Growth and Death by the Numbers
OK, you know that the Growth Scale changes income by 2% for every tick, but what about that .2% population chance? Well, advanced spread sheet technology, I ran some equations and came up with concrete numbers.
Methodology: I basically ran two seperate serieses of equations. The first was simply to track the population chanced caused by the Growth/Death Scale. The equation was simple, (growth multiplier)^(# of Turns). Therefore, Growth 2 after 10 turns would be 1.004^10 which is approximately 1.04, or you'll have 4% more people then what you started with. And since there is a direct correlation between population and gold income, you nab an extra 4% of gold as well. The second check was a bit more complicated. For a given # of turns, I took the average population change over all turns so far, and then multiplied that averaged by the scale's money multiplier. On the spreadsheet, this looked like Average(B4:B10)*1.02. B4 through B10 represent spread sheet cells with the population adjustments for turns 1 through 6. The 1.02 multiplier represents the 2% extra money you'll recieve for Growth 1.
Caveats:
1) Unless you spread your domain then your growth/death effects won't matter. So, though my chart says Growth 3 will give you a whopping extra 46% gold after 102 turns, more likely you'll recieve less then that as most of your territories won't have converted at the game's beginning.
2) Dominions 3 has plenty of ways to kill population, and none of these are taken into account with my chart. For example, if you have a destructive domain (LE R'lyeh and Ermor), then these charts really don't apply to you.
3) Dominions 3 rounds population to the 10's. In practice this means your capital will recive/loose 60 population per every tick of Growth/Death for the first several turns. My charts don't take this staggered growht into account.
4) My numbers represent additional gold over the several turns. Not how much additional gold you recieve per turn at the end of X number of turns. Expect gold income to below my given percentage for most of the turns, and significantly higher by the later turns.
5) I recently read a developer post claiming Neutral (growth and death at zero) provinces do experience small population growth. If that's the case, I never personally observed a neutral province gain population.
With out further ado:
Turns D 3 D 2 D 1 Neutral G 1 G 2 G 3
6.. 92% 95% 97% 100% 103% 105% 108%
12. 91% 94% 97% 100% 103% 107% 110%
18. 89% 93% 96% 100% 104% 108% 112%
24. 88% 92% 96% 100% 104% 109% 114%
30. 86% 90% 95% 100% 105% 110% 116%
36. 85% 89% 95% 100% 106% 112% 118%
42. 83% 88% 94% 100% 106% 113% 121%
48. 82% 87% 93% 100% 107% 115% 123%
54. 80% 86% 93% 100% 108% 116% 125%
60. 79% 85% 92% 100% 108% 118% 128%
66. 78% 84% 92% 100% 109% 119% 130%
72. 76% 83% 91% 100% 110% 120% 133%
78. 75% 82% 91% 100% 110% 122% 135%
84. 74% 82% 90% 100% 111% 124% 138%
90. 73% 81% 90% 100% 112% 125% 140%
96. 71% 80% 89% 100% 112% 127% 143%
102 70% 79% 89% 100% 113% 128% 146%
If anyone has any comments or concerns (It's quite possible I made mistakes), feel free to let me know. I'm working on the charts in Open Office right now, but am not quite ready to release them. When I am, I'll post them as an attachment.
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