Suggestion to autocasting search spells

[RonD]

thejeff said:

I'd much rather search a Waste site (+20%) that already had 3 sites than a farm (-10%) that had none.

Am I missing something?

Hmmm. Suppose you're searching with Acashic Record and the base chance is 50%.

For the Waste province, the chance to find a site is 70%.

For the Farm, the chance to find 0 sites is 0.6^4 = 13%, so the chance to find 1 or more sites is 87%.

Its more complicated when searching with the individual spells (because the Waste site must have already been searched with some).


I wouldn't have spent any more than 10 seconds working that out, because I seriously doubt we will ever see a complicated auto-search algorithm. The devs prefer to spend time adding cool new content - and that's fine by me.

[thejeff]

No, the chance in the Farm is 40%.

It's not 4 separate checks against the percentage. If there is one site, then the code checks to see if there is another one, and so on, up to 4 sites.
If the first check fails, there are no sites there.

[RonD]

Emily Latella said:
Oh. That's very different.


Never mind.

[Folket]

I pretty certain that there is four seperate checks for sites.

Try in single player and use the astral spell that searches all sites on all province. You will find that only a few provinces havce zero sites.

[RonD]

thejeff said:
No, the chance in the Farm is 40%.

It's not 4 separate checks against the percentage. If there is one site, then the code checks to see if there is another one, and so on, up to 4 sites.
If the first check fails, there are no sites there.

It looks like this is not correct. I tweaked Boron's testmap. I took out all the terrain statements (so everything is plains), set ownership for a boatload of provinces to one of the nations (turned out to be 67 provinces total), and used the Seraphs to cast Acashic record on all 67). I created the game with site freq set at 50%.

By your explanation, about 1/2 should have had 0 sites, but here's what I got:

0 sites - 6
1 site - 13
2 sites - 29
3 sites - 17
4 sites - 2

[Folket]

Wiiieeehh!!

My 670th post.

[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.