Site Searching Statistics Questions
 

You'll have to excuse me because I R not guud at math, but I have a few site searching questions.

1) If you use a site searching spell like Haruspex and don't find anything, does it have any effect on the chance of finding a site of another magic path? I would think that not finding a nature site would also eliminate the chance of finding a nature/astral site or nature/anything site as well. So as you eliminate more and more magic paths, the chance of there being a site in the remaining paths gets smaller and smaller. Is this correct?

2) Follow up question. If you search nature 1 and don't find anything, how does that affect your chances of finding a site at nature 2, 3, or 4? Presumably the greatest chance of finding a site is at level 1, but the better sites are rarer. Is this correct as well?

Re: Site Searching Statistics Questions
 

The more you find out what's NOT there the higher the chance gets that something ELSE is there. If you already remote site searched a province and didn't find any sites at all, then unless it's farmland there's a high probability that something else is there. If you already found one or two sites, that could mean that those are all, though. It could be a magic site which is from a path unaccessible to you, like blood. Strong hints for magic sites are: unnatural scales of cold that can't be explained by or even contradict dominion influence can indicate that a water site is there, death means death (d'oh), heat can indicate fire and I think luck can indicate the presence of an astral site. This was really useful to search for magic sites more effectively for me. You should always search those provinces where you have found the least magic sites so far. Depending on terrain there's a higher/lower chance for some paths, too, check Edi's DB or I think somebody even made a list somewhere.

Re: Site Searching Statistics Questions
 

I believe that the sites are all rolled up randomly by the generation mechanism for each map. When it is created all the sites are already distributed. That being said, let me try to give some insight as best I can. I'm not good with probability, Ich is, so hopefully he'll respond.

1) AFAIK, sites are only related to one particular magical type. A sight that produces both earth, water, fire, and astral gems will only be a site of one type. This means that searching all the nature sites to level 4 will not reduce the chances of finding an astral site that also produces nature gems.

2) It's useful to look at the # of sites in a distribution along the levels. There are more level 1 sites then level 2 so on and so forth with their being more level 2 sites then level 3 and more level 3 than level 4. Literally 95% of sites are level 1-3 which is why I always advocate that rainbow site searching mages take level 3, not 4, of a given magic path if all you care about is finding sites. You'd have to actually bring up Edi's open office spread sheet with every site in it, organize it by a given type, and then count the # of sites of a particular level to figure out the probabilities.

Suffice it to say, I don't consider a province fully searched until I've done so up to at least level 3. I would never site search, unless I was desperate, with a level 1 path mage. I would site search with a level 2 in multiple paths like EA Ten'Chi's flying capital only mages, or with a mage in 3-4 in a single path.

Hope that helps.

Jazzepi

Re: Site Searching Statistics Questions
 

To elaborate on what Ich said: Sites are discovered based on a SINGLE path. The types of gems that a site gives is independent of the discovery path. For example, the clam fields site produces S gems, but requires W to find. The dying forest (produces 1N1D) is ONLY found by a nature search, death will not uncover it.

That being said, the vast majority of gem sites are found by searching the same path...W searches yield W gems, etc. Generally any off-type gems will be in addition to one or more gems of the searched path, but it's not always true.

Failed searches will generally mean that there is a higher liklihood that searching other paths will pay off. For example, with a 50% site frequency the chance of having 0 sites in a province (disregarding terrain mods) is approx. 6%, so empty provinces are somewhat of an exception, meaning it's proportionally more likely that sites are hiding in the unsearched paths. Likewise, only 6% of provs will have 4 sites, so a province that already has 3 sites in it is unlikely to merit further searches. (there are 4 potential slots for sites in each province, and .5^4 is how I'm getting the percentages here, the .5 will change based on site frequency). The higher the site % the more this will hold true.

