View source for Talk:On the Trail

==Island rares ==

Does this work on the [[mysterious island]] frat rares? --[[User:Macoronikevin|Macoronikevin]] 02:42, 15 March 2009 (UTC)

:I believe there is (now) a limit of 1 of each "hero" (rare monster) per ascension.  There was a time in the past (a couple years ago?) when people were getting multiple ascots per ascension (I forget which mechanic was used -- spooky putty, maybe), and the devs decided this was a bug. -[[User:Greycat|Greycat]] 19:59, 15 April 2010 (UTC)
:*Yeah, that happened the first few days after Spooky Putty released. It was sealed up quickly.  On the Trail does not affect Island Rares. --[[User:MindlessGames|RoyalTonberry]] 20:03, 15 April 2010 (UTC)

==Initial Spading==
Initial spading shows approximately 50% of the monster it is used on when adventuring in the correct area.  I used it on a Harem Girl and 22 out of 40 adventures (the duration of the effect) were combat with Harem Girls. 16 were non combat adventures, and 2 were with other monsters.
--[[User:IpseDixit|IpseDixit]] 08:46, 26 June 2007 (CDT)

Not sure if the harem girls are the best test for this. I've always gotten the impression they show up way more often than harem guards, and the huge number of noncombats are a problem, too. Someone should try it on the goatlet or something.

*Actually, the number of Non-Combats would seem to confirm the findings, or at least mean that the effect only affects the battle queue, and non-combats remain unchanged (otherwise it would change combat frequency, and that's not indicated by anything in the description.)  Also, the harem girls do not show up in a 22 to 2 ratio to guards.  Theres a high statistical improbability that that would happen by chance. --[[User:IpseDixit|IpseDixit]] 08:55, 28 June 2007 (CDT)

*I would venture to say that it is a lot higher than 50%.  I'm going after the pink bat eyes in the entryway, and so far out of 8 adventures, I've had 8 albino bats.  9th gave me a regular old bat, and 10th was a pine bat.  I'm going to venture out on a limb and say at least 75%, maybe as high as 90%.  [[User:Rithe|Rithe]] 21:41, 28 June 2007 (CDT)

*I think it doubles the monster's frequency. I went to the spooky forest and got on the scent of a spooky vampire. I did 40 adventures with the scent and 40 without. Here's my data:
Monster (without effect) / (with effect) <br>
Bar 4 / 3 <br>
Mummy 5 / 1 <br>
Vampire 5 / 11 <br>
Triffid 3 / 4 <br>
Warewelf 4 / 3 <br>
Wolfman 4 / 3 <br>
Non-combat 14 / 14 <br>
I plan on doing some more spading to confirm this as the days go on. Note that the first time I used it on the spooky vampire, it was from the non-combat version. I counted [[An Interesting Choice]] as a non-combat in both cases. --[[User:Andylicious|Andylicious]] 17:35, 6 July 2007 (CDT)

*I used the odor extractor in the 8-bit realm on an Octorock.  I then fought 17 octorocks in the next 40 adventures.--[[User:CrimsonMirage|CrimsonMirage]] 05:59, 31 August 2007 (CDT)

I'd say the best way to determine the proportion would be the Wine Cellar.  Exactly two types of enemies, with no noncombats, would make determining the effect much easier.--[[User:DoctorWorm|DoctorWorm]] 08:55, 27 July 2007 (CDT)

Done. On a level 15 DB, using 2 odor extractors on a sommelier, and then letting it run out:

monster (with/without effect)<br>
sommelier: 71/38<br>
wine rack: 9/42<br>
This, I think, is a strong indication that each occurs roughly half the time normally, and that the odor extractor multiplies the frequency by 170-180% (~50%->~85%); if I remember, I'll try to do this again in a few days when I have more odor extractors.[[User:Ponder Stibbons|Ponder Stibbons]] 00:42, 14 August 2007 (CDT)

I tried the odor extractor on the Dairy Goats in the Goatlet. Of forty adventures, all combat, 29 of those were the target monster, and 11 were one of the other two available monsters. Has anyone else noticed that the frequency of non-target monsters increases substantially past the 20-turn mark? Only two adventures in the first 20 were non-target, then nine after. An effect of the odor growing older, the trail going cold? The 40th adventure was non-target. --[[User:Electra310|Electra310]] 00:47, 22 August 2007 (CDT)

I used an odor extractor in the dungeons of doom, and got the monster I wanted six straight times.  Then I got a non-combat, and a mixture of other monsters and non-combats for several adventures until I got the requested monster again three straight times.  Perhaps it works this way: Each time you get the monster you're trailing, there's an x% chance that you will "lose" the trail.  After that, you adventure normally until you get the monster you're trailing again.  x could be constant or vary with the number of OtT adventures left/adventures since you last encountered that monster.  There could also be some number of guaranteed adventures with that monster at the start.

