Suggestion to autocasting search spells

[DrPraetorious]

Yeah, there are 4 50% chances to have a site, which is why the average is 2.

A brief explanation of what order to search in:
Let us pretend that each province has 2 50% chances to have a site, of which half will be fire sites and half will be earth sites.

So, if we look at 160 provinces:
40 will have no sites.
40 will have one fire site.
40 will have one earth site.
20 will have one earth site and one fire site.
10 will have two fire sites.
10 will have two earth sites.

Now, we've done some earth searching, and we want to know: which provinces should we search for fire?
a) Sites which haven't been searched are expected to have: (40 + 20 + 10 * 2) / 160 = 0.5 fire sites each.
b) Sites which have been searched, and which contained two earth sites, have 0 fire sites each (guaranteed).
c) Sites which have been searched, and which contained one earth site are expected to have: 20 / (20 + 40) = 1/3 fire sites each.
d) Sites which ahve been searched, and which contained zero earth sites, are expected to have: (40 + 10 * 2) / (40 + 40 + 10) = 2/3 of a fire site each!

So category B is not worth searching at all.
Category D > Category A > Category B.

This is a particular case of the well-known "Monty Hall" paradox:
http://en.wikipedia.org/wiki/Monty_Hall_problem

[thejeff]

Apparently I was misled by comments from the devs. The game is complex enough, not even they understand it anymore.

I'm not entirely convinced by the (correct) Monty Hall argument.
Largely because of the terrain modifiers. Provinces with multiple sites are more likely to be in terrain with better chances and thus may still have a better chance of more.
Waste with 2 sites or farmland with none?

More importantly, I really care less about the order they're searched in. I don't want to have to come back and check for skipped provinces once the autosearching is done. Once that's hashed out, tweaking for the most efficient order would be appreciated, but I won't really care.

[DrPraetorious]

I agree with thejeff 100%.

The only requirement is that the site-searching algorithm should be good-enough that you don't bother by hand.

I'd propose "priority score" like (4 - sites found) * (4 - level in this path searched)^2, and never searching anything with a score of 0.

The issue with non-standard terrains is that, *I BELIEVE*, they have a linear effect on the site frequency.

If the site frequency is 75%, it's 65% in farmland and 85% in swamps, *I THINK*, and who cares?

OTOH, if the site frequency is 30%, sites are twice as frequent in swamps and that makes a big difference.

[Lazy_Perfectionist]

Hmm... interesting. With that priority score above...

0/0 = 64
1/0 = 48
2/0 = 32
3/0 = 16

0/1 = 36
1/1 = 27
2/1 = 18
3/1 = 9

0/2 = 16
1/2 = 12
2/2 = 8
3/2 = 4

0/3 = 4
1/3 = 3
2/3 = 2
3/3 = 1

#/4 = 0
4/# = 0

So, the very lowest priority is hunting for ultra-rare level 4 sites. Fine, that. I don't like the rest of it because its not very intuitive. But I do like the results, even if I can't predict where it'll search easily. But the auto searching isn't about predicting anyways. The way the numbers fall is fine enough by me.

I would put in a few additional variables. For Dark Knowledge, for instance, I would heavily favor land provinces over water provinces, though there are a few possibilities...

As there are currently zero underseas blood sites in the game, I'd set the priority to something like 1, (if I boosted all other scores by one, so this would be the lowest). This would allow mod-sites to be found eventually, while keeping in mind nothing will likely ever be found underwater - and they'd be searched dead last.

[DrPraetorious]

I don't want it to get too complicated, but yeah, we could have a priority score modifier for terrain, sure:
Farmlands, x0.9
Mountain, x1.2
Mountain + Earth, x2
Forest, x1.2
Forest + Nature, x2
Swamp, x1.2
Swamp + Death, x2
Wasteland, x1.2
Wasteland + Fire, x2
Ocean + Water, x2
Coast + Water, x1.5
Ocean + Blood, x0.1

Something like that?

[thejeff]

That would be nice, though unlikely to happen. You could tweak the values and calculate the exact chances of a site in a particular path. (And then the chances of VoT or AR if some paths have already been searched?) If I understand the Bayes argument correctly, the chances go up if you've already searched other paths and found nothing, so add that in.

I'm still going to override it to not search provinces I think are vulnerable. And I'm still going to try to search everything I expect to hold.

So I really see this as fiddling with the details of something that remains basically broken. The important part is letting it search provinces with 2 sites and not searching capitals. My next priority would be searching paths that have been partially searched. Order comes a long way after that.

[Lord_Bob]

It's more obvious if viewed as two marble bags. You have three marbes, 2 black and 1 white. You put one in one bag and two in another. There is a base chance of 33% of the white marble being in bag one and a base chance of it being in bag 2 of 66%. But then you take a black marble out of bag 2(which you will obviously be able to do). Now there is only one marble in each bag. So reaching in will pull only that marble out. But the BAG PROBABILITIES HAVE NOT CHANGED.