Ultra and ISF Comparison

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Re: Ultra and ISF Comparison

Postby Cralis on Wed 11 Mar 2015 00:55

It's almost like you've been listening to some of our internal conversations. This is similar to another (more complicated) proposal we've discussed with the same net effect: the more partners involved, the less you make from each one.

Hmmmm.
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Re: Ultra and ISF Comparison

Postby szurkey on Thu 12 Mar 2015 04:14

Cralis wrote:It's almost like you've been listening to some of our internal conversations. This is similar to another (more complicated) proposal we've discussed with the same net effect: the more partners involved, the less you make from each one.

Hmmmm.

I hate to disappoint you, but I haven't been listening to your internal conversations.

The m^(n+a) has the advantage that each additional trade partner cost the the same percentage of income.

The a / (b + n) has the advantage that it is non-linear, and you lose an ever decreasing percentage of income.
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Re: Ultra and ISF Comparison

Postby szurkey on Sat 14 Mar 2015 07:10

Analytics for a / (b + n)

Assumptions:
All trade agreements are equal value (I know they're not, but it does make it much easier to do analysis)

Number of Trade Agreements (NTA)

Trade Income Multiplier (TIM) := a / (b + n)

Step Loss (SL):= 1 - [a / (b + n)] / [a / (b + (n - 1))] for all n > 1
Measure of reduction of TIM you are giving up for adding that trade agreement.

Value Loss (VL): = Step Loss * (n - 1) for all n > 1
Measure of how much income of all of all previous trade agreements you are giving up to add that trade agreement.
When TIM = Value Loss you are at the break event point. Adding that trade agreement give you NO increase in trade income.

Example, let a = 8, b = 11
Code: Select all
NTA   TIM      SL      VL
1   0.6667      
2   0.6154   0.0769   0.0769
3   0.5714   0.0714   0.1429
4   0.5333   0.0667   0.2000
5   0.5000   0.0625   0.2500
6   0.4706   0.0588   0.2941
7   0.4444   0.0556   0.3333
8   0.4211   0.0526   0.3684
9   0.4000   0.0500   0.4000
10   0.3810   0.0476   0.4286
11   0.3636   0.0455   0.4545
12   0.3478   0.0435   0.4783
13   0.3333   0.0417   0.5000
14   0.3200   0.0400   0.5200
15   0.3077   0.0385   0.5385
16   0.2963   0.0370   0.5556
17   0.2857   0.0357   0.5714
18   0.2759   0.0345   0.5862
19   0.2667   0.0333   0.6000
20   0.2581   0.0323   0.6129
The inflection point is this example is 9 trade agreements. You get no additional income by adding a ninth trade agreement.

If someone would like to pull one of their Ultra games and plug real numbers in and look at how this affects trade income, I would be very interested.
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Re: Ultra and ISF Comparison

Postby szurkey on Sat 14 Mar 2015 14:03

And just in case you think that formula of the form a^(b + n) aren't possible solution:
Code: Select all
a: 0.95   
b: 7   
SL: 0.05   
NTA   TIM     VL
1   0.6634   
2   0.6302   0.0500
3   0.5987   0.1000
4   0.5688   0.1500
5   0.5404   0.2000
6   0.5133   0.2500
7   0.4877   0.3000
8   0.4633   0.3500
9   0.4401   0.4000
10   0.4181   0.4500
11   0.3972   0.5000
12   0.3774   0.5500
13   0.3585   0.6000
14   0.3406   0.6500
15   0.3235   0.7000
16   0.3074   0.7500
17   0.2920   0.8000
18   0.2774   0.8500
19   0.2635   0.9000
20   0.2503   0.9500
The inflection point in this example is between 9 and ten trade agreements.
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Re: Ultra and ISF Comparison

Postby krenshala on Tue 29 Sep 2015 19:27

I know this is old, but ...

For the above formulae/tables, am I reading it correctly that this is the income per-partner being modified? If so then adding additional trade partners may continue to grant additional income, depending on the actual value of the trade deal.