If true, this would mean that you should get a lot of clumps of that monster, possibly interspersed with long stretches without it.  Has this been anyone else's experience? --[[User:Deusnoctum|Deusnoctum]] 01:07, 3 October 2007 (CDT)


Data for using it on a [[Gnollish Gearhead]] in [[Degrassi Knoll]], adventures in order:

G = Gearhead
C = Other combat adventure
N = Non-combat adventure

G G N C C C N N G C N G C G C N C C G C G G C G G C G G G N G C C G N C G N C G

40 adventures
16 target creature
15 non-target combat
8 non-combat

No apparent pattern among them (neither "losing the trail" near the end or clumps of being on- or off-target).
Does not appear to decrease the rate of combat vs. non-combat adventures (actually higher than average rate in this case).
Given that there are 9 possible combat encounters, the Gearhead should normally come up 1 out of every 9 times, but in my set, it was more like 1 out of every 2.
--[[User:BaruMonkey|BaruMonkey]] 11:25, 19 October 2007 (CDT)

* The Gearhead has a higher chance of finding then the other combat encounters (without On The Trail).

Ok. Tested in the oasis, after finding the pyramid (so, no "quest" non-adventures). In 40 adventures, I had 23 Oasis mosters, 9 different monsters, 8 mandatory "ultrahydrated" adventures. I let someone else doing the math!--[[User:Luos|Luos]] 03:24, 20 October 2007 (CDT)

In the Valley Beyond the Orc Chasm; 40 adventures, 14 target monsters, 26 others. None of the semi-rare ASCII art.--[[User:Homey1337|Homey1337]] 08:45, 15 November 2007 (CST)

== Rares ==

I tried using the Odor Extractor on Zim Merman in the war zone, and did not get him again.--[[User:Foggy|Foggy]] 07:59, 9 July 2007 (CDT)

Does it work on not one-time semi-rare encounters (like that super bean counter)? --[[User:Akatosh|Akatosh]] 09:21, 29 July 2007 (CDT)

I could use Transcendent Olfaction on Some bad ascii art. Didn't encounter it again the next 40 turns though.  --[[User:Bismuth|Bismuth]] 21:29, 19 February 2009 (UTC)

Has anyone tested the effects of using this effect on multiple monsters at once?--[[User:Pulaski|Pulaski]] 12:13, 5 August 2007 (CDT)
*Yes, "You're already on the trail of something right now. You wouldn't want to overload your nose, would you?" --[[User:Catch-22|Catch-22]] 01:52, 14 August 2007 (CDT)

== Decreasing Effectiveness ==

I did three runs of On the Trail in the wine cellar.  In the first two, I went after Sommoliers; on the third, I went after Possessed Wine Racks.
The first time, I got a success rate of 90%; the second, 87.5%; the third, 85%.
A small sample size, I'll admit, but worthy of consideration, I think.

Maybe the effectiveness of odor extractors decreases by 2.5% with each consecutive use in the same area.--[[User:Blzbob|Blzbob]] 15:44, 7 October 2007 (CDT)

I don't think we should test this only in the cellar, some tests should be done in areas with lots of monsters to see if it's still 90% of the monsters or if it just increases it by 90% of the original chance of that monster...--[[User:Lote|Lote]] 16:21, 10 October 2007 (CDT)

*Certainly not ''only'' in the Cellar, yes, for the very reason you cite.  But, in further news: the -2.5%-per thing isn't right.  I got Cellar success rates of 95%, 92.5%, 87.5%,and, then, 90% in one day.  But, so far, (though, only in the Cellar), The rates have not been less than 85% or more than 95%, so, as many as six wrong monsters or as few as two are possible.--[[User:Blzbob|Blzbob]] 17:54, 10 October 2007 (CDT)

The explanation for this is simple- The skill doesn't override the que's adventure-skewing properties away from monsters you've encountered a lot. Thus, the more you use it in a single area, the less effective it gets, as eventually the que overrides the power of the skill. This makes it so you can't just farm one area over and over with it.