As for levels, I generally do fine with manual searches, which cover mostly levels 1 and 2, but if you're looking for powerful discount sites you'll want to search to level 4, especially in astral and death. I'm not really sure how the site freq/terrain mods/site rarity/site income all combine in terms of how many gems you'll get per level from 1-4 on average though, since they're poorly documented from what I've seen, and my ability with that many probability interactions is lacking.

Higher level also isn't always better, most of the gem types have a level-3 search site that produces just a single gem.

Re: Site Searching Statistics Questions
 

From what I recall, barring special maps... Though what I recall is quite limited, and hardly the entire deal...

Terrain has certain modifiers on probability, and sites that can be generated. We'll assume 40%, however.

When the game is started, each province (capitals excepted) gets four separate rolls for sites. For each site that is found, it rolls for what kind of site is there. If that roll produces a rare site, then it rerolls to see if it keeps that site. If it produces a unique site, and that site is already taken, it selects another.

Wastelands have a higher chance of having sites, while farmlands have a lower chance. Once its figured out whether a province contains a site, the probability of a province containing a site of a particular path is determined by the number of possible sites. That is, you'll never find blood underwater, death is unlikely, and water common, simply because of available selection.

A site can only be of one path. It can generate gems of more than one path, but it still belongs to only one path. There are water sites that produce fire gems, and fire gems only. You can get a clue by looking at the icon, or loading up Edi's database and sorting the sites sheet by type.

Re: Site Searching Statistics Questions
 

Very helpful stuff, thanks. I'm actually more of an "Acashic Record" everything type of player, but I'm trying to be more practical.

Re: Site Searching Statistics Questions
 

I don't think this is quite right. From what I remember about statistics the logic is like this. If you flip a coin 10 times and it comes up heads every time, what is the chance it'll come up heads the next time you toss it? Answer: 50% because the coin has no memory. Likewise, a province that has generated 3 magic sites has exactly the same chance of having a 4th as an unsearched province has of having at least one site if I understand how the sites are generated. You're right that a completely virgin province has only a 6% chance of having 4 sites, but a province that already has 3 sites revealed has a 50% chance of having a 4th with a 50% site frequency*.

That * is because there is another factor effecting your chances, which is again a bit counterintuitive. The more paths you've searched, the less likely you are to find more sites, regardless of how many you've found so far. As an example, consider a province that you've already searched in 7/8 paths. Assuming for a second that all paths had an equal frequency of sites, with a 50% site frequency the chance of there being at least one site there is (site frequency) * (chance of a given site being the path you haven't searched) or 0.5 / 8. Think about it this way, if you're casting aschric record you'll get the highest payout targeting provinces that have not been searched at all.

This is a little misleading though, as you usually don't care what your chances are that there are undiscovered sites, you care what your chances are of finding a site if you for example cast gnome lore. The thing is, from a statistical standpoint the paths are completely independent, if you search a province for astral it does not effect your chances of finding an earth site there regardless of whether you uncover an astral one. This is because what you really care about is "what is the chances a given province has at least one earth site?" which is not effected by the existence of astral sites - its 0.5 / 8. (disregarding the small chance that there are 4 non-earth sites, which complicates the math and doesn't change the chances too much)

Re: Site Searching Statistics Questions
 

I'm not sure that's a correct analogy either, Baalz. (I'm not a statistician though, so I may very well need correcting.) The key difference, I think, is that the random chance has *already* been decided. Granted, if Dom3 checked that province each and every time a sitesearch spell was cast, there would be an equally slim chance each time of finding a suitable magic site regardless of how many sites have previously been revealed. But the game creates the sites randomly when the map is first generated.

Let's use your coin-toss analogy for the sites. I have *already* tossed the coin four times. In a random order, you check three of those tosses, and discover heads all three times. What is the chance that the fourth (randomized) pick will be tails? Well, let's see what options we have left:

HHHH
THHH
HTHH
HHTH
HHHT

So, from the options that are left--assuming a completely random pick order for the 'revealed' coins--the chance of the final coin coming up tails is *four times* the chance of it coming up heads.

