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.

Re: Growth and Death by the Numbers
 

One issue is that random event differences have a significant impact.

Plagues, for example, are one of the most severe negative events - and can happen to you even if you take death-but-not-misfortune.

So the best way to get a real handle on the income is to start a bunch of games with slightly different settings run for X turns, and see how much money you have on average http://forum.shrapnelgames.com/images/smilies/happy.gif. Of course this is rather more work.

I had various data on this lying around, it wasn't complete, but I lost a bunch of it in the HD crash.

Also, growth has a big (but in need of quantification) effect on the severity of aging. You might throw fifty elderly mages into the mix and see how they do.

All that said, your math looks right to me.

Re: Growth and Death by the Numbers
 

there is no post from me in this thread http://forum.shrapnelgames.com/image...s/rolleyes.gif

i should read better the next time

Re: Growth and Death by the Numbers
 

Re: Growth and Death by the Numbers
 

Saint Dude is correct, my scales tell you how much gold you get OVER THE COURSE OF THE GAME. While at the end of 102 turns you will have increased population by your 80%+ figure and will earn that much more gold per turn, you won't have that much extra gold for most of your turns (unlike Order which gives +/- 7% gold per tick no matter what turn and the aggregate won't change over number of turns.

As for the role of random events... too much variable is involved. For example, large nations are sort of "buffered" from random events due to hard limit of random events occurring. No matter how valuable the territory, if you have 50+ it won't matter how badly it gets hit with Misfortune. Then, its much harder to quantify the effects of free gems and magic items that high luck players get. Obviously, the additional effects of growth, minimizing/aggrevating old age problems, additional supply, are things players will have to consider when designing their strategy. This chart is more to quantify just how much extra money you'll get/loose using growth/death (a lot more then 2%).

Re: Growth and Death by the Numbers
 

Good job, OmikronWarrior! Thanks for doing that, I like looking at numbers. http://forum.shrapnelgames.com/images/smilies/happy.gif

It's true that Growth gives more benefits than just money, like you say. But, unfortunately, your chart there I think quantifies what most people have been saying for some time now --that Growth as a money-making strategy is just not as good as Order.

It seems that the break-even point is around turn 50 or so, according to your chart. At that point, Growth and Order will give you about equal extra money per turn. And, this is even assuming that the growth scale was in each of those provinces from the start of the game, which of course isn't true. So, in reality, we're looking at more of a turn 60-70 or so break-even point, maybe even later. On a really big map, Growth may work out to be better than Order, but for most games, the money you get from turn 1 to turn 70 will be a much bigger incentive, so Order would be better.

And this isn't even factoring in that at the "break-even point", Growth will still be far behind Order in terms of money gained to that point.

This seems like good evidence that either Growth should be changed to at least +3% (as in CB mod), or that Order should be lowered to maybe +6 or +5%. Alternatively, the Growth % per turn could be raised.

Re: Growth and Death by the Numbers
 

Well, that's good evidence that Growth and Order should be changed if the only thing you want to balance is money.
It's harder to calculate the other effects of both scales.

Re: Growth and Death by the Numbers
 

so if you ended the chart at, say, turn 30, then the actual additional amount per turn would be higher at the turns just before turn 30, then now as youv ended the chart at turn 102?

either i am misunderstanding you, or your math is off.

Re: Growth and Death by the Numbers
 

Keep in mind that in order to get the benefit of Order/Turmoil, you still need to spread your domain as well. What these charts show me is less that Growth is an equal alternative to Order as a money maker, but a good money maker in its own right that compliments Production.

In joke format, people without Growth or Order
take the bus to work, people with just Order drive BMWs, people with just Growth take the bus but retire early, but people Growth and Order fund the Russian space program to get to work.

OK, on a given turn (lets call it T(1)), a province will make X amount of money based on Y amount of population. Unless there are modifiers in play. Lets assume Growth 3. So, you make X*1.06 money. Now on T(2), your population has changed to Y*1.006, and since base money is directly proportional to population, you'll earn X*1.006*1.06. What my figures tell you is money made on T(1) and T(2) AVERAGED. Or they would if I bothered to do Turn 2.