==Theories==

With the current spading (and a bit of guess work), we can see the following effects: 
* There is no (real) effect on the combat frequency.
* The more different monsters in an area, the less chance to see the 'trailed' one.
* The more different monsters in an area, the bigger the procentual effect.

My theories (based on the written effects above),
* After the RNG has decided which monster you will encounter, there is a check if it is the trailed encounter. Do this till you tried about 2 times, if you didn't find the monster by then, just ignore the 'On the trail' and find a random monster.
* (This one sounds more difficult to implement) The chance to find a monster is more, but then in this way: let's say we have 4 monsters, all with a 25% chance to encounter it. Then 'On The Trail' will roughly multiply the chance to encounter the monster by about 6-8 (don't know, let's say 6). This makes the 'trailed' monster have a chance of 150%, and the others have a chance of 75% (added up). Scale this back to 100%, that makes 66,6% (2/3) chance to encounter the 'trailed' monster, and 11,1% (1/9) for the others.

Method 1:
{|
!number monsters :
!percentage trailed :
!percentage each untrailed
|-
|1
|100,0%
|0,0%
|-
|2
|87,5%
|12,5%
|-
|3
|70,4%
|14,8%
|-
|4
|57,8%
|14,1%
|-
|5
|48,8%
|12,8%
|-
|6
|42,1%
|11,6%
|-
|9
|29,8%
|8,8%
|}

Method 2 (with multiplication 7):
{|
!number monsters :
!percentage trailed :
!percentage each untrailed
|-
|1
|100,0%
|0,0%
|-
|2
|87,5%
|12,5%
|-
|3
|77,7%
|11,1%
|-
|4
|70,0%
|10,0%
|-
|5
|63,6%
| 9,1%
|-
|6
|58,3%
| 8,3%
|-
|9
|46,7%
| 6,7%
|}

Method 2 (with multiplication 6):
{|
!number monsters :
!percentage trailed :
!percentage each untrailed
|-
|1
|100,0%
|0,0%
|-
|2
|85,7%
|14,3%
|-
|3
|75,0%
|12,5%
|-
|4
|66,6%
|11,1%
|-
|5
|60,0%
|10,0%
|-
|6
|54,5%
| 9,1%
|-
|9
|42,9%
| 7,1%
|}

This shows that method 2 has a higher efficiency, at high numbers of different monsters.

This hopefully gives people some ideas, because they are only guesses. --[[User:Mercantilia|Mercantilia]] 05:59, 20 October 2007 (CDT)

'''Roulette Wheel?'''
That second idea sounds plausible to me, and actually quite easy to implement. Instead of thinking of things in percentages, think of it like a Roulette wheel. Suppose we have 3 monsters (A, B, and C), and we assign each monster a number based on their relative frequency. So if we wanted all three monsters to show up equally likely, give them all a value of 1 (any number will do as long as they're all equal). Then pick a number between 1 and (1+1+1)=3, to get your monster. Suppose you want monster A to show up twice as often as each other monster, or 25% of the time, then you would do your values A=2, B=1, and C=1; selecting your random number between 1 and (2+1+1)=4. The data above (albeit pretty sparse), would indicate that On the Trail doubles the value of the target monster. 

And implementing this would be very easy; I've done it in the past for stochastic software myself. I have no idea if this is at all correct, but if I were to implement this feature, that's what I'd do.

If my theory is correct, then if we take the usually evenly-frequent areas, ignoring non-combat, we should see the following distributions:

2 Monsters (eg Wine Racks): 66% targeted, 33% non-targeted

3 Monsters (eg Goatlet): 50% targeted, 25% for each non-targeted monster

4 Monsters (eg Haunted Bathroom): 40% targeted, 20% for each non-targeted monster

5 Monsters (eg Sleazy Back Alley): 33% targeted, 16% for non-targeted monster

I would spade more myself, but I'm saving up for a Tome (55 more days!!), then I'll be able to spade until the cows come home! Until then the above locations seem like good spading locations. Also, should we group our spading by number of monsters in the area?
--[[User:Andylicious|Andylicious]] 18:13, 26 December 2007 (CST)

There is some useful data at [http://www.hardcoreoxygenation.com/forums/viewtopic.php?t=3816 the HCO forums] on this.--[[User:Starwed|Starwed]] 01:51, 27 December 2007 (CST)

I think I like the basic roulette model quite a bit: everything in the above forum thread can fit with that type of model.  Just not in quite the way you describe.  If the chance of encountering a monster was 1/X before hand, it becomes (1+7)/(X+7) afterwards, and every other monster that was Y/X becomes Y/(X+7).

