Talk:Gold Mine/@comment-70.193.133.9-20130219162149

Actually... These "Time to Profitability" calculations are way off... First "profitability" in this case would be the first unit of resource made AFTER recovering both initial build cost, plus the opportunity cost. The "opportunity cost" in this case is the cost (to you) of the upgrade AND the resources you would have earned if you had stayed at the same level and not gone ahead with the upgrade. If you wrote equations for both the production of the resource at the original level over time and production of the resource at the new level over time minus the cost of the upgrade and plotted them on a graph where X is time and Y is total resources generated during time X, the "Time to Profitability" is the value of X at the point at which these two lines intersect. Essentially, you are trying to figure out how many days (or hours) it takes for the newly upgraded mine / collector to reach the same amount of total resources generated as the mine / collector from the previous level, with your build costs factored in.

Example:

Upgrading from Level 10 to Level 11 Elixir Collector...

Cost of upgrade: 168,000 Gold - I know, it's a different type of resource, but since the gold mines and elixir collectors each generate the same amount of their respective resource when at the same level, let's assume (for simplicity's sake) that if you are upgrading your elixir collector from level 10 to level 11, that you are also upgrading a gold mine from level 10 to level 11 and you've kicked off the upgrades at the same time.

Thus the two upgrades have cost you 168,000 elixir and 168,000 gold. The upgrades will complete at the same time, and thus will start producing resources at the same time and at the same rate. Because of this, we can just assume that the elixir collector needs to generate an additional 168,000 elixir and the gold mine needs to generate an additional 168,000 gold to cover the costs of each build.

Being that one of the goals of this game is to upgrade to the max... I don't think this is an unlikely scenario. It also keeps things relatively simple, and ensures that our calculation of "Time to Profitability" is a calculation of the minimal time to profitability (assuming that the mine and the collector being upgraded were never attacked, and never left sitting full so that they were always producing resources and all resources produced were actually collected and not lost).

y ( Or ) = x ( Nr - Or ) - C

Where:

y = Build Time for upgrade (in days)

x = Minimum time to profitability (in days)... What we are solving for

Or = Old daily rate of resource generation

Nr = New daily rate of resource generation

C = Cost of upgrade

In our example:

y = 5, Or = 60,000, Nr = 72,000, C = 168,000

5 ( 60,000 ) = x ( 72,000 - 60,000 ) - 168,000

300,000 = x ( 12,000 ) - 168,000

468,000 = x ( 12,000 )

468,000 / 12,000 = x

x = 39 days

However, as a previous poster mentioned... In the real world, you get attacked multiple times a day. And if you went under the same assumption the previous poster did, that the attack was decent enough to give you a 12 hour shield, you really would only be receiving 50% of the daily amount each mine / collector could generate. In theory, this would push the minimal time to profitability out quite farther than 39 days... probably, like the previous poster state, well past 50 days... if not more.