Now, to bring it back to Dom3, that would mean that if a coinflip determined whether there was a site, then if you'd already revealed 3 sites, there would only be a 20% chance of a fourth site being revealed.

Or are the basic assumptions I've started with flawed?

Re: Site Searching Statistics Questions
 

This isn't like a coin flip though. It's more like for every province you have three cups (actually, nine) and one pea (actually, zero to four) under one of the cups. You want to find the peas. You can turn up one cup at a time. For a province where you haven't searched yet, that's three cups and lifting one of them is a 33% chance of finding the pea. If you already lifted one of them and did not find the pea, then you'll have a 50% chance of finding the pea if you try again for that province. This is better than trying another province where you only have a 33% chance of finding one.

This is, of course, a very simple model which isn't exactly like what we have in the game, so don't take it literally.

Re: Site Searching Statistics Questions
 

Well, the problem is that I remember none of this math.

Hmmm... I think this would be a working model... Though a bit innacurate, fairly approximate.

Take four quarters, toss them, and put them down on a table. Heads is a site, tails, no sites. The table is the province. Now put a blank napkin on the coins that came up tails. No site here. For each coin heads up, write F, E, W, A, S, B, N, D, H on a napkin, representing each site path, including holy. Not looking, randomly take one of these napkins and put it on top of the coin, letter hidden.

To further complicate the model, you could write a number representing the level of the path. But for simplicities sake, we'll assume the site will only be searched with level nine remote site searches, e.g. Dark Knowledge, and ignore the site level.

One logic flaw with this model is the idea that sites of all paths are equal. Holy is notably rarer, for instance, because there just aren't as many sites.

Re: Site Searching Statistics Questions
 

Okay, I think Baalz has trouble with the reverse scenario than I described: If I already found something, how big is the chance I'll continue to find something if I search more?

Those things are not independent. For every site searching, there are two things that come into the equation: One, how many sites there are in the province, two, how many you found already. If there are two sites in a province and you already found two, then you can search all you want but that won't make a new site pop up. That's because those sites are rolled for before the game starts. If they'd be rolled for when the site search is being made, you would be correct.

Re: Site Searching Statistics Questions
 

The inaccuracy of indypendents example is that the unknown "head" probability has four positions to be at (so you would have to compensate with a factor of 4 here), while each tail in the example only has one position (while having four "cases" instead).

Probably pretty fuzzy explanation, but if we simplify to Baalz original 4 random coin flips, 3 known the chance for the last unknown is 50% heads and 50% tails (as Baalz wrote).

That said I am not sure about the mechanic behind site distribution so I am not sure how well the coin flipp theory works. It is however always better to search provinces with few sites for the simple reason that 4 sites is the maximum (thus you cannot find 2 new sites, if you have already found 3 for example).

Re: Site Searching Statistics Questions
 

Ich has it correct, and there's a distribution that is used precisely for this issue; it is the hypergeometric distribution.

Consider the following. A province in ME, by default, has a 40% chance of having a site. Let us assume no terrain modifiers are in place.

The number of sites that are available to find is given by the binomial distribution. The probabilities are:

0 - 0.1296
1 - 0.3456
2 - 0.3456
3 - 0.1536
4 - 0.0256

(Incidentally, this means that the average number of sites in a province with a per-site chance of 40% is 1.6.)

Therefore, if you have an unsearched province, and you cast Gnome Lore on that province, the probability that you find an earth site is the probability that there are X sites, and that there is at least one site among those X. That is:

[P(1 site) AND (Probability that site is Earth)] OR [P(2 sites) AND (Probability that the first site is earth OR Probability that the second site Earth)] OR [P(3 sites) AND (Probability that first site is Earth OR Probability that second site is Earth OR Probability of third site is Earth)] OR [P(4 sites) AND (Probability of first site is Earth OR Probability of second site is Earth OR Probability of third site being Earth OR Probability of fourth site being Earth). Since AND is mathematically multiplication, OR is mathematically addition, and P1 OR P2 OR P3 ... is equal to 1-P1*P2*P3..., we have, assuming equal chances of each type of site in this province:

(0.1296)(0) + (0.3456)(0.111) + (0.3456)(0.210) + (.1536)(0.298) + (0.0256)(0.376)

= 0.1663

or an 16.33% chance of finding an Earth site in that province.