Here are the predicted rates when using it in a zone with N evenly distributed monsters:
{|
!N||%
|--
|2||89%
|--
|3||80%
|--
|4||73%
|--
|5||67%
|--
|6||62%
|--
|7||57%
|--
|8||53%
|--
|9||50%
|}
A lot of the data fits well with this model, and none of it has the statistical power to contradict it.  Tracking bloopers (in a zone w/ 8 monsters) was the largest outlier; I might try to gather some more data on them with a multi.  --[[User:Starwed|Starwed]] 02:30, 27 December 2007 (CST)

== Ultra-rares? ==

Would this work on ultra-rare monsters? Has anybody tried it? Do you get a message or anything if it does not work? --[[User:Tornan Steel|Tornan Steel]] 07:42, 19 January 2008 (CST)
:It's been stated on the radio that it doesn't increase your chances of encountering the ultra-rare again.  Which is stated [[odor extractor|here]].  --[[User:Flargen|Flargen]] 09:40, 19 January 2008 (CST)

== Data ==

===Spookyraven Wine Cellar===
Alrighty ladies and gentlemen, this will be a bit lengthy.
Five consecutive days using the Skill, only using on Sommeliers.
I am including all of the information so that you may see the order in which I got all of the adventures.<br>
Legend:<br>
O = adventure occurred with On The Trail (geared toward Sommeliers)<br>
S = Skeletal Sommelier<br>
W = wine rack<br>
<pre>
1  2  3  4  5  6  7  8  9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
S  SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO
S  SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO WO
S  SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO WO SO SO 
S  SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO SO WO 
S  SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO 
S  WO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO

234 adventures with olfaction, 23 Wine Racks, 211 sommeliers

S  SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO 
S  SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO WO SO SO SO 
S  SO SO SO SO WO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO WO 
S  SO SO SO SO SO SO WO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO WO SO SO WO SO SO SO SO WO SO SO WO SO SO SO SO 
S  SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO

195 adventures with olfaction, 23 wine racks, 172 sommeliers

S  SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO WO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO WO SO
S  SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO 
S  SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO 
S  SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO 
S  WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO WO SO SO WO SO WO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO

195 adventures with olfaction, 22 wine racks, 173 sommeliers

S  SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO 
S  SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO WO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO 
S  SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO 
S  SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO SO SO 
S  SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO WO SO SO SO

195 adventures with olfaction, 21 wine racks, 174 sommeliers

S  SO WO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO WO SO SO SO SO SO SO SO SO SO SO
S  SO WO SO SO SO SO SO SO SO WO SO SO SO SO WO WO SO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO 
S  SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO WO SO WO SO SO SO SO SO SO WO SO SO SO SO WO SO SO 
S  SO SO SO SO WO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO 
S  SO SO WO SO SO SO SO WO SO WO SO SO SO SO SO WO SO SO SO SO SO SO SO WO SO SO SO SO SO WO SO SO SO SO SO SO WO SO SO

195 adventures with olfaction, 28 wine racks, 167 sommeliers
</pre>
aggregate:<br>
1014 adventures with olfaction, 117 wine racks, 897 sommeliers<br>

In summary, it looks like with On The Trail in a place that has two monsters, you can expect to encounter the trailed one roughly 88.5% of the time.  I did note that the last day had a rather high wine rack count while trying to trail sommeliers as compared to the other days which held pretty steady.
--[[User:MindlessGames|MindlessGames]] 01:38, 27 January 2008 (CST)

And again, being bored, I decided I should beef up this area's data some more.
Did not pickpocket a single dusty bottle!
<pre>
1072 Adventures
1014 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage  95% Conf Error 
possessed wine rack                     32        55.17       112          11.05       1.97           
skeletal sommelier                      26        44.83       902          88.95       1.97           
</pre>
--[[User:MindlessGames|MindlessGames]] 00:22, 19 April 2008 (CDT)

