Lothengriol
Greenhorn
Here's a fun optimization problem that according to my forum search has yet to be fully analyzed: Quartz vs. Fire Quartz.
In every crystalarium setup, a shrewd farmer may wish to grow a variety of minerals. Yet crystalaria are a scarce resource for the beginning farmer, and even a veteran ploughman of many moons and many suns can value a strongly-informed distribution of their hardworking mineral-makers. The question of Quartz vs. Fire Quartz as regards crystalaria has many complications preventing there from being a winner for all situations. Some confounding variables include:
- Quartz can be traded 5:1 for bombs, while Fire Quartz cannot be traded or turned into Quartz at all
- Fire Quartz can be smelted in a furnace for three times Quartz's output, saving two coal for each batch (and each batch takes the same 90 minutes to process)
- Crystalaria produce 3 Quartz or 1 Fire Quartz per day
- Fire Quartz takes 21 hours and 40 minutes to produce compared to Quartz's 7 hours
From these we learn Quartz's main strength is in its versatility, while Fire Quartz is best for Refined Quartz production only. This does not tell us how these two minerals compare to each other, though! For this I will dive more deeply into the inputs and outputs of each.
For the following equations:
C = Coal
Q = Quartz
FQ = Fire Quartz
RQ = Refined Quartz
B = Bombs
M = Minutes
D = Days
Furnace:
Quartz: 1 C+ 1 Q + 90 M = 1RQ
Fire Quartz: 1 C + 1 FQ + 90 M = 3 RQ
Balancing these to match outputs, we get:
1 RQ = 1 C + 1 Q + 90 M
1 RQ = 1/3 C + 1/3 FQ + 30 M
FQ = 3 Q
So for producing Refined Quartz with a Furnace, Fire Quartz is unsurprisingly better by a factor of three. How about trading/buying Bombs?
For Quartz, this is a much easier process when compared to Fire Quartz, but we can still make comparisons. For Fire Quartz, we can sell it directly for 100g, which would be worse profit over time than diamonds in crystalaria overall. This shouldn't involve the Gemologist profession because of where this will occur in the progression of the game (yes this is a qualitative value judgment on my part), but I'll include that math anyway:
Crystalarium & Furnace (Bombs only, Q vs. FQ):
30 D = 90 Q = 18 B
30 D = 30 FQ = 3 B (1.3 B with Gemologist)
But what about a hybrid approach, where you produce enough Fire Quartz to match (or out-produce) a hypothetical Quartz-based Refined Quartz production regime, and sell the rest for Bombs? This is also bad, but could make sense under weird self-imposed circumstances. The Fire Quartz crystalarium production equation can be modified like so to produce a few different hybrid production equations. I will only consider the simplest of cases, where the Fire Quartz is used to produce either one or two Refined Quartzes and the rest of the Fire Quartz is sold for bombs:
Crystalarium Only (FQ -> RQ + B):
30 D = 30 FQ = 60 RQ + 1 B (1.3 B with Gemologist)
30 D = 30 FQ = 30 RQ + 2 B (2.6 B with Gemologist)
Let's compare this to using some (one-third in the first equation and two-thirds in the second) of our crystalaria to produce Quartz and the rest as Fire Quartz:
Crystalarium Only (Q + FQ -> RQ + B):
30 D = 20 FQ + 30 Q = 60 RQ + 6 B
30 D = 10 FQ + 60 Q = 30 RQ + 12 B
This is an outright better deal than buying the bombs with Fire Quartz sales, which reflects the general rule in Stardew Valley that things traded are cheaper than things bought. Hopefully this is a helpful comparison. Let's move on to what I think is the more interesting case, involving that post-Community Center item:
If you have enough coal but not enough cash, it might be a good idea to run Quartz through your limited number of crystalaria. But later in the game when you have enough extra money that bombs are no longer difficult to purchase, Fire Quartz seems to be the better option. Eventually, with enough crystalaria, it may again become worthwhile to duplicate Quartz, finally coming full circle.
What do you all think? Which paths have your experiences in Refined Quartz production led you down?
In every crystalarium setup, a shrewd farmer may wish to grow a variety of minerals. Yet crystalaria are a scarce resource for the beginning farmer, and even a veteran ploughman of many moons and many suns can value a strongly-informed distribution of their hardworking mineral-makers. The question of Quartz vs. Fire Quartz as regards crystalaria has many complications preventing there from being a winner for all situations. Some confounding variables include:
- Quartz can be traded 5:1 for bombs, while Fire Quartz cannot be traded or turned into Quartz at all
- Fire Quartz can be smelted in a furnace for three times Quartz's output, saving two coal for each batch (and each batch takes the same 90 minutes to process)
- Crystalaria produce 3 Quartz or 1 Fire Quartz per day
- Fire Quartz takes 21 hours and 40 minutes to produce compared to Quartz's 7 hours
The Heavy Furnace increases smelting's efficiency:
- Fire Quartz produces 15-20 Refined Quartz for every 3 Coal
- Quartz produces 5-6 Quartz for every 3 coal
- Batch processing time remains the same as before for each
- Fire Quartz produces 15-20 Refined Quartz for every 3 Coal
- Quartz produces 5-6 Quartz for every 3 coal
- Batch processing time remains the same as before for each
From these we learn Quartz's main strength is in its versatility, while Fire Quartz is best for Refined Quartz production only. This does not tell us how these two minerals compare to each other, though! For this I will dive more deeply into the inputs and outputs of each.