Its late, however, so my gut feeling that the table above only tells part of the story may not be accurate. Unfortunately, being late, I can't brain well enough to tell what I think it should be. :/
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Re: Ultra and ISF Comparison

Postby szurkey on Fri 02 Oct 2015 14:28

krenshala wrote:I know this is old, but ...

For the above formulae/tables, am I reading it correctly that this is the income per-partner being modified? If so then adding additional trade partners may continue to grant additional income, depending on the actual value of the trade deal.

Its late, however, so my gut feeling that the table above only tells part of the story may not be accurate. Unfortunately, being late, I can't brain well enough to tell what I think it should be. :/

It's not that old...

Yes, all of the income you get from everyone you trade with is modified. Note that each power has it's own unique "n". Also, if you keep adding trade partners, eventually, it will cost you income. You might still want the deal to cement an alliance.
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Re: Ultra and ISF Comparison

Postby szurkey on Sun 06 Mar 2016 06:21

In my continuing quest to lower income in Ultra, I've been looking at changing asteroid belts back to what they were in ISF. In ISF asteroid belts do not give an income modifier, but rather a build rate modifier for space based industry (SY). In ISF, the first asteroid belt adds +50% to the HS a (SY) can build per turn, and each additional (SY) adds an additional +20% to the HS a (SY) can build per turn. I consider this to be way too powerful. Also, this is a not a continuous function (it bothers the math geek in me). Consider the following formula:

Build Rate Modifier = 1 + ((m^2) * (Number of Colonize Asteroid Belts)^0.5) / 10
where m is the base percentage for one asteroid belt time ten ( 10 * x%).

For example if you want a 25% increase for the first asteroid belt :
Build Rate Modifier = 1 + ((2.5^2) * (1))^0.5 / 10 = 1.25

Note that I keep all fractions until the end, and then drop them. So for a build rate of 14 HS per month, one colonized asteroid belt would give a FRD(14 * 1.25) = 1FRD(7.5) = 17 HS per month. Also note that this is for COLONIZED asteroid belts with at least 20 PU on them. This way to get the bonus, you have to spend the money and stick your neck out both with the (SY) and the PU on the asteroid belts. I am not sure what the actual value for m should be, but somewhere between 2 to 4 seems right. Don't forget you can use fractions, such as m = 1/3 * 10 = 3.33333... A few values for m = 2.5:

0 asteroid belts -> modifier of 1.0 (ISF = 1.0)
1 asteroid belts -> modifier of 1.25 (ISF = 1.5)
2 asteroid belts -> modifier of 1.3536 (ISF = 1.7)
3 asteroid belts -> modifier of 1.4330 (ISF = 1.9)
4 asteroid belts -> modifier of 1.5 (ISF = 2.1)
5 asteroid belts -> modifier of 1.5590 (ISF = 2.3)
6 asteroid belts -> modifier of 1.6124 (ISF = 2.5)
7 asteroid belts -> modifier of 1.6614 (ISF = 2.7)
8 asteroid belts -> modifier of 1.7071 (ISF = 2.9)

Also to further restrict income, I've been looking at reducing the population of the Asteroid Belts by the following formula:

max PU = FRD( 20 * (radius in LM)^0.5).

This gives limit of between 20 PU at 1LM (so you can always get the build rate modifier of a binary where the habitable is in the other system) and 324 PU at 264LM (the max you can get on table W6.03). This means no more asteroid belts with 1,000's of PU on them. There are other options than the square root if you consider it too powerful. Changing it to the ^(5/8) will give a max PU of 652 PU at 264 LM.

My final modifications for asteroid belts is to change the colonization costs and REI based on where they are on table W6.04. Asteroid belts inside of the inner edge of the Biozone are Extreme and have a REI of 120%. Asteroid belts in the Rocky Planets zone and in the Biozone or further out are Desolate with a REI of 110%. Asteroid belts in the Gas Planets zone have are Desolate with a REI of 100%. Asteroid Belts in the Ice Planet zone are Desolate with a REI of 90%. These REI's are based on my formula for mineral richness Expected Value + 10% for being an asteroid belt.
Last edited by szurkey on Sun 06 Mar 2016 12:35, edited 1 time in total.
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Re: Ultra and ISF Comparison

Postby Cralis on Sun 06 Mar 2016 12:33

Why keep the ast pop producing incoming if you're adding back the construction bonus?