===The F'c'le===
I always had On The Trail geared toward Clingy Pirates.
I missed casting trails a few times, so that's why there are 10 untrailed clingy pirates instead of 6
<pre>
227 Adventures
185 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
chatty pirate                           4         9.52        19           10.27     
cleanly pirate                          7         16.67       18           9.73      
clingy pirate                           10        23.81       101          54.59     
creamy pirate                           8         19.05       15           8.11      
crusty pirate                           7         16.67       20           10.81     
curmudgeonly pirate                     6         14.29       12           6.49      

Total Trails Cast: 6
how many times did the trailed monster occur in each adventure after casting?
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     0   3   3   2   5   3   2   1   4   3   2   0   4   5   2   2   2   2   2   1   

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     2   2   5   3   4   3   4   3   1   3   1   1   2   3   2   3   5   3   2   1   
</pre>
--[[User:MindlessGames|MindlessGames]] 14:32, 5 March 2008 (CST)

===Sonofa Beach===
What about Sonofa Beach?  Does it not help there?--[[User:Stone sheik|Stone sheik]] 13:51, 4 February 2008 (CST)
*Many people have thought that, but I have not seen any evidence that this effect increases combat frequency. Since that zone has a single-combat, I don't think it helps. --[[User:Bagatelle|Bagatelle]] 18:54, 4 February 2008 (CST)

In answer.. ran this with +5% combat adventures, arguably I should not have done that, but here you go.
<pre>
286 Adventures
234 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
A Latter-Day Litter Letter              6         11.54       9            3.85      
Zerg Rush                               3         5.77        18           7.69      
Beach Blanket Yahtzee                   4         7.69        24           10.26     
Hippies Don't Surf                      5         9.62        17           7.26      
Can't Beat the Evil Thing               1         1.92        4            1.71      
Mystical Crap                           4         7.69        11           4.70      
Dad-a-Chick                             3         5.77        21           8.97      
The Walking-Stick Rebellion             3         5.77        12           5.13      
lobsterfrogman                          6         11.54       25           10.68     
We Apologize To Our English Players For 3         5.77        15           6.41      
Anchors Weigh                           2         3.85        20           8.55      
One Man's Treasure                      2         3.85        16           6.84      
The Wake-Up Call of Kermithulhu         3         5.77        20           8.55      
Forget It                               5         9.62        15           6.41      
What a Maroon                           1         1.92        4            1.71      
Save the Texas Prairie Chicken          1         1.92        3            1.28      
</pre>
--[[User:MindlessGames|MindlessGames]] 20:04, 5 February 2008 (CST)

===The Castle in the Clouds in the Sky===
Here's some data that goes with another spading project I'm doing (which will have massive implications for the Advanced Farming page).
Trailing only Goth Giants.
<pre>
1020 Adventures
889 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Alphabet Giant                          19        14.50       83           9.34      
Furry Giant                             20        15.27       77           8.66      
Goth Giant                              28        21.37       482          54.22     
Possibility Giant                       21        16.03       78           8.77      
Procrastination Giant                   21        16.03       80           9.00      
Raver Giant                             22        16.79       89           10.01     


Total Trails Cast: 28
how many times did the trailed monster occur in each adventure after casting?
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     0   15  16  11  13  13  14  16  11  9   7   13  13  15  11  16  12  10  14  8   

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     12  8   14  12  14  14  11  15  10  10  11  9   13  15  11  12  15  11  14  14   
</pre>
--[[User:MindlessGames|MindlessGames]] 14:49, 5 March 2008 (CST)

===Copse of the Deep Fat Friars===
I've been spading Hellions in the post-quest Friar's gate for N=7 monsters. I had +5% combat, so the only non-combats were Leavesdropping every once in a while. I haven't done non-On The Trail spading yet, and I didn't keep track of monsters between sniffings. If we need my KolMafia logs, I can go to those. I would also like to point out that, when totaling my 40-adventure runs, the targeted Hellions had a standard deviation twice the size of the others, meaning that the total number of Hellions in a 40-adventure run varied much more than the other monsters varied. Might help in figuring out the mechanic. --[[User:Andylicious|Andylicious]] 22:47, 24 February 2008 (CST)