Now, what happens if you have an Earth site in a province, and then cast Astral Probing on the same Province? Then the probability is:

P(2 sites)*(1-P(that site is not Earth) + P(3 sites)*(1-P(neither site remaining is Earth) + P(4 sites)*(1-P(none of the three sites remaining is Earth).

Or

0.3456*0.111 + 0.1536*0.210 + 0.0256*0.298

= 0.0783

Or an 7.83% chance of finding an Astral site in a province that already has another Earth site, _provided you did not search for the Earth site_. If you did, then it is 0.0876, or an 8.76% chance.

I hope this makes sense. If anyone wants other probabilities (especially the way this all changes if you select a different per-site probability), just let me know. http://forum.shrapnelgames.com/images/smilies/wink.gif

Re: Site Searching Statistics Questions
 

I do belive you are incorrect VedalkenBear. It was a while since i studied statistic (I will give you that) but probabilites change if we get to know something about the result (like knowing that we have 1 earth site). The binomical chances you listed:

0 - 0.1296
1 - 0.3456
2 - 0.3456
3 - 0.1536
4 - 0.0256

are probably correct if you have no prior knowledge (I have not dubble checked this but I will trust them). They will however change once it is known that we have 1 site (from the earth check - obviously now the chance of having 0 sites is 0). This will change the result on the following calculation....

Re: Site Searching Statistics Questions
 

VedalkenBear - first class analysis.

What I think would be most helpful (and you have provided ample evidence of ability) would be a table showing the average number of sites per province with the settings of 10,20,.....100%. (The values higher than 75 are available using map edit.)

Thank you.

Re: Site Searching Statistics Questions
 

Ok, without actually checking the numbers I followed you up through the 16.33% chance of an earth site.

For the astral search:
Why (1-P(site is not Earth))? Isn't that the same as the chance that the site is Earth? Where does the chance that the site is astral come in?

Nor do I see where you get the 8.76% if you have searched for an earth site.

If there isn't an earth site, but you've searched for one, how does that change the probability of finding an Astral site?

Re: Site Searching Statistics Questions
 

Evilhomer: Actually it doesn't. The other calculation used the probability of 2 sites (0.3456) multiplied by the chance that the second site (since the first is already occupied) is the appropriate kind.

The binomial numbers above came right out of Excel's BINOMDIST function. Also, I know they're correct because I've had to use that exact P for Work Measurement several times.

Remember, the number of sites are mutually exclusive. Having 2 sites is not dependent on having 1. Obviously, you can't have 2 without having 1, but in a probabilistic sense, the states are mutually exclusive and independent.

Re: Site Searching Statistics Questions
 

Zounds!

Re: Site Searching Statistics Questions
 

Hey, I'm an Industrial Engineering student, and probability/statistics are used in every single one of my classes. I hope I'd be good at it.

As for the expected number of sites per province, it really is just (4*p). I've verified it for several different values of p in Excel, and it follows exactly.

Now, if someone were to give me the actual terrain differences on the different types of sites, I could do some more advanced analysis.

Re: Site Searching Statistics Questions
 

I am not sure we understand each other here I must say. I will give you an example:

The same hypergeometric distribution GIVEN that we have 4 sites in that province would be:

0 - 0.0
1 - 0.0
2 - 0.0
3 - 0.0
4 - 1.0

In the same way the distribution you gave would change GIVEN that we have atleast 1 site, so using this:

0 - 0.1296
1 - 0.3456
2 - 0.3456
3 - 0.1536
4 - 0.0256

just cannot be accurate for the second calculation (when we know we have atleast 1 site). Maybe I misunderstood you somewhere along the way, a bit to tired to go into detailed math analysis.

