Finding enemy searched magic sites.

Edi · #1 July 19th, 2007, 09:10 AM

Site occurrence and site type are checked at the same time. Roll if site exists, roll possible site (reroll once if rare), roll if next site exists, repeat until all slots filled or existence check fails, whichever comes first.

thejeff · #2 July 19th, 2007, 09:20 AM

Which means, I think, that while it is unlikely that a province will have more than 2 sites, a province known to have 2 sites is just as likely to have another one as a province with no sites is.

But my statistics is years behind me, so I may be missing something.

Jazzepi · #3 July 19th, 2007, 09:26 AM

Well, if it works like Edi says then the process is something akin to this, ignoring the selection of the actual site.

1st site : Roll, if you succeed, add a site. If you fail, discontinue.
2nd site : Roll, if you succeed, add a site. If you fail, discontinue.
3rd site : Roll, if you succeed, add a site. If you fail, discontinue.
4th site : Roll, if you succeed, add a site. Discontinue.

So to get a number of sites past 1 you have to succeed multiple times in a row. I think that makes every site past the first less and less likely to be there. But I could be very, very wrong.

Jazzepi

vfb · #4 July 19th, 2007, 10:07 AM

Jazzepi, you are right that 1-site provinces will be more frequent than 4-site provinces, for the reasons you stated.

But you are discounting the fact that we know there are 2 sites discovered in the province, at the point the auto-searcher stops searching.

Given that Province 1 is unsearched, the probability of a least one site available to be found is the site frequency.

Given that Province 2 has been searched and 2 sites have been found, the probability of at least one more site available to be found is also the site frequency. The province is guaranteed to have passed the first 2 site existence checks.

Since site searching is done by path, though, the chance of finding a site in a specific path in Province 2 is slightly lower than the chance of finding a site in Province 1. That's because Province 1 has 4 potential sites, but Province 2 only has 2 potential sites.

But Province 2 is still worth searching IMO.

MaxWilson · #5 July 19th, 2007, 10:10 AM

I've seen some controversy over whether failing a site discontinues generating other sites, but it doesn't matter for our purposes. As long as site occurrence is rolled before actually generating the site type site, frequencies for different paths are not independent. Finding a death site affects the chance of there being air sites in a province, because there are on average only x sites and air sites and death sites are mutually exclusive. This would not be the case if the % were rolled separately for each path:

1. Roll % of there being an air site. If you fail, discontinue.
2. Roll % of there being an air site. If you fail, discontinue.
3. Roll % of there being an air site. If you fail, discontinue.
4. Roll % of there being an air site. If you fail, discontinue.

1. Roll % of there being an fire site. If you fail, discontinue.
2. Roll % of there being an fire site. If you fail, discontinue.
3. Roll % of there being an fire site. If you fail, discontinue.
4. Roll % of there being an fire site. If you fail, discontinue.

etc. In that case there would be very few provinces with only 1 site (because at least one path should come up positive) and very few provinces with 8+ sites (when all paths come up positive), and finding an air site would not make it any less likely that there are death sites. But if site type is determined after occurrence, then skipping provinces with 2+ sites is a pretty reasonable thing to do because few provinces will have more than that anyway. Or, if you don't skip them, at least do them last.

-Max

vfb · #6 July 19th, 2007, 10:14 AM

It's not reasonable to stop searching.

You know that there are 2 sites. The first 2 checks passed. The chance of another site existing is the same as the chance of at least one site existing in an unsearched province.

MaxWilson · #7 July 19th, 2007, 10:43 AM

[thinks] Oh, I see. You're right, if Dominions uses Jazzepi's discontinue-on-fail algorithm P(3 sites | 2 sites) = site freq, and maybe you shouldn't skip them. However, I don't believe that it does discontinue on fail because (w/ site freq 45) I don't see anything close to 55% of provinces having zero sites. The distribution of sites I actually see looks more like a binomial, which makes skipping 2-site provinces reasonable after all.

Binomial probability calculator
P(1+ sites) = 91%
P(2+ sites) = 61%
P(3+ sites) = 24%
P(at least 3 sites | at least 2 sites) = 24/61 = 40%

Assuming that all sites are equally likely in a given terrain, that gives a 91/8 = 11% chance of finding a site in a "fresh" province with a site-searching spell, and a 40/8 = 5% chance of finding a site in a province that already has 2 sites.

-Max

Edit: no, that's wrong. There's more than an 91/8 = 11% chance of finding a site with a spell, since there could be more than one site there. But I'm too lazy to do the math at the moment, and I've made my point.

vfb · #8 July 19th, 2007, 11:18 AM

Oh.

Yeah, you're right, at "Special Site Frequency=45", there are way too many sites for '45' to be a percentage chance for a site to appear, with failure preventing further site generation.

Whatever the formula is, I'd still prefer not to have site searching stop when 2 sites are found, simply because even at '45', there are way too many sites that would not be found.

In one EA game I'm in, default settings, I have 56 provinces. I've searched all paths except holy, and didn't search Air in a few provinces.

Here's the breakdown:

Provinces with 1 site: 9
Provinces with 2 sites: 11
Provinces with 3 sites: 19
Provinces with 4 sites: 17

(Skewed by maybe 1 Caspar and one Alchemy Factory thingy I think.)

jutetrea · #9 July 19th, 2007, 11:22 AM

I just want an option that I can force them to follow the list, I want to see every site searched for every path I have available. I don't care if it already has 2 sites or not.

Those rare sites that you might find 1 or 2 of in a game can completely change the game. On the other hand, if you DON'T find any of those sites, you just wasted a ton of gems and mage time. I still think its worth it though.

I'd also rather have the list be proximity based to capital rather than suddenly railroading my search pattern over to newly conquered enemy territory, but that's minor.