<pre>
1028 adventures with On the Trail
Encounter Name             On the Trail    Percentage
Demoninja                      86             8.4%
Fallen Archfiend               82             8.0%
G imp                          86             8.4%
Hellion                       514             50.0%
L imp                          82             8.0%
P imp                          98             9.5%
W imp                          80             7.8%

</pre>

This has probably already been spaded, but here's my control data for Friar's N=7. I'll have my multi do some other controls, maybe the kitchen. --[[User:Andylicious|Andylicious]] 09:06, 29 February 2008 (CST)
<pre>
565 adventures not on any trail
Encounter Name             On the Trail    Percentage
Demoninja                      75             13.4%
Fallen Archfiend               79             14.0%
G imp                          85             15.0%
Hellion                        92             16.3%
L imp                          77             13.6%
P imp                          75             13.3%
W imp                          82             14.5%
</pre>


===Hole in the Sky===
I've just observed 17 Astronomers out of 39 adventures. That's 43.6% in a 9 monsters zone. More data points would be useful here. --[[User:O 3 141592|O 3 141592]] 05:02, 25 February 2008 (CST)

Here is the data I have for Astronomers in the [[HitS]], I am NOT sure if they are evenly distributed without trailing, I will be following this up whenever I can get a multi to do 1000 untrailed adventures in HitS.
<pre>
1185 Adventures
1014 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Astronomer                              26        15.20       408          40.24     
Burrowing Bishop                        19        11.11       74           7.30      
Family Jewels                           15        8.77        60           5.92      
Hooded Warrior                          15        8.77        81           7.99      
Junk                                    17        9.94        65           6.41      
One-Eyed Willie                         18        10.53       60           5.92      
Pork Sword                              20        11.70       64           6.31      
Skinflute                               17        9.94        64           6.31      
Trouser Snake                           12        7.02        70           6.90      
Twig and Berries                        12        7.02        68           6.71     

Total Trails Cast: 26
how many times did the trailed monster occur in each adventure after casting?
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     0   8   11  11  10  10  6   11  9   13  14  9   10  10  11  9   9   10  15  11  

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     4   13  11  11  13  9   12  12  9   10  11  11  13  8   8   8   11  11  13  13  
</pre>
--[[User:MindlessGames|MindlessGames]] 15:49, 25 February 2008 (CST)

Here is some [[Hole in the Sky|HitS]] data ''without'' On the Trail, for frequency control spading:
<pre>
300 Adventures
0 Adventures with On The Trail
Encounter name                          No Trail  Percentage 
Astronomer	                        37        12.3%
Burrowing Bishop                        28        9.3%
Family Jewels                           31        10.3%
Hooded Warrior                          28        9.3%
Junk                                    32        10.7%
One-Eyed Willie                         34        11.3%
Pork Sword                              26        8.7%
Skinflute                               29        9.7%
Trouser Snake                           28        9.3%
Twig and Berries                        27        9.0%
TOTAL                                  300        100.0%
</pre>
Not (nearly) enough to be conclusive, but hopefully that will help get us there.
--[[User:Alomir|Alomir]] 15:30, 26 February 2008 (CST)

*A note: I recently came across a couple indirect questions about this data.  I cannot speak for Alomir or O3141592, but my data comes entirely after the update that said there are no longer two identical Astronomers.--[[User:MindlessGames|MindlessGames]] 17:29, 12 March 2008 (CDT)
: My data is from after the change too. --[[User:O 3 141592|O 3 141592]] 17:37, 12 March 2008 (CDT)

more control data..
<pre>
1000 Adventures
Encounter name                       No Trail      Percentage                             
The Axe Wound                        102           10.20
The Beaver                           98            9.80
The Box                              105           10.50
The Bush                             99            9.90
The Camel's Toe                      92            9.20
The Flange                           93            9.30
The Honey Pot                        95            9.50
The Little Man in the Canoe          96            9.60
The Muff                             103           10.30
The Astronomer                       117           11.70
</pre>

These are my best guesses for the mappings from Male->Female, based on item drop and ML:<br>
Trouser Snake -> Box<br>
Skinflute -> Camel's Toe<br>
Family Jewels -> Bush<br>
Burrowing Bishop -> Axe Wound<br>
Junk -> Flange<br>
One-eyed Willie -> Muff<br>
Pork Sword -> Beaver<br>
Twig and Berries -> Honey Pot<br>
Hooded Warrior -> Little Man in the Canoe<br>

