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Universe habs, what governs them? 
Mon, 03 September 2012 09:42 

sprocket
Messages: 138 Registered: November 2002 Location: Illinois US

Chief Warrant Officer 1 


After having played in many games both online and solitaire, I have consistently encountered that when your habs are set to a ratio that is what you will never see, also online games seem more skewed than solitaire games.
As an example I in Reanimation last year with habs that were 1/7 but it turned out to be closer to 1/25.
Currently I am finding a similarly disproportionately poor planet draw in my current game (my habs are very wide so I wont die) but still I am maybe half of what I should based on the ratio the race wizard indicates.
So I guess the question is: whats the malfunction? Is there a formula for getting the habs set so you get the right proportion of planets?
Dieter of sprockets



Re: Universe habs, what governs them? 
Mon, 03 September 2012 13:08 

The malfunction seems to be that the planets u want are on the other side of the universe or are in the hands of your enemies, or worse...your allies.
However, if you factor in all the planets, irrespective of the distance from your hw or who holds them, you will find that they do match up.
I know my minefields.. but I'm a chaff sweeper.
I used to curse when I got stuck in traffic... till I realised I AM traffic.



Re: Universe habs, what governs them? 
Mon, 03 September 2012 13:24 

Mark Hewitt
Messages: 105 Registered: June 2006 Location: Calgary, Alberta, Canada

Master Chief Petty Officer 


I hope it's just the possible skew of a small sample. As this (like virtually everything else in Stars! has been researched.
I quote from the Stars! Compendium v0.5 (got it off of www.itp.unihannover.de/~krohn long ago) quoting Jason Cawley (rec.games.computer.stars 1999, Apr 29) and Bill Butler (rec.games.computer.stars, 1999 May 01) below in the spoiler tag. (And I've used the knowledge to computer actual probability, e.g. instead of using just "1 in 4" I know a particular race has 0.191 probability of find initial green planets. I now compute this for every race I look at as it's not too hard.)
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Quote:
7.3.2 Distribution of Gravity, Temperature and Radiation
I was under the impression that the grav temp and rad randomizing were some sort of Gaussian centered around the center for each bar.
It is not a Gaussian, but a trapezoid. The last 10 clicks on each end are less likely to occur, each progressively less likely in linear fashion. The program generates the actual values for those two ranges as RANDOM(10) + RANDOM(90), which gives the trapezoid. And that is for grav and temp only  rad is just RANDOM(100), with all values equally likely.
By the way, as another fellow mentioned the actual endpoint values don't occur, in any of the three ranges. Probably for rounding reasons  RANDOM(x) just uses RANDOM(1) times x then does something with the excess fraction (rounded or dropped, etc). The rounding may be ``inwards" rather than ``up or down" (e.g. if it is distance from the center and rounded down).
Quote:
Are you sure about the above distributions? I can think of other curves!
Total data points(planets) collected in each variable = 19900 . The data was sorted into 101 bins for each variable. A histogram was constructed for all 3 (rad, temp, grav).
First, the findings:
Radiation
Totally flat minus the endpoints which do not exist. We can say this with certainty since the average bin contained 201 planets. A value of 0 for the endpoints lies 14 standard deviations away from the mean. This is about as certain as you get. In truth I can only conclude that the endpoints are 1/50th as likely as every other point, but I will consider 0 to be a d### good bet. There were fluctuations outside of 2SD (standard deviation) for the whole data set, but nothing unexpected. Since 95% of the data should fall between 2 standard deviations of the mean you should expect 5% to fall outside of this and that is what I found.
I should also note that there were no significant deviations from the mean. By this I mean that I found no data points with twice the likelyhood of the rest of the data points, or something extreme like that.
In short: No surprises in the radiation range
Temperature
The theory is that the temp range starts at 0 at the endpoints, goes linearly up to the full percentage at 10 clicks in from the end and is flat from there on out. Theoretically this gives a 1/90 probability for each bin in the flat section.
Taking an average of the numbers in bins 1090 we get 221.1 planets. This works out to 1 / 90.39 which is quite close to the predicted value of 1/90.
Next I looked at the end region and compared the actual data to the predicted data. I took into acount statistical fluctuations and compared the data to the expected line you should get if the theory is correct. The fit is quite nice. There are fluctuations in the results but all in all it looked good. I also compared the data to the theoretical line you should get if the corner fell 8 clicks out instead of 10. The fit was not as good this time. The line fell outside of 2SD for quite a few data points.
From the data it would appear that the theoretical distribution is accurate. At least with 19,900 data points the fit was good. Can I conclude that this ``IS" the right distribution...no, but I can conclude that using this distribution will give you no bad results. Either the theoretical distribution is correct, or there is no noticable d
...