For the following equations:
C = Coal
Q = Quartz
FQ = Fire Quartz
RQ = Refined Quartz
B = Bombs
M = Minutes
D = Days
Furnace:
Quartz: 1 C+ 1 Q + 90 M = 1RQ
Fire Quartz: 1 C + 1 FQ + 90 M = 3 RQ
Balancing these to match outputs, we get:
1 RQ = 1 C + 1 Q + 90 M
1 RQ = 1/3 C + 1/3 FQ + 30 M
FQ = 3 Q
So for producing Refined Quartz with a Furnace, Fire Quartz is unsurprisingly better by a factor of three. How about trading/buying Bombs?
For Quartz, this is a much easier process when compared to Fire Quartz, but we can still make comparisons. For Fire Quartz, we can sell it directly for 100g, which would be worse profit over time than diamonds in crystalaria overall. This shouldn't involve the Gemologist profession because of where this will occur in the progression of the game (yes this is a qualitative value judgment on my part), but I'll include that math anyway:
Crystalarium & Furnace (Bombs only, Q vs. FQ):
30 D = 90 Q = 18 B
30 D = 30 FQ = 3 B (1.3 B with Gemologist)
But what about a hybrid approach, where you produce enough Fire Quartz to match (or out-produce) a hypothetical Quartz-based Refined Quartz production regime, and sell the rest for Bombs? This is also bad, but could make sense under weird self-imposed circumstances. The Fire Quartz crystalarium production equation can be modified like so to produce a few different hybrid production equations. I will only consider the simplest of cases, where the Fire Quartz is used to produce either one or two Refined Quartzes and the rest of the Fire Quartz is sold for bombs:
Crystalarium Only (FQ -> RQ + B):
30 D = 30 FQ = 60 RQ + 1 B (1.3 B with Gemologist)
30 D = 30 FQ = 30 RQ + 2 B (2.6 B with Gemologist)
Let's compare this to using some (one-third in the first equation and two-thirds in the second) of our crystalaria to produce Quartz and the rest as Fire Quartz:
Crystalarium Only (Q + FQ -> RQ + B):
30 D = 20 FQ + 30 Q = 60 RQ + 6 B
30 D = 10 FQ + 60 Q = 30 RQ + 12 B
This is an outright better deal than buying the bombs with Fire Quartz sales, which reflects the general rule in Stardew Valley that things traded are cheaper than things bought. Hopefully this is a helpful comparison. Let's move on to what I think is the more interesting case, involving that post-Community Center item:
"15-20 Refined Quartz for every 3 Coal" is a little ambiguous. On the Stardew Valley Wiki's Talk Page for Heavy Furnaces, user 群星之尘 believes from looking at the code that Refined Quartz has an even 1/6th probability of producing any of the outputs in the range of 15 to 20 Refined Quartz, averaging out to 17.5. This would be analogous to the rest of the Heavy Furnace's outputs having an even probability of producing either 5 or 6 outputs, so even though he says he isn't sure of this, I am inclined to believe him. What this all means is that not only are Fire Quartz and Quartz smelted at greater efficiencies in a Heavy Furnace compared to a regular Furnace, but Heavy Furnaces make Fire Quartz more efficient to smelt relative to Quartz, too! Here's the math behind that:
Regular Furnace:
3 RQ per FQ
1 RQ per Q
FQ = 3 Q
Heavy Furnace (average):
3.5 RQ per FQ
1.1 RQ per Q
FQ = 3.18 Q
This is a small difference (+6%), but it's a nice bonus that accumulates over both time and scale. Let's look at the other cases with Heavy Furnaces now:
Crystalarium & Furnace (Bombs only, Q vs. FQ):
30 D = 90 Q = 18 B
30 D = 30 FQ = 3 B (1.3 B with Gemologist)
Crystalarium Only (FQ -> RQ + B):
30 D = 30 FQ = 70 RQ + 1 B (1.3 B with Gemologist)
30 D = 30 FQ = 35 RQ + 2 B (2.6 B with Gemologist)
Crystalarium Only (Q + FQ -> RQ + B):
30 D = 20 FQ + 30 Q = 70 RQ + 6 B
30 D = 10 FQ + 60 Q = 35 RQ + 12 B
Regular Furnace:
3 RQ per FQ
1 RQ per Q
FQ = 3 Q
Heavy Furnace (average):
3.5 RQ per FQ
1.1 RQ per Q
FQ = 3.18 Q
This is a small difference (+6%), but it's a nice bonus that accumulates over both time and scale. Let's look at the other cases with Heavy Furnaces now:
Crystalarium & Furnace (Bombs only, Q vs. FQ):
30 D = 90 Q = 18 B
30 D = 30 FQ = 3 B (1.3 B with Gemologist)
Crystalarium Only (FQ -> RQ + B):
30 D = 30 FQ = 70 RQ + 1 B (1.3 B with Gemologist)
30 D = 30 FQ = 35 RQ + 2 B (2.6 B with Gemologist)
Crystalarium Only (Q + FQ -> RQ + B):
30 D = 20 FQ + 30 Q = 70 RQ + 6 B
30 D = 10 FQ + 60 Q = 35 RQ + 12 B
If you have enough coal but not enough cash, it might be a good idea to run Quartz through your limited number of crystalaria. But later in the game when you have enough extra money that bombs are no longer difficult to purchase, Fire Quartz seems to be the better option. Eventually, with enough crystalaria, it may again become worthwhile to duplicate Quartz, finally coming full circle.
What do you all think? Which paths have your experiences in Refined Quartz production led you down?
