Preliminary L8 Quest Knowledge

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Pewt
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Re: Preliminary L8 Quest Knowledge

Post by Pewt » Thu Jun 20, 2013 8:47 am

Draco Cracona wrote:I'm looking at this data, and I'm wondering if anyone's seen any failures for assassins at +25% combat after 50 or even 60 turns? I'm seeing failures there for the +1% data.
My most recent one has a failure after 50. I've been stopping at 60 though so no clue there.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jun 20, 2013 9:06 am

Ah, thanks, pewt. Checking, there's atually a 50+ failure on WM's data. Will try running something like 15*(1+turns/10) and comparing to Gui's data and your data. Trying to find something that factors in +combat without breaking the low-turn data is tricky, unless it's something useless like +com/5.

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Re: Preliminary L8 Quest Knowledge

Post by Fred Nefler » Thu Jun 20, 2013 10:06 am

Are we sure +combats does anything beyond making the adventure possible?

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Re: Preliminary L8 Quest Knowledge

Post by lostcalpolydude » Thu Jun 20, 2013 10:10 am

Fred Nefler wrote:Are we sure +combats does anything beyond making the adventure possible?
No, one goal is to answer that question.
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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jun 20, 2013 10:23 am

Fred Nefler wrote:Are we sure +combats does anything beyond making the adventure possible?
The data samples indicate that it might, based on the consistent ~10% non-assassins at turns 50+ for +1%, compared to the rare non-assassins at T50+ for +25%. There appears to be minimal difference between the datasets for turns 1-10, though, which are the important ones.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jun 20, 2013 11:24 am

Okay, a few tests ran:

Assassin rate of (12.5+plusCombat/5)*(1+advcount/10) gives the following:

+25%:

First 10 turns: 1.9ish assassins expected.
50 turns: 27.2 assassins expected.
First three assassins: 12 turns expected.

+1%:
First 10 turns: 1.4ish assassins expected.
50 turns: 19.5 assassins expected.
First three assassins: 15 turns expected.

We can assume that +1% is close enough to a non-combat related variant.

+25% combat seems to be about 25 assassins in the first 50 adv. Notably off from the 19-20 expected without a combat modifier variable.
+1% seems to be about 20-22 assassins in the first 50 adv. Not far off the expected value.

That seems to roughly fit our data, I think. Caps out at 57 adv for the +25% combat case, and 74 for the +1% case.

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Re: Preliminary L8 Quest Knowledge

Post by ungawa » Thu Jun 20, 2013 6:44 pm

1% Combat

Code: Select all

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Re: Preliminary L8 Quest Knowledge

Post by DarthDud » Sun Jun 23, 2013 12:28 pm

Draco Cracona wrote:Okay, a few tests ran:

Assassin rate of (12.5+plusCombat/5)*(1+advcount/10) gives the following:

+25%:
First 10 turns: 1.9ish assassins expected.

+1%:
First 10 turns: 1.4ish assassins expected.
Errr... these expectations do not match your formula, right? Like, if we entirely ignore your advcount variable, and just assume each turn at +25% is the minimum .175, we'd expect 1.75 in the first 10 turns. With the formula as-written, we'd actually expect 2.7125.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Sun Jun 23, 2013 3:01 pm

DarthDud wrote:
Draco Cracona wrote:Okay, a few tests ran:

Assassin rate of (12.5+plusCombat/5)*(1+advcount/10) gives the following:

+25%:
First 10 turns: 1.9ish assassins expected.

+1%:
First 10 turns: 1.4ish assassins expected.
Errr... these expectations do not match your formula, right? Like, if we entirely ignore your advcount variable, and just assume each turn at +25% is the minimum .175, we'd expect 1.75 in the first 10 turns. With the formula as-written, we'd actually expect 2.7125.
Uhh. Shit. I'll look at what I've screwed up over the next few days, thanks.

EDIT: Bug found. I is dumb.

+25% combat seems to be about 25 assassins in the first 50 adv.
+1% seems to be about 20-22 assassins in the first 50 adv.

Now to see if I can match this.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Mon Jun 24, 2013 11:21 am

Right, I seem to have a new candidate:

assassinRate = min(1, (0.25*0.01/10)*(1+turnsSpent/10)) (numbers for assassins in first 50 and in first 10 agree with wolfram, roughly, done to check for bugs).

+25% combat:

25.87 assassins in the first 50 Adv;
11.21 adv for first 3 assassins;
2.17 assassins in the first 10 adv.

+1% combat:

21.74 assassins in the first 50 adv;
12.79 adv for the first three assassins;
1.82 assassins in the first 10 adv.

These agree with our numbers pretty well. It's a heavier suppression on the combat modifiers than I would have expected, capped at 57 adv for +25% combat, and 70 adv for 1% combat. Shows minimal turn savings for running the extra +24% combat on the first three assassins.

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Guiseppi
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Re: Preliminary L8 Quest Knowledge

Post by Guiseppi » Wed Jun 26, 2013 11:41 am

Yeah, for 3 assassins, the difference between +1% and +25% is ~1.6 turns? That's a lot less than I had expected.

