Site Searching Statistics Questions

[lch]

Well, I don't have a problem of hearing that what I'm writing is complete rubbish 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:

[Evilhomer]

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

Pretty much same here. But for me geeky is not equall to bad .

May I ask how you found that new distribution, Evilhomer?

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 (though I am still pretty sure the binomical distribution changes if 1 earth site is given or not)

[VedalkenBear]

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.

[thejeff]

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?

[Tequilich]

this hurts my brain

[VedalkenBear]

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.

[thejeff]

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?

[VedalkenBear]

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.

[Evilhomer]

Unfortunaly the distribution changes once again if we have found 1 earth site using gnome lore . (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.

If I could get probabilities for the different paths/terrains, I could come up with a very nice table summarizing everything

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).

[sector24]

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...