Theoretical limits on bruteforcing

jere · 2014-02-13 15:56:12

Occasionally someone will ask if there is a limit on tool stacking. I've responded that you'd never need (or even be able to use) more than 900 tools, since there are only 900 tiles in a house. But I wondered if we can define a better upper limit.

We've often seen houses valued around $100k. I've been at $500k momentarily. jwg has been $1M. But $100k is definitely more common. I'm sure you've asked yourself: will we ever see multiple $1M houses? $5M? $10M? Are we only at our current levels because we, collectively, still have a lot to learn about building?

I've calculated another limit that may have insight: 311. Simply put, you don't need to visit every tile; you only need to be adjacent to every tile. 311 is the minimum of number of tiles you have to visit to get adjacent to all tiles. Here's an illustration: http://castledraft.com/editor/QTSLMW

Now, there's only 8 essential tools: crowbar, ladder, explosives, torch, gun, cutter, water, meat. Buying 311 of each of these (brand new) would cost just under $2.5M. Assuming rational players, we can definitively say we will never see two houses that are both over $2.5M. Why? Because it would take 0% risk for one to take out the other with guaranteed profit. Not just minimal risk. I'm saying no risk at all and no chance of coming out empty handed.

The practical limit is of course much lower. Huge sections of pits require fewer ladders because you can see across the pits. Powered doors require lots of space for power (and for whatever puzzle turns them off). Which really leaves huge swaths of concrete and steel. 311 explosives is under $400k and 311 torches is $250k. Thrown in a handful of other items and the practical limit is well below $1M.

This is all sort of academic I guess, but hopefully you find it interesting.

Last edited by jere (2014-02-13 17:21:42)

Pandamonium · 2014-02-13 17:10:53

How about we limit backpack space to <311?

joshwithguitar · 2014-02-13 18:04:22

The total tool limit would be more like 622 - the reason: dogs placed in walls can cause you to use more than one tool per tile. If, say, you have a checker board pattern of dogs and concrete this requires 1 explosive + 1 gun + 2 meat (or 2 more guns) per 2 tiles - except for around corners. So that is close to 2 tools per tile crossed.

I was thinking that meat is not an essential tool as it is made obsolete by guns but it is true that if you brought 311 of each tool including dog food then you should be able to break through any house, while if you omitted dog food 311 guns would not be enough to deal with potential dogs.

Of course a house mostly made up of mostly checkered dogs and walls would not be particularly practical...

jere · 2014-02-13 18:13:45

I considered the issue with meat, but it's mostly negligible. Even if you brought 900 meat (entire house is dogs), you're talking $90k. Compared to $2.5M it's not really significant.

If, say, you have a checker board pattern of dogs and concrete this requires 1 explosive + 1 gun + 2 meat (or 2 more guns) per 2 tiles - except for around corners. So that is close to 2 tools per tile crossed.

Well, I meant 311 of each. In the ideal world, you would bring 311 of exactly the right tools for the tiles you cross, but if you knew what those were it wouldn't be a brute force at all.

Pandamonium · 2014-02-13 18:48:21

joshwithguitar wrote:

Of course a house mostly made up of mostly checkered dogs and walls would not be particularly practical...

I'm struggling with the maths, but using a small sample size.
What would be the minumum number of tools used for say

http://castledraft.com/editor/JZ1DOy

joshwithguitar · 2014-02-13 18:56:32

As you see the vault without any tool use and the dogs won't step on the dead cats, bringing 7 ladders will guarantee you'll get to the vault. You could do it cheaper by replacing a few ladders with explosives, a club and dog food just in case there is a dog behind the cement wall you explode.

Pandamonium · 2014-02-13 19:26:47

joshwithguitar wrote:

the dogs won't step on the dead cats.

sigh, animal behavior skill still is a very unknown entity to me.
How can you stop the dogs from falling into the pits? (trying to make it as expensive as possible to bruteforce)

Edit: Typo

Last edited by Pandamonium (2014-02-13 19:29:21)

iceman · 2014-02-13 21:03:19

Pandamonium wrote:

joshwithguitar wrote:
the dogs won't step on the dead cats.
sigh, animal behavior skill still is a very unknown entity to me.
How can you stop the dogs from falling into the pits? (trying to make it as expensive as possible to bruteforce)
Edit: Typo

Something like this will work:
http://castledraft.com/editor/sQWSIb

As long as the pits they can step in are *beside* a dead cat, they won't step in it (unless you're on that tile, in which case you'll be in for a rude awakening)

The Castle Doctrine Forums

#1 2014-02-13 15:56:12

Theoretical limits on bruteforcing

#2 2014-02-13 17:10:53

Re: Theoretical limits on bruteforcing

#3 2014-02-13 18:04:22

Re: Theoretical limits on bruteforcing

#4 2014-02-13 18:13:45

Re: Theoretical limits on bruteforcing

#5 2014-02-13 18:48:21

Re: Theoretical limits on bruteforcing

#6 2014-02-13 18:56:32

Re: Theoretical limits on bruteforcing

#7 2014-02-13 19:26:47

Re: Theoretical limits on bruteforcing

#8 2014-02-13 21:03:19

Re: Theoretical limits on bruteforcing

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