Re: Universe habs, what governs them? 
Mon, 03 September 2012 14:44 

Some additional info and graphs you can find here:
* Charts of habitability spread and mineral concentrations, by Alan L. Kolaga.
Note the different spread of temp and grav on the one hand and for rad on the other.
1 in 4 in the race wizard is often enough a very rough estimation. Especially since it doesn't say anything about the quality of the planets. A helpful calculator to get a better overview:
* Overall Planet Habitability and Race Econ Calculator, original Author: Henk Poell, additions by: Tiib, M.A, C.R et al.
You can see quite well some of the effects for:
* wide hab: many planets but most of low quality
* 1 imm, 2 narrow: low number of initial planets but most of them quite good while lots of possible good planets still need terraforming from yellow to green (which needs time you might have or not depending on the game sttings).
As often as I sit in despair in front of the Starsmap and wondering where my green planets are supposed to be, in general I'd say that it often enough works out surprisingly well balanced. Especially when taking into account the low number of stars for example in a small/normal galaxy: just 128.
But chance is surely also playing an important role. It does make a difference wether 2 of your 4 estimated 70+%planets are within 162ly or all 4 are on the other side of the galaxy.
It's one of the things you need to adapt to: If your nearby draw of habitable planets is poor, a focus on scouting and early aggressive expansion is needed and often enough... after the game... one might even think that it helped to win the game to feel forced to be aggressively expanding from very early on.
[Updated on: Mon, 03 September 2012 14:57] Report message to a moderator



Re: Universe habs, what governs them? 
Mon, 03 September 2012 21:51 

I feel it's confirmation bias.
When you get fewer good planets, you think "The RNG has screwed me again!"
When you get more good planets, you think "My race design is awesome!"




Re: Universe habs, what governs them? 
Tue, 04 September 2012 02:13 

Mark Hewitt
Messages: 105 Registered: June 2006 Location: Calgary, Alberta, Canada

Master Chief Petty Officer 


Altruist, Coyote, and Sprocket have the right spirit. >:)
Altruist wrote on Mon, 03 September 2012 12:44Some additional info and graphs you can find here:
* Charts of habitability spread and mineral concentrations, by Alan L. Kolaga.
Note the different spread of temp and grav on the one hand and for rad on the other.
1 in 4 in the race wizard is often enough a very rough estimation. Especially since it doesn't say anything about the quality of the planets. A helpful calculator to get a better overview:
* Overall Planet Habitability and Race Econ Calculator, original Author: Henk Poell, additions by: Tiib, M.A, C.R et al.
I've used the information in the first post (which is identical to the references I quoted above) to figure out how to calculate hab %. Unfortunately it looks like Poell et al's habcalc gets a slightly higher figure, and I'm fairly sure my method is correct.
hab % = <grav weighted width> x <temp weighted width> x <rad weighted width> / 801900
where 801900 is the full weighted width of each range multiplied together: 90 x 90 x 99 = 801900.
Weighted range is <high value>  <low value> + 1  <end adjustments> where the values are as they are on rad scale or the numbers shown on the hab caculator. Here's those numbers from a race design I wrote out recently:
Grav immune [ 0100: 90 wide]
Temp 160  160 [105090: 81 wide]
Rad 77  99 [778899: 23 wide]
(1 in 5, calc 0.209)
The end adjustments are values to subtract from the raw width to get the proper weighting if the end rad values are 0 or 100 (easy) or the end grav/temp numbers are 09 or 91100 (not so easy). If your range is wide enough to be in both ends, correct for both ends.
Rad
0 100 1
Grav & Temp
0 100 5.5
1 99 4.5
2 98 3.6
3 97 2.8
4 96 2.1
5 95 1.5
6 94 1.0
7 93 0.6
8 92 0.3
9 91 0.1
Immunity gives ranges the full width, for rad 99 and for grav/temp 90.
[Updated on: Tue, 04 September 2012 02:16] Report message to a moderator



Re: Universe habs, what governs them? 
Tue, 04 September 2012 11:19 

Mark Hewitt wrote on Tue, 04 September 2012 08:13[...]
I've used the information in the first post (which is identical to the references I quoted above) to figure out how to calculate hab %.
I guessed so.
But I thought links to the graphs and calculators might be nevertheless interesting for other curious readers.