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Re: Preliminary L8 Quest Knowledge

Post by Snaelda » Thu Jun 27, 2013 8:09 am

So basically as long as you have some access to +NC no need to spend extra resources on getting more

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jun 27, 2013 9:09 am

Yeah, pretty much any +combat is equal when you start suppressing them to that amount. Seems like a strange mechanic to use, though.

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Re: Preliminary L8 Quest Knowledge

Post by DarthDud » Wed Jul 03, 2013 5:17 pm

Draco Cracona wrote:Right, I seem to have a new candidate:

assassinRate = min(1, (0.25*0.01/10)*(1+turnsSpent/10)) (numbers for assassins in first 50 and in first 10 agree with wolfram, roughly, done to check for bugs).
What did you actually intend this formula to be? Since this formula is clearly not what you are actually using for your numbers, given:
(1) it has no +combat term.
(2) On turn 50 it gives an assassin rate of 0.0015

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 04, 2013 6:20 am

Urgh. Again, I prove to be stupid by not actually checking the formula I post, sorry- not quite sure where that one came from, it looks like I missed the base 12.5% chance out and had the combat modifier set to 25. Should be chance = (0.125+wombatMod*0.01/10)*(1+advCount/10), with wombatMod being the combat modifier (between 1 and 25).

Guess nobody else really looks at what I post either, though!

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Re: Preliminary L8 Quest Knowledge

Post by lostcalpolydude » Thu Jul 04, 2013 8:56 am

Draco Cracona wrote:Guess nobody else really looks at what I post either, though!
I think a lot of us read the conclusion but glazed over at the equation.
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Re: Preliminary L8 Quest Knowledge

Post by Guiseppi » Thu Jul 04, 2013 10:55 am

^^^

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Re: Preliminary L8 Quest Knowledge

Post by blisterguy » Thu Jul 04, 2013 7:48 pm

I don't even understand equations like this, when they're posted. High school maths was nearly 20 years ago for me.
Draco Cracona wrote:Should be chance = (0.125+wombatMod*0.01/10)*(1+advCount/10), with wombatMod being the combat modifier (between 1 and 25).
Sooooo I think from this I need to run +combat, yeah? I have no idea what it means as far as figuring out my expected number of turns is. Like, people try to explain it to me, but they start using words like "floor" and I'm like "the only floors we had when I did maths at school were the ones that held our desks and chairs up."

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Fri Jul 05, 2013 2:02 am

blisterguy wrote:I don't even understand equations like this, when they're posted. High school maths was nearly 20 years ago for me.
Draco Cracona wrote:Should be chance = (0.125+wombatMod*0.01/10)*(1+advCount/10), with wombatMod being the combat modifier (between 1 and 25).
Sooooo I think from this I need to run +combat, yeah? I have no idea what it means as far as figuring out my expected number of turns is. Like, people try to explain it to me, but they start using words like "floor" and I'm like "the only floors we had when I did maths at school were the ones that held our desks and chairs up."
Basically, +combat has a small effect after the first 1%. chance = (0.125+wombatMod*0.01/10)*(1+advCount/10), when split up is basically saying that you have a base chance of 12.5% every adventure, increased by your combat modifiers divided by 10, so at +25% combat you're looking at 15% for this first term. The second term is basically a way to increase the rate every adventure you spend. The major thing to note is that you have combatRate/10, which means that your combat rate modifiers have only a small effect.

Anyway, the overall results are as posted earlier-

+25% combat:

11.21 adv for first 3 assassins;

+1% combat:

12.79 adv for the first three assassins;

Showing a whopping +1.58 turn savings for running that extra +24% combat.

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Re: Preliminary L8 Quest Knowledge

Post by blisterguy » Tue Jul 09, 2013 6:24 pm

Weas farmed up a bunch of data with Faxnet which can be found here. Let's hope it helps confirm your findings!

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Wed Jul 10, 2013 5:08 am

Oooh, thanks. Very interesting to see that data, will have to try and have a good comparison later. Puts the cap at 66 for +25%, at least, which is good to know. Interesting about the guaranteed assassins, though.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Wed Jul 10, 2013 9:07 am

Cross-posted from KoLSpading:

Okay, some thoughts after trying to fit these two to the same formula:

I can't get a continuous function that fits roughly 6% and 10% starting assassin chance with caps of 60 and 66. My best guess, currently:

(0.05 + combatMod/5)+(floor((Adv)/6)*6*0.015).

I got to the first term, 0.05 + combatMod/5, by looking at the turn 1 information. You've got about 5% and 10% respectively, so the only thing that fits, really, is a 5% base and +1% per 5lb of combat modifiers. I originally had this base rate multiplied by the turns spent, but that just wouldn't fit. After moving the combat modifier term out, I still couldn't get it to fit until I moved the base out as well.

The second term just came from trying to fit the two caps together; the two datasets called for roughly similar multipliers for the adventureCount, but they weren't quite the same, so I looked over the graphs and noticed that it could easily be based on the floor of the adv/5 or similar, and so running with that roughly fits.

EDIT: Fixed MC results, by adding the guaranteed assassins in.