Re: Site Searching Statistics Questions
 

Thejeff: Sorry, the 1-(P of not Earth) was supposed to be not Astral.

The 'if not searched' value included the probability in the Astral analysis that an Earth site could be any one of the remaining sites (that is, the probability of the site NOT being Astral was 8/9). If Earth was searched (at level 4 or 9), then the probability that the sites could be Astral would be 1/8, not 1/9. The slightly higher value takes this into account. (I had this value at hand because I initially forgot Holy sites, and therefore had done all the calculations for 1/8 instead of 1/9.)

Re: Site Searching Statistics Questions
 

Probability mathematics make my head hurt. That is all.

Re: Site Searching Statistics Questions
 

Oh, I'm using the binomial not the hypergeometric. The binomial probabilities are simply the probabilities of a given number of sites in a province. These states are not dependent on one another. If the site placement algorithm checked for a first site, found none, and _did not check anymore_, that would be conditional probability.

Basically, for the second calculation you have:

0 sites in province (trivial case): 0
1 site in province (also trivial): 0
2 sites in province, 1 is earth, chance that the second is earth: Probability that there are two sites in province * 1-(Probability that the first is not Astral(1)*Probability that the second is not Astral(0.875) = 0.3456*(1-(1*0.875)

And so on. If the probabilities change given one state, that means the probabilities are conditional. The only way for that to happen in this case would be if the site search algorithm were to stop checking for sites if any check failed. That AFAIK does not happen.

Re: Site Searching Statistics Questions
 

Okay, this does sound wrong. http://forum.shrapnelgames.com/images/smilies/happy.gif As said before, the sites that are in a province are determined when the game starts, not when a site search is being made. Either there is a specific site in a province or there isn't. What you're dealing with regarding to statistics is in which of the five possible scenarios zero/one/two/three/four sites in the province you are and then if you picked the right path which covers one of these sites. Unless you found any sites, all these five scenarios go into your equation to find a site or not. So there's a 20% chance for that specific scenario and then tied to that a xx% chance to find a new site. These xx% chances from the different scenarios add up. Once you found some sites, you cancel out those chances from the scenarios that are no longer possible, so the overall probability to find a new site goes down. I hope that this makes any sense.

Re: Site Searching Statistics Questions
 

Ich: Actually, there isn't a 20% chance for each scenario. There is a 0.4 probability of a site being placed, with a maximum of 4 sites being able to be placed. This is a pure binomial distribution. Even in the case of 0.5 probability, there isn't a flat chance.

I agree that they are determined when the game starts. However, we cannot look at a province and tell how many sites are in it. Therefore, we must take into account the various probabilities regarding the number of sites.

Once that is done, you have the scenario I described in my initial post. To go over it again:

If there are 0 sites in a province, and you search for an Earth site, the probability that you will find an Earth site is 0.

If there is 1 site in a province, and you search for an Earth site, the probability that you will find an Earth site is 1/9. (Assuming equal probabilities)

If there are 2 sites in a province, and you search for an Earth site, the probability that you will find at least one Earth site is the probability that both sites are not Earth sites, subtracted from 1.

etc.

Now, those are all _conditional_ probabilities. Since the events are independent (the number of sites does not affect the types of sites), the total probability is the product of the two. Therefore, the probability of one site (0.1296) multiplied by the probability that the site is an Earth site (0.1111) will be the probability of their being one site in the province AND that site being Earth.

Since we do not know the number of sites in the province, we must find the probabilities of each case, and then sum them to find the overall probability of finding at least one Earth site in a province when we search it. That is the probability I gave you.

Re: Site Searching Statistics Questions
 

I finally decided to be math geeky, so here goes:

Binomical distribution GIVEN 1 site is earth (when we entered province // no searches done).

sites - probability
0 - 0.000
1 - 0.216
2 - 0.432
3 - 0.288
4 - 0.064

Chance of finding one or more astral sites using a level 9 search spell (assuming all types of sites have the same probability, not true but whatever...)

