Summary?
Spend gems on buying chests better in the long run?
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Value of Gemming
Note: Refer to the Expected Value Calculation if you want to know how we got them.
Note: The total value is:
Total Value = Gold + Commons * 2 + Rares * 20 + Epics * 2000 + Legendaries * 40,000
(1) Gemming the cycle
If you gem all silver chests and silver chests only,
You'll spend 3240 gems per cycle, or 4320 gems per 30 days. Every 30 days, you get an extra 0.6515 cycles. Note that you are not getting more free chests and crown chests which constitute a huge part of the income in a cycle.
Expected Value per 500 gems Arena 6 Arena 7 Arena 8
Gold 1865 2077 2723
Commons 278 311 397
Rares 33.5 37.5 48.2
Epics 2.01 2.24 2.91
Legendaries 0.078 0.087 0.110
Total Value 10,230 11,413 14,681
The same value applies if you gem any chest.
(2) Buying chests
Giant Chest
Expected Value per 500 gems Arena 6 Arena 7 Arena 8
Gold 1642 1698 1861
Commons 246 254 279
Rares 27.4 28.3 31.0
Epics 0.495 0.510 0.559
Legendaries 0.0245 0.0252 0.028
Total Value 4652 4800 5277
Magical Chest
Expected Value per 500 gems Arena 6 Arena 7 Arena 8
Gold 390 373 428
Commons 49.8 47.6 54.5
Rares 13.0 12.4 14.3
Epics 2.17 2.07 2.38
Legendaries 0.081 0.077 0.086
Total Value 8330 7936 9023
Super Magical Chest
Expected Value per 500 gems Arena 6 Arena 7 Arena 8
Gold 412 423 446
Commons 52.7 54.0 56.9
Rares 13.8 14.1 14.9
Epics 2.29 2.35 2.48
Legendaries 0.066 0.066 0.063
Total Value 8013 8153 8338
(3) Buying from the shop
If you buy 10,000 gold for 500 gems,
Expected Value per 500 gems Arena 6 Arena 7 Arena 8
Total Value 10,000 10,000 10,000
Buying anything beyond the first card will decrease the value of your gems.
(4) Value needed per time, and time saved per gem
Total value needed to upgrade to max: 21,211,072
Total time needed to upgrade to max at maximum efficiency: 9.8 years
Gemming Chests in A8
Magical Chest: Value per 500 gems: 9023 -> Time saved: 1.6 days
Super Magical Chest: Value per 500 gems: 8338 -> Time saved: 1.4 days
Gemming the Cycle in A8
Note: Even though you get more value from gemming the cycle, gemming the cycle saves you less time than opening chests because you are still waiting for other parts of the chest cycle to complete.
Gemming all silver chests: Value per 500 gems: 5145.4 -> Time saved: 0.9 days
Gemming all golden chests: Value per 500 gems: 8976.5 -> Time saved: 1.5 days
Buying 5 Epics
Note: The time saved from buying epics is very low despite having the highest value because you are waiting a day per 100 gems.
Buying 5 epics with 10,000 gold: Value per 500 gems: 10,000 -> Time saved: 0.6 days
I have a question though. I'm a bit confused with the paragraph "Value of gemming". I'm only going to use Arena 8 values to explain my confusion.
In point (1), you say that the expected total value for 500 gems is 19575 and that the same value applies for any chest. In point (4), you say that the expected total value for 500 gems is 5145.4 for silver chests and 8976.5 for gold chests.
But if I compare points (2) and (4), the numbers are the same.
Answer:
The value 19575 is the extra value you get across a 30 day timespan using 500 gems by speeding the cycle (this includes the magical, giant, and potential SMCs).
The value 5145.4 is the inherent value of the silver chests themselves.
The reason why we calculate these separately is because the former is about how much extra value you get by speeding up a cycle within a 30 day timespan. The latter is about how much value you are getting from your gems by opening chests instantaneously as an alternative to buying chests from shops (and we showed that this provides far less value than buying chests directly). Think of 5145.4 as the value of if you're buying silver chests directly from the shop (and it's horrible value).