Re: Growth and Death by the Numbers
 

One way to balance order might be to make it more vulnerable to unrest. Turmoil is like the Dukes of Hazard -- they don't pay taxes on their moonshine and sometimes raise a rumpus but the boys will be back helping Pa on the farm soon enough. Order has quiet, well maintained towns but they need to call the police (patrollers) when there's trouble.

I think having unrest go down by 3 - Order points per turn would be reasonable.

Re: Growth and Death by the Numbers
 

Order originally lowered unrest.

Re: Growth and Death by the Numbers
 

I thought it still did. http://forum.shrapnelgames.com/images/smilies/happy.gif

I definitely feel more confident raising the taxes in provinces with Order instead of Turmoil. It seems like I get less unrest and the unrest that I do get is easier to put down.

Re: Growth and Death by the Numbers
 

Yeah, I hear what you're saying OmikronWarrior. Growth does seem to be a good money-maker judging by your numbers. It's just, if you took Growth instead of Order intending to make money on it, it's like you're saying "I'm going to survive for 100 turns and then I'll really cash in!"

I don't think you can always assume you're going to survive that long.. http://forum.shrapnelgames.com/images/smilies/wink.gif It just seems worth it to take Order and get the money in the short run and use that money to buy troops to expand to get more money. But, maybe a Growth-3 defensive strategy, possibly combined with clamming or bloodstones, with the intent of being peaceful and just hoarding the wealth, could be viable.

Re: Growth and Death by the Numbers
 

Growth also protects your old mages from early death, saving you a lot every late winter. Growth also keeps your provinces from getting plagues, while Order keeps all events in check and enables the "tax collection went well" events.

Re: Growth and Death by the Numbers
 

I've become a growth, order and luck fan myself. Usually I only take growth 1, primarily because point distribution issues.

I found that I have much more success and a lot less troubles with positive scales than negative scales. Of course this is from a SP perspective, so I'm not competing against a double bless opponent.

Re: Growth and Death by the Numbers
 

ow, ok, i get it now, thanx. i thought you meant the figures given were cumulative.
but then actually, the money made on any turn will actually be higher then the perentage you give for that turn, instead of this only being so for the later turns. cause every figure given with a turn is an avarage of earlyer turns. but i see now that with later turns you didnt mean 'later turns on the chart', but 'the later turns up to the turn you are looking at'.

really nice chart btw, im deffinitely trying a growth scale next time. 'get and defend the rich provinces early' make a good stratagy with that..

Re: Growth and Death by the Numbers
 

Since it was brough up... here are the figures adjusted by Order 3, or 1.21. Also, I've given up getting Open Office to look respectible, so I'm sticking with Excel. Sorry all you open sourcers out there. I'll be adding the zip to the original post shortly.

D 3 D 2 D 1 Neutral G 1 G 2 G 3
0 114% 116% 119% 121% 123% 126% 128%
6 112% 115% 118% 121% 124% 127% 131%
12 110% 113% 117% 121% 125% 129% 133%
18 108% 112% 116% 121% 126% 130% 135%
24 106% 111% 116% 121% 126% 132% 138%
30 104% 109% 115% 121% 127% 134% 141%
36 102% 108% 114% 121% 128% 135% 143%
42 101% 107% 114% 121% 129% 137% 146%
48 99% 106% 113% 121% 130% 139% 149%
54 97% 104% 112% 121% 130% 140% 151%
60 95% 103% 112% 121% 131% 142% 154%
66 94% 102% 111% 121% 132% 144% 157%
72 92% 101% 110% 121% 133% 146% 160%
78 91% 100% 110% 121% 134% 148% 163%
84 89% 99% 109% 121% 134% 150% 167%
90 88% 98% 109% 121% 135% 151% 170%
96 86% 96% 108% 121% 136% 153% 173%
102 85% 95% 107% 121% 137% 155% 177%

EDIT: On another note, taking and holding rich provinces is a good idea no matter what your scales, as is build forts on them since administration proves ANOTHER money multiplier and helps makes sure they don't fall into enemy hands.

Re: Growth and Death by the Numbers
 

The money multiplier from building a fortress will rarely, in my opinion, pay for the cost of building it in the first place, given other things you could spend the money on and the probable length of the game.

And a fort under siege won't help you protect your income from the province that much.