And actually, a neat way to do that might be to have the pop produce "HS" worth of bonus instead of income. So for example, if each PU produced 0.1 HS of bonus, and your Build Rate is 10, then the 50% would 'allow' up to 15 Build Rate and it would take 50 PU on the belt to provide it. Then each additional 50 PU would support one more shipyard, and so on.

This would both give a reason for PU without income generation, AND make large and/or multiple belt systems more valuable (since they'll be able to support more shipyards).
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Re: Ultra and ISF Comparison

Postby szurkey on Thu 10 Mar 2016 06:50

Cralis wrote:Why keep the ast pop producing incoming if you're adding back the construction bonus?

And actually, a neat way to do that might be to have the pop produce "HS" worth of bonus instead of income. So for example, if each PU produced 0.1 HS of bonus, and your Build Rate is 10, then the 50% would 'allow' up to 15 Build Rate and it would take 50 PU on the belt to provide it. Then each additional 50 PU would support one more shipyard, and so on.

This would both give a reason for PU without income generation, AND make large and/or multiple belt systems more valuable (since they'll be able to support more shipyards).

The problem with this is that it requires a more complex formula, and probably a macro, to code. I really don't want to go there. I like having just six cells per system (including both components of close binary systems) to track this, one for number of asteroid belts, one for colonized asteroid belts with a minimum of 20 PU, one for the modifier, and three for the description of the cells.

This will also make one large asteroid belt at say 264 MU much more valuable for (SY) than say an asteroid belt at 5 MU. If anything, the asteroid belt closer to the star should be more valuable than one way out because the star will bake out all the ices (not just water ice), and transit time to and from the habitable planet with the (SY) in orbit will be much less. Granted, Ultra doesn't model this.

If anything, I would get rid of the +10% asteroid belt modifier to the REI. This would drop Return on Investment down to:
Extreme AB 110%
Other Rocky AB 100%
Gas AB 90%
Ice AB 80%

By comparison, all AB in Ultra are Desolate to colonize and have a REI of 105%, and generate a +10% bonus to every PU and IU in the system or close binary system (if applicable). If you factor in the bonus to the REI of the AB in Ultra to just one AB, you get an effective REI 115.5%. So even my initial idea of a +10% asteroid belt modifier still provides an effective lower REI than UItra, because only Extreme AB have an REI of 120%, and they are much more expensive to colonize than Desolate.
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Re: Ultra and ISF Comparison

Postby Cralis on Thu 10 Mar 2016 18:15

szurkey wrote:The problem with this is that it requires a more complex formula, and probably a macro, to code.


It's not that bad. You just need a "per system" Build Rate and a modifier based on AB PU (do a lookup for that). But it does add more complexity. Well, unless you want it to auto-assign the extra BR, then you're probably right. I just thought it was an interesting idea.

I really don't want to go there. I like having just six cells per system (including both components of close binary systems) to track this, one for number of asteroid belts, one for colonized asteroid belts with a minimum of 20 PU, one for the modifier, and three for the description of the cells.


No problem. Just an idea.

This will also make one large asteroid belt at say 264 MU much more valuable for (SY) than say an asteroid belt at 5 MU. If anything, the asteroid belt closer to the star should be more valuable than one way out because the star will bake out all the ices (not just water ice), and transit time to and from the habitable planet with the (SY) in orbit will be much less. Granted, Ultra doesn't model this.


Could just do +1 BR per belt...

If anything, I would get rid of the +10% asteroid belt modifier to the REI. This would drop Return on Investment down to:
Extreme AB 110%
Other Rocky AB 100%
Gas AB 90%
Ice AB 80%

By comparison, all AB in Ultra are Desolate to colonize and have a REI of 105%, and generate a +10% bonus to every PU and IU in the system or close binary system (if applicable). If you factor in the bonus to the REI of the AB in Ultra to just one AB, you get an effective REI 115.5%. So even my initial idea of a +10% asteroid belt modifier still provides an effective lower REI than UItra, because only Extreme AB have an REI of 120%, and they are much more expensive to colonize than Desolate.


Got it.
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