Even more control data.
<pre>
3092 Adventures
0 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf
Astronomer                              383       12.39       1.18    
Burrowing Bishop                        304       9.83        1.07     
Family Jewels                           300       9.70        1.06     
Hooded Warrior                          315       10.19       1.09     
Junk                                    308       9.96        1.08     
One-Eyed Willie                         299       9.67        1.06     
Pork Sword                              303       9.80        1.07     
Skinflute                               310       10.03       1.08     
Trouser Snake                           286       9.25        1.04     
Twig and Berries                        284       9.18        1.04     
</pre>


Under these assumptions, combining Alomir's with mine gives...
<pre>
4392 Adventures
Encounter name                          No Trail  Percentage 
Astronomer	                        537       12.23
Burrowing Bishop                        434       9.88
Family Jewels                           430       9.79
Hooded Warrior                          439       10.00
Junk                                    433       9.86
One-Eyed Willie                         436       9.93
Pork Sword                              427       9.72
Skinflute                               431       9.81
Trouser Snake                           419       9.54
Twig and Berries                        406       9.24
</pre>
--[[User:MindlessGames|MindlessGames]] 13:47, 25 May 2008 (CDT)

:Feel free to take any of the numbers from my [http://afh.s4.bizhat.com/viewtopic.php?t=1042&mforum=afh project on areas with unequal encounter probabilities]. :)  --[[User:Narolf|Flolle]] 16:23, 23 March 2008 (CDT)
<pre>
1335 Adventures
1092 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf    On The Trail Percentage  95% Conf Error 
Astronomer                              29        11.93       4.16        446          40.84       2.97           
Burrowing Bishop                        29        11.93       4.16        69           6.32        1.47           
Family Jewels                           22        9.05        3.68        73           6.68        1.51           
Hooded Warrior                          23        9.47        3.76        84           7.69        1.61           
Junk                                    24        9.88        3.83        67           6.14        1.45           
One-Eyed Willie                         25        10.29       3.90        56           5.13        1.33           
Pork Sword                              22        9.05        3.68        76           6.96        1.54           
Skinflute                               21        8.64        3.61        66           6.04        1.44           
Trouser Snake                           20        8.23        3.53        83           7.60        1.60           
Twig and Berries                        28        11.52       4.10        72           6.59        1.50           
</pre>
--[[User:MindlessGames|MindlessGames]] 19:14, 31 July 2008 (CDT)

===Oasis===
Here's my data from the Oasis, including the data I already posted 2 days ago. I will probably add more in the next days. I was always trailing beatles. --[[User:O 3 141592|O 3 141592]] 12:56, 27 February 2008 (CST)
{| border=1
|-
! blur !! rolling stone !! oasis monster !! beatles !! #combats !! % trailed
|-
| 6 || 3 || 4 || 19 || 32 || 59,4%
|-
| 5 || 5 || 2 || 20 || 32 || 62,5%
|-
| 3 || 1 || 3 || 25 || 32 || 78,1%
|-
| 3 || 3 || 3 || 23 || 32 || 71,9%
|-
| 3 || 3 || 3 || 23 || 32 || 71,9%
|-
| 4 || 3 || 4 || 21 || 32 || 65,6%
|-
| 3 || 3 || 2 || 25 || 33 || 75,8%
|-
| 5 || 5 || 4 || 18 || 32 || 56,3%
|-
| 1 || 4 || 5 || 23 || 33 || 69,7%
|-
| colspan="6"| total
|-
|33 ||30 ||30 ||197 ||290 || 68,0%
|}


The conversation above about decreasing effectiveness got me thinking about the effect possibly "wearing off" toward the end of the 40 adventures. So what I did is went over MindlessGames' raw data of the Cellar and looked at the Wine Rack frequency for each adventure "slot" - that is, for each of his 25 runs, how many times did the Wine Rack show up in the first adventure, the second, and so on up to the 39th. I found that the smallest=1, largest=6, avg=3.01, stdev=1.528 for N=25 runs. No obvious trend, either. So I guess it's non-news that it doesn't really wear off, but just in case anyone else thought of trying that. --[[User:Andylicