Agent Rounding

From EU3 Wiki

You may have already noticed a very minor problem with the way the number of agents (merchants, colonists, diplomats, etc.) is displayed on the main screen. But if you haven't, this little section is for you.

If you are using each agent as they become available (and keeping their count well below 5), you needn't worry about this.

But if you let the count get full (i.e., get to 5) before sending out your agent, you may well be losing agents. Why?

The agent counts in the main display are truncated to their integer, but each month, fractional agents are added. A worst case example:

• Your agent count says "4" and you're waiting on the "5" to send one out. And you get 6 agents per year. Ok.
• But beneath the hood (if you hover your cursor over the agent), you may actually have, say, 4.80 agents present. Meanwhile, they're being added at a rate of 0.50 per month (6 per year / 12 months per year).
• Next month, you see "5". But what happened was 4.80 + 0.50 = 5.30, which then became exactly 5, because you can't go above that.
• 0.30 of your 0.50 was lost - you got less than half of what you should have.

As soon as you're aware of this problem, it's trivial to solve. But you should be aware of it!

There are two approaches:

1. Simply keep your eye on the exact numbers, by hovering your mouse on the agents. A little table is provided below, for "per year" to "per month" conversion. Don't let the monthly addition push you over 5.
2. Simply use an agent as soon as the count reaches 4 - assuming you get less than 12 per year. If it's less than 12/year, then it's less than 1/month, and you'll never eat a fraction of an agent if you send them off whenever the main-display count says 4.

If you've got a trading empire and get 12 or more mercants per year, the number shown on the main screen could increase by 2 at the beginning of a month. For example, you get 16 merchants per year, which equals 1.25 per month. Your screen says "3" but the actual number might be e.g. 3.90. 1.25 + 3.90 = 5.15 ... and you just lost 0.15 of the 1.25, if you didn't send them out when the screen said "3".

If you get exactly 12 per year, it can't increase by 2 in a month - but you could eat a fraction, if you don't send an agent off when it reaches 4. That's because the number of agents might actually be more than exactly 4. If you add exactly 1, then truncate to 5, you lose a fraction.

So send agents off, relative to a "rule of 12". If you get less than 12 a year, send the agent off when the count reaches 4. If you get 12 to 23 per year, send them off when the count is 3. If lucky enough to get 24-35, send them off at 2. Et cetera.

Here's a little table that's nothing more than dividing the number on the left by 12. It converts number per year, to number per month, for your convenience:

    Per  Per
   Year  Month
                     12  1.000       24  2.000
      1  0.083       13  1.083       25  2.083
      2  0.167       14  1.167       26  2.167
      3  0.250       15  1.250       27  2.250
      4  0.333       16  1.333       28  2.333
      5  0.417       17  1.417       29  2.417
      6  0.500       18  1.500       30  2.500
      7  0.583       19  1.583       31  2.583
      8  0.667       20  1.667       32  2.667
      9  0.750       21  1.750       33  2.750
     10  0.833       22  1.833       34  2.833
     11  0.917       23  1.917       35  2.917

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