Re: Universe habs, what governs them? 
Tue, 04 September 2012 19:25 

Marduk
Messages: 345 Registered: January 2003 Location: Dayton, OH

Ensign 


I usually get roughly the estimated proportion of systems, but I have had some games where it is wildly skewed one way or the other. The smaller and sparser the universe and the narrower your hab settings, the greater the likelihood this will occur. There are roughly a million system hab variations... if you are only seeing a couple of hundred systems there are a lot of potential gaps.
Especially if you have two fields at minimum width (I don't remember your hab settings, but I've done it often enough), it doesn't take much unevenness in the distribution to have a huge impact on the final tally of habitable and good systems. I got tired of that, so I mostly go with an immunity and one wide, one narrow. That almost guarantees being close to the estimated hab. As noted, you may still have to conquer a lot of territory to find those good systems...
One out of five dentists recommends occasional random executions to keep the peasants cowed and servile.



Re: Universe habs, what governs them? 
Wed, 05 September 2012 01:36 

Mark Hewitt
Messages: 105 Registered: June 2006 Location: Calgary, Alberta, Canada

Master Chief Petty Officer 


m.a@stars wrote on Tue, 04 September 2012 12:44Mark Hewitt wrote on Tue, 04 September 2012 08:13I've used the information in the first post (which is identical to the references I quoted above) to figure out how to calculate hab %. Unfortunately it looks like Poell et al's habcalc gets a slightly higher figure, and I'm fairly sure my method is correct.
Interesting!
That Calculator uses a "best approximation" math that's about 1% off in many cases.
How does you math compare with the actual habs as displayed by Stars! itself?
Or did you mean the "hab ratio" as displayed by the RaceWizard?
I'm also finding the habcalc is give percentage chance of a random world being green as 1% higher than I calculate it.
I use my formula (stated above) to calculate the chance of a random world being green as a decimal fraction, e.g. 0.213. To convert to and from percentage chance, multiply or divide by 100. To get the race wizard "1 in x" x value, take the reciprocal of the decimal fraction chance and round it to a whole number.
My decimal fractions tend to agree with the race wizard "1 in x" chance, with my values allowing small changes in chance to be seen.
Marduk wrote on Tue, 04 September 2012 17:25I usually get roughly the estimated proportion of systems, but I have had some games where it is wildly skewed one way or the other. The smaller and sparser the universe and the narrower your hab settings, the greater the likelihood this will occur. There are roughly a million system hab variations... if you are only seeing a couple of hundred systems there are a lot of potential gaps.
Especially if you have two fields at minimum width (I don't remember your hab settings, but I've done it often enough), it doesn't take much unevenness in the distribution to have a huge impact on the final tally of habitable and good systems. I got tired of that, so I mostly go with an immunity and one wide, one narrow. That almost guarantees being close to the estimated hab. As noted, you may still have to conquer a lot of territory to find those good systems...
Yes, sometimes there isn't enough stars in a universe (or close to your homeworld, d### it all! >:) to have all the habs match the true distribution that you find when you have enough, certainly for 10,000+.
As the Stars! random number generator can be seeded (with a value in the universe .def file, allow you to recreate the same universe over and over again), it must be a pseudo random number generator. It could still be very close to true random. If you could extract the initial random numbers output (usually a real number x where 0 =< x < 1) you could do the pi/4 test. To test how random the numbers are, take N pairs x and y of random numbers and calculate:
sum for every pair ( if x^2 + y^2 =< 1 then 1 else 0 ) / N
which is pi/4 for a true random number generator when N is big enough.




Re: Universe habs, what governs them? 
Thu, 13 September 2012 12:26 

iztok
Messages: 1218 Registered: April 2003 Location: Slovenia, Europe

Commander 


Hi!
Quote:online games seem more skewed than solitaire games.
If that makes you feel better, you're not alone in this
In ALL my time with Stars! I can't remember a single online game where I had better planet draw, than my race was designed with. In games, where hab draw mattered (non1WW or nonimmune), it was always a "point" or two worse than I expected, up to the most extreme last game, where my race was dualimmune AR with 1in3 hab, but got 1in8 within 2 W9 jumps.
Feel better now? I certainly do.
BR, Iztok



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