Site Searching: statistical test / modding logistics

[Bastiat]

Edi previously noted that he thought that the number of sites in a province spawned with an exponential distribution (roll for first site, if successful roll for second, if not stop, etc) while Kalijamaha suggested that the distribution of number of sites in a province was binomial.

http://forum.shrapnelgames.com//show...t=33791&page=4

This should be fairly easy to verify in a dummy game where you just perform Acashic on every province and then count.

1. Is it possible to do this with a switch, or is there a mod that automatically has all research and unlimited gems, so that I can speed the ability to do that statistical analysis?

2. Also, is it possible to make a map with just one terrain type? It would be nice to isolate that variable.

I started playing the game a month or so ago but havent delved into the mods or custom map options as yet. Thanks for the assistance- I look forward to posting the results.

[Squirrelloid]

Originally Posted by Bastiat

Edi previously noted that he thought that the number of sites in a province spawned with an exponential distribution (roll for first site, if successful roll for second, if not stop, etc) while Kalijamaha suggested that the distribution of number of sites in a province was binomial.

http://forum.shrapnelgames.com//show...t=33791&page=4

This should be fairly easy to verify in a dummy game where you just perform Acashic on every province and then count.

1. Is it possible to do this with a switch, or is there a mod that automatically has all research and unlimited gems, so that I can speed the ability to do that statistical analysis?

2. Also, is it possible to make a map with just one terrain type? It would be nice to isolate that variable.

I started playing the game a month or so ago but havent delved into the mods or custom map options as yet. Thanks for the assistance- I look forward to posting the results.

a Mod nation with national mages that have 9 in every path should get the research done quick. Could also mod starting gem income to be a large amount of astral.

I think you'd have to draw the map yourself to make it all mountains.

[archaeolept]

yeah there's a mod for testing... check out the debug mod.

also, it's easy just to edit a .map file and change all the terrains to whatever you feel like.

[thejeff]

Wouldn't it be easiest to do this with a mod setting all sites to level 0?
Though making that mod might take some typing.

Otherwise just mod Akashic to 1 gem, 1S to cast and research level 0. And boost capital site income for your nation.
You'll still need to take the provinces I think?

[Burnsaber]

Making a map just mountains is easy. Just set all terrain as mountain in the .map file. (The terrains won't look like mountains, but sinse you are just testing a theory, it should work), you can also use .map command to make yourself to start with the most provinces on the map.

As for the Acashic record, try this:

#selectspell "Acashic Record"
#researchlevel 0
#pathlevel 0 1
#fatiguecost 0
#end

That code makes Acashic Record researchlevel 0 and only to require 1 astral to cast. It also makes it free to cast.

[Omnirizon]

for the statistically impaired:

binomial distribution simply means "number of successes over n trials"
so if there are 4 possible slots for a site, then there are four independent trials (one for each slot). Because they are independent, the probability for n slots is simply n times the probability of a success.

I think exponential is being used to describe the shape of a distribution where later trials are dependent on earlier trials, thus making the distribution drop off steeper. unlike the binomial distribution, there cannot be a test for 'slot 2' unless the test for 'slot 1' was successful. So obviously there will be fewer provinces with 2 or more sites.

To test these hypothesis, we would need to gather data on the number of sites that do appear in each province in the game, build the distribution they form, and compare it to a binomial and an exponential distribution, and see which one it more closely approximates. Comparing distributions like this is called a "Goodness of fit test", because we are seeing how well an observed distribution fits a hypothetical one.



strip out all the jargon and math-babble, and statistics (even math in general) is extremely simple. problem is, people have formed a myopic hyper-specialized language that, unfortunately, draws upon other words with other meanings in other contexts but completely different meanings when used in statistics. when one trys to ferret out meanings of words in statistics, they are faced with an impenetrable wall of formalized expressions which require prior explanation from someone familiar with the expressions and who can explain them in natural language along with noting the specialized, context specific, meanings of words. This problem has been compounded in the american school system by a systematic 'dumbing' of mathematics in american schools where math concepts are presented without explaining the underlying logic because it was believed it was 'too complex'. In reality, the underlying logic is very simple (thus why it is logical at all), and by leaving this out children are left feeling that they know 'a little bit about math' but that there is this whole mystical world behind this which takes hyper-specialized experts to understand. nothing is further from the truth, as evidinced by the way in which children in even underdeveloped countries with second-rate education systems outperform american children in mathematics.

ooops. I was ranting. sorry.

[Illuminated One]

Hmm, let's suppose you started the game via --comptrn and some AIs (you can watch the AI) and mod all spells out except Acashic, which you make free.
Make the game host automatically for 100 turns via batch/shellscript you should see everything - takes maybe 2h, no idea.

Though I guess just having something go through the fatherland file and collect the data into a spreadshead would save a lot of work.