-even with the cost of vials. He has less coins to spend on new recipes compared to A. (boo)
Methodology (feel free to skip)
Every item you craft is sped up with the help of other players (12hrs for each 4-star)
Crafting slots are fully utilized & there is no time delay between crafts
Every item crafted will be a 4-star furniture (I am aware that there are only 15 4-star recipes and many more 3* recipes. However, most of the furniture you craft would be 4-star recipes that you have already learnt on top of the new recipes. Furthermore, 3-star furniture takes less time and coins to obtain so my calculations should not be too far off)
We will ignore load limits (as you unlock more realms, load costs should not matter)
Number of crafting slots = (s)
Adeptal Energy required to get to the next earning rank (r) ~eg. 1500 from Cozy to Queen-Size
Additional coins earned per hour in the next rank (d) ~eg. if you go from 16/hr to 20/hr, d=4
Number of Vials of Adeptal Speed purchased per day (x)
Calculate the amount of Adeptal Energy gained per day without vials = 90*2*s = 180s (given that you craft 4-star recipes that give 90 energy, twice a day every 12hrs)
Calculate the time taken to the next earning rank without vials = r / 180s
Calculate the amount of Adeptal energy gained per day using X vials = 180s + 90x
Calculate the time taken to reach the next earning rank using X vials per day = r / (180s+90x)
Calculate the difference in time obtained in step 2 & 4 (lets call this T)
This means that using x number of vials per day will help you reach the next earning rank T days faster than if you didn’t use vials. In other words, now you have T days where you are earning extra coins because of your early rank-up. Now for part 2:
Calculate the extra earnings in that time difference = T * 24hrs * d
Subtract the amount you spent on the vials = (T*24*d) – [r/(180s+90x)]*10x
Voila! We have determined how many extra coins you have that can be used for new blueprints!
Now if we let y = the extra coins you got. We can simply the equation to make a fancy formula:
Where y = Extra coins earned, x = No. of vials bought per day, s = No. of crafting slots, r = Adeptal energy required to reach the next earning rank, d = Additional coins earned per hour in the next earning rank
Results & Interpretation
The goal is to see how many vials you should buy each day to maximize the amount of coins you earn.
You can plug that equation into sites like https://www.desmos.com/calculator and play around with the values to understand the relationship between the variables. Here are a few things I found.
If your next earning rank gives you +4 coins/hour, it is always beneficial to buy 5 Vials of Adeptal Speed everyday. You will gain more coins in the long term despite spending 50 coins per day. (This only applies if you have ≤ 4 crafting slots which is the majority of players in this category)
If your next earning rank gives you +2 coins/hour, you should not buy any Vials of Adeptal Speed. You will lose more coins because getting +2 coins/hour isn’t enough to outweigh spending 50 coins everyday. (This only applies if you have ≥ 3 crafting slots which is the majority of players in this category)
The amount of Adeptal energy required to get to the next earning rank does not influence the cost/benefit of buying Vials of Adeptal Speed.
Here are some graphs to illustrate my points:
Graph representing an early-mid game situation
Graph representing a mid-late game situation
Thank you for taking the time to read my post. If there are any better ways to approach this problem, do let me know!