P(2)*(chance of 1+ astral site=1/8)+P(3)*(chance of 1+ astral site=15/64)+P(4)*(chance of 1+ astral site=169/512)

=

0.143 (or 14% if you wish)

So the chance decreases, but not by as much as reported by valkenbear. Same calculation provided that we have searched using gnome lore (and found 1 site) will follow..

*Note the "chance of 1+ astral site" changes, being 1/8 in the first bracket and (1/8*7/8)+(7/8*1/8)+(1/8*1/8)=15/64 in the second bracket, and so forth

Re: Site Searching Statistics Questions
 

Yeah, my bad about the zero/one/two/three/four being equally possible. That was simplifying it too much, although I wouldn't want to do this in a full detail analysis which would include at which level you searched for the sites already, what terrain we have, etc. - this can get overly complicated.

What's only important: How many sites there are (a random variable), how many sites we found already and how much we searched already / how many search possibilities are left.

Re: Site Searching Statistics Questions
 

May I ask how you found that new distribution, Evilhomer? I think I see where you're going, but I'm missing that part. (And I am mildly affronted at the fact that you call this 'math geeky'. This is what I'll be doing for a living soon.)

Re: Site Searching Statistics Questions
 

I beat a hasty retreat before the math. I yield the field rather than suffer an ignominious defeat. I'll be watching from the sidelines, though.

Re: Site Searching Statistics Questions
 

LP: Aw, that doesn't help. I need people to catch me on stuff. :p

Re: Site Searching Statistics Questions
 

Well, I don't have a problem of hearing that what I'm writing is complete rubbish http://forum.shrapnelgames.com/images/smilies/happy.gif so let's see what people say about this formula to determine the possibility to find a new site with a search, where SITES is the variable how many sites there are in the province, sites is how many we found already and searches is how many remote site searches have been done: http://www.shrapnelcommunity.com/thr...2dbc5cb11d.png

Re: Site Searching Statistics Questions
 

Pretty much same here. But for me geeky is not equall to bad http://forum.shrapnelgames.com/images/smilies/happy.gif.

0 - 0.000 trivial, we know we have atleast 1 site

1 - 0.216 we have 3 remaining "maybes", chance of having all as negatives are (6/10)*(6/10)*(6/10).

2 - 0.432 Chance of having exactly one additional site 3*(4/10)*(6/10)*(6/10)

and so forth....


Edit: I might have very well have misunderstood how sites are distributed to be honest....

As I understand it 4 checks are made with some percentage chance and for each "positive" a site is added, if i am wrong about this much does fall http://forum.shrapnelgames.com/image...es/redface.gif (though I am still pretty sure the binomical distribution changes if 1 earth site is given or not)

Re: Site Searching Statistics Questions
 

Ah, so it's binomial. I'm trying to figure out how to write it in binomial form. Is that just the binomial of 3s, shifted once? Seems like it.

Well, let me recalculate everything and see if we can get some terrain-specific issues.

Re: Site Searching Statistics Questions
 

So what's the generic equation?

I can't quite get there. Even assuming equal chances and that paths are fully searched or not at all.

Having found one or more sites, just shifts the P(1+sites) over in the equation. From:
P(1)*1/8 + P(2)*15/64 + ...
to:
P(2)*1/8 +P(3)*15/64 + ...
for 1 known site.

Having searched a path increases the P(1+sites)?
From:
1/8, (1/8*7/8)+(7/8*1/8)+(1/8*1/8)
To:
1/7, (1/7*6/7)+(6/7*1/7)+(1/7*1/7)
for searching one path?