MC results:

+5%:

Avg assassins over 60 adv: 29.91 [expected: 29.73]
Avg length of time for 3 assassins: 14.39

+25%:

Avg assassins over 60 adv: 32.18 [expected: 34.34]
Avg length of time for 3 assassins: 12.76

+25% numbers are still slightly too low, but 5% numbers sound about right. Thoughts? Suggestions?

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Wed Jul 10, 2013 11:19 am

Pretty certain that we're dealing with 1.5% per adv in the zone, with either (combatModifier/2)% or (combatmodifier/5+5)% added on top of that (latter version is a stepwise one as well). Too hard to differentiate between them really, in practice.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 11, 2013 8:05 am

Right, both of the two remaining equations are similar enough that we won't be able to discriminate between them well.

We have, as practical results:

Using Darzil's equation: chance = combat/2+adv*1.5:

+1% com: 15.45 turns for first 3 assassins.
+5% com: 14.60 turns for first 3 assassins.
+10% com: 13.61 turns for first 3 assassins.
+15% com: 12.74 turns for first 3 assassins.
+20% com: 11.96 turns for first 3 assassins.
+25% com: 11.26 turns for first 3 assassins.

Using Darth's equation: chance = combat/(365-5*combat)+adv*1.5:

+1% com: 15.59 turns for first 3 assassins.
+5% com: 15.04 turns for first 3 assassins.
+10% com: 14.32 turns for first 3 assassins.
+15% com: 13.56 turns for first 3 assassins.
+20% com: 12.72 turns for first 3 assassins.
+25% com: 11.80 turns for first 3 assassins.

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Re: Preliminary L8 Quest Knowledge

Post by Guiseppi » Thu Jul 11, 2013 9:36 am

Thanks for continuing to follow up on this, Draco. I don't really have much to add, except to say that people are still reading this thread, even if we don't have much to add. :)

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 11, 2013 9:59 am

Guiseppi wrote:Thanks for continuing to follow up on this, Draco. I don't really have much to add, except to say that people are still reading this thread, even if we don't have much to add. :)
It's actually quite interesting how it works; for example, you are guaranteed an assassin on turn 11, 21 and 31- these kick in regardless of number of previous assassins, and drastically shorten the length of time needed for 3.

Anyway, now we've got two nigh-indistinguishable formulae, I just thought that the expected turns were useful for the actual meat and bones of the thread :) I need to finish working on a MC of the slope at some point, just to compare the two. Silly thing.

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Re: Preliminary L8 Quest Knowledge

Post by lotsofphil » Thu Jul 11, 2013 11:11 am

Draco Cracona wrote:you are guaranteed an assassin on turn 11, 21 and 31- these kick in regardless of number of previous assassins, and drastically shorten the length of time needed for 3.
!?!?! Wow. Is this something just found out, or have I missed this all along?

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Re: Preliminary L8 Quest Knowledge

Post by transplanted_entwife » Thu Jul 11, 2013 11:39 am

lotsofphil wrote:
Draco Cracona wrote:you are guaranteed an assassin on turn 11, 21 and 31- these kick in regardless of number of previous assassins, and drastically shorten the length of time needed for 3.
!?!?! Wow. Is this something just found out, or have I missed this all along?
That was my reaction too, Phil.
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Re: Preliminary L8 Quest Knowledge

Post by ungawa » Thu Jul 11, 2013 12:01 pm

Yea, after reading that I followed up in the kolspading thread blisterguy linked. That's very interesting.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 11, 2013 12:13 pm

lotsofphil wrote:
Draco Cracona wrote:you are guaranteed an assassin on turn 11, 21 and 31- these kick in regardless of number of previous assassins, and drastically shorten the length of time needed for 3.
!?!?! Wow. Is this something just found out, or have I missed this all along?
Very recent finding- that was the first thing noticed from Weas' data.

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Re: Preliminary L8 Quest Knowledge

Post by Guiseppi » Thu Jul 11, 2013 12:57 pm

Check out blisterguy's link to the kolspading thread. They dumped all of weas' data into a chart, and the first thing that popped out is a 100% chance of encountering assassins on turns 11, 21, and 31. Interesting stuff.

Draco, I like the new formulas. Even if they're so close as to be indistinguishable, they both show enough difference between +1% combats and +25% combats (~4 turns for three assassins) to indicate that it's worth running as much as you can.

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 11, 2013 2:15 pm

And to complete the analysis, I have finally simulated the peak.

Expected length, assuming a 20lb slimeling and +233% items total, as well as -25% combat and a base 95% combat rate, is 21.12 turns. Way slower than the assassins at even +1% combat.

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Re: Preliminary L8 Quest Knowledge

Post by lotsofphil » Thu Jul 11, 2013 3:29 pm

Can anyone check if runaways/wandering monsters/hipster fights advance the 11/21/31 counter?

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Re: Preliminary L8 Quest Knowledge

Post by Draco Cracona » Thu Jul 11, 2013 4:45 pm

Just tried 8 runs, then had non-assassin followed by 2 assassins, so one on 11 there. I would be surprised if that was not increased by runaways.

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