Talk:Gold Mine/@comment-6617823-20130220195330/@comment-6617823-20130220200025

More background on the math in case anyone is wondering, or trying to figure it out for themselves...

I completely understand the concept of forgoing a resource during the build time of the upgrade, and I have factored that into my calculations. However, you cannot simply ignore the cost of the upgrade. It is a cost to you, and therefore by paying that cost you are at a deficit until it is recovered. Because Gold Mines and Elixir Collectors generate the exact same amount of their respective resource when they are at the same level, there is a 1:1 relationship between the two.

For instance if you have both a level 1 gold mine and a level 1 elixir collector and you collect whatever is in them at the EXACT SAME TIME, and come back in 1 hour and collect them again, you will receive 200 units of gold from the mine and 200 units of elixir from the collector. Thus, there is a 1:1 relationship between the amount of gold produced in 1 hour and the amount of elixir produced in 1 hour when the two resource buildings are at the same level.

This is the part that seems to lead to a lot of confusion, and hence that's why I simplified it in my example by assuming you were upgrading a gold mine and an elixir collector from level 10 to level 11 at the exact same time, because they would both then take 5 days to upgrade, and begin production at the exact same time 5 days later.

If you do this, you've spent 168,000 elixir to upgrade the mine and 168,000 gold to upgrade the collector. Thus once the two structures have finished upgrading, each one needs to generate not only the amount of gold and elixir you've forgone during the 5 days of upgrading, but also each one needs to generate an additional 168,000 units to make up for the cost of the upgrades. The elixir collector must generate an additional 168,000 units to pay for the gold mine and the gold mine must generate an additional 168,000 units to pay for the elixir collector.

(Side note: It doesn't even really matter if you upgrade the two at the same time if you put it all into the perspective that eventually you will upgrade all of your mines and all of your collectors to level 11. Each resource building upgraded to level 11 has a total cumulative build cost of 362,550 units of the OTHER resource... Since at the end of the day, even if you had a fully upgraded village, you'd have the same number of mines as collectors. Thus, you can say that mines and collectors come in pairs. You can assume that each gold mine / elixir collector pair pays for each other's upgrade costs, if not at the same time, they will at some point. So each mine/elixir pair must generate an additional 362,550 units of its resource to cover the cumulative lifetime of upgrades to the paired resource building)

Because of this you can say, for simplicity's sake that each structure is already "in the hole" 168,000 units at the time they finish upgrading to level 11. Once they've made that amount back, then they're at zero. In the meantime, if you hadn't done the upgrade, you would have earned 5 days worth of gold and elixir at the old rate. So the new gold mine and elixir collector must "catch up" to the total amount of resources that would have been generated had you not gone through with the upgrade AND it must match the total amount of resources generated that would have been generated by the mine / collector at the previous level. In my explanation I mentioned plotting the equations of these lines on a graph, and the point at which they intersect is your time to profitability.

If you have a graphing calculator handy... plot these two lines:

f(x) = 30 + 6x

f(x) = 7.2x - 16.8

The y-axis on your graph would be total resources generated over time X

The x-axis on your graph would be time

They intersect where X = 39. This is the point at which the new mine or elixir collector has paid off the cost of upgrading the other structure AND has caught up to what the old mine or collector would have produced had it not been upgraded.

To derive these formulas is simple.

We'll start with the first one...

f(x) = 30 + 6x

f(x) = (Build Time)(Old Daily Rate) + (Old Daily Rate)(x)

For level 11 the build time is 5 days. The old daily rate is 60,000 (a level 10 structure generates 2,500 units per hour, and there are 24 hours in a day... thus 2,500 x 24 = 60,000)

f(x) = (5)(60,000) + 60,000x

f(x) = 300,000 + 60,000x

You can cancel out the extra zeros to simplify the equation...

f(x) = 30 + 6x

voila!

Second equation...

f(x) = 7.2x - 16.8

f(x) = (New Daily Rate)(x) - Cost of Upgrade

For level 11, the daily rate is 72,000 unites (3,000/hr x 24hrs = 72,000). We know the cost of the upgrade is 168,000 of the OTHER resource... and we know there is a 1:1 relationship between elixir and gold production when mines and collectors are upgraded to the same level, so...

f(x) = 72,000x - 168,000

Since we got rid of the extra zeros in our other equation, we do the same thing here...

f(x) = 7.2x - 16.8

Plot those two equations on the graph and they intersect at x = 39

30 + 6x = 7.2x - 16.8

46.8 = 1.2x

46.8 / 1.2 = x

x = 39

If you can't tell by now, I've put A LOT of thought, and even more math behind this whole thing... It didn't take me too long, since like I said, I have a very strong finance and accounting background and I'm very well versed in cost / profit analysis (I'm a consultant, we have to price out bids on contracts all the time...)... And like I said before... The table as it stands now, is incorrect.

You can go even further by assuming that you will be attacked and could possibly lose up to 50% of your gold or elixir generated per day... This effectively doubles the time to profitability... So assuming that you were collecting regularly from your mines and collectors and not letting them sit full and thus taking them out of production, you can assume that your MINIMUM time to profitability after upgrading from level 10 to level 11 will be between 39 and 78 days. If you're not collecting regularly, and your buildings sit idle and unproductive, you can assume it could potentially be more than 78 days if you were regularly under attack...

Isn't math fun :)