Re: Site Searching Statistics Questions
 

this hurts my brain

Re: Site Searching Statistics Questions
 

I'm not sure about generic equations. I can generally apply the distributions, but as you can see I prefer to generate probabilities 'from first principles' rather than rely on formulae. And even then, as EvilHomer shows, I sometimes get it wrong. http://forum.shrapnelgames.com/images/smilies/wink.gif

Re: Site Searching Statistics Questions
 

EvilHomer: I'm not sure that's right. or I'm misunderstanding you.

Take the extreme case: There are 3 known sites in a province.
One remaining maybe: so 40% chance there is yet another site. Is that right?
Is it independent of how much searching you've done?
Obviously with all paths searched the chance is 0%. Is it still 40% with only 1 path left?

The probabilities should change, since 0, 1 and 2 are now at 0%, but not to 60/40. I think it's because they're not ordered?

Re: Site Searching Statistics Questions
 

Tequilich: To be quite honest, if this hurts, you don't have to read it. Presuming you do, would you prefer a precis of the results?

Thejeff: I'm pretty sure Homer is correct at least in his updated binomials. If I could get probabilities for the different paths/terrains, I could come up with a very nice table summarizing everything.

Re: Site Searching Statistics Questions
 

Unfortunaly the distribution changes once again if we have found 1 earth site using gnome lore http://forum.shrapnelgames.com/images/smilies/happy.gif. (Basically since then we can exclude additional earth sites)

Take the extreme case: There are 3 known sites in a province.
One remaining maybe: so 40% chance there is yet another site. Is that right? Yes, if none has searched the province.
Is it independent of how much searching you've done? No
Obviously with all paths searched the chance is 0%. Is it still 40% with only 1 path left? No, it is very small.

This is not hard but indeed very tedious. I among many others would find it interesting indeed. I suggest only to do it for the standard case (no searches or sites found).

Re: Site Searching Statistics Questions
 

When I think about how much time wasted on this, it makes me proud to have started this thread. I just want to take Evilhomer and VedalkenBear and kidnap them to work in my math dungeon. Where...sinister math things are done...yeah...

Re: Site Searching Statistics Questions
 

Maybe I'm misreading his intent:
Are those binomials just for no searches done?
If so, how does finding a site with a search affect things?

Edit: Ok, you posted while I was typing. Thanks. I was thinking of them independently. And I still think that may be possible.

I'd love to see a table without the probabilities for the different paths/terrains. Assume 40% and equal chances. Just chances by number of sites found and number of paths searched would be great. Seeing the hard numbers would help me think about it, at least.

I'd be very impressed if you could come up with a nice table with all the probabilities. Way to many variables to format nicely. http://forum.shrapnelgames.com/images/smilies/happy.gif

Re: Site Searching Statistics Questions
 

Oh, yeah someone started this thread...hmm let me check the original questions http://forum.shrapnelgames.com/images/smilies/happy.gif. (and please not the evil math dungeon)

Here is the deal as I belive. Searching with say a nature spell and not finding any nature sites will not change your chances to find a "pure" astral site.

It will obviously remove sites that can be found using both astral and nature (if there are such sites, not delved into the database to be honest).

Searching using a nature spell and finding one or more nature sites will will decrease the chance of finding additional "pure" astral sites on some later search.

Searching with nature-1 and not finding anything will drastically decrease the chance of having nature site(s) in that province. It will NOT however change the chance of having a site that requires higher nature to find (n2-n4 search needed). So you will not decrease the chance of having a rare nature site there. Funny enough if you find a nature site using n1, you decrease the chance of having rare nature sites there.

Easy rule of thumb: start searching provinces where you have not searched before and work your way up. Try to search with atleast level 3 in each path in each province that you belive you will be able to hold.

Re: Site Searching Statistics Questions
 

If I can get the data, I will provide the probabilities. With appropriate calculations shown so that people can check it for inconsistencies. :p

Re: Site Searching Statistics Questions
 

Ah, what a lovely forum this is. This makes me happy. There can't be many game forums where you'd get such an educated discussion. Sadly I'm too tired to follow all this now, so I will try to take a look tomorrow. I really like probability questions.