Site Searching Statistics Questions

[IndyPendant]

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?

[Lazy_Perfectionist]

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.

[Evilhomer]

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).