Talk:Gold Mine/@comment-144.118.210.91-20130526165809/@comment-2170536-20130526192741

The way the catch-up point works is this:

Imagine two identical Gold Mines, both level 4. You decide to upgrade #1, and leave #2 at level 4. Gold Mine #1 begins to upgrade for the next two hours, while Gold Mine #2 continues to produce gold.

After two hours, Gold Mine #1 is finished upgrading and is now level 5. In the meantime, Gold Mine #2 has continued to produce gold at a rate of 800 per hour, producing a total of 1,600 gold during the time Gold Mine #1 was upgrading. Had you not upgraded Gold Mine #1, it would have also produceed 1,600 gold in that time, but it produced nothing because it was currently being upgraded.

Now that Gold Mine #1 is level 5, however, it begins producing gold faster than Gold Mine #2. The question is, how long will it take before Gold Mine #1 can produce enough extra gold to make up for the 1,600 it didn't produce while upgrading? Remember it is not overall production, because we are trying to calculate how long it takes before we produce the same amount of gold we would have if we hadn't upgraded, and the old mine (#2) is still producing at the lower level. Therefore, because its production rate went up by 200 per hour (800 at level 4 and 1,000 at level 5), it will require a total of 8 hours to produce that 1,600 gold over and above what the level 4 Gold Mine is producing.

So when Gold Mine #1 finished upgrading, it was 1,600 gold behind #2 in production. Eight hours later, they are even: Gold Mine #1 produced 8,000 gold (0 for the first 2 hours and 8,000 for the next 8), and Gold Mine #2 also produced 8,000 gold (1,600 for the first two hours and 6,400 for the next 8). The "catch-up time," therefore, is 8 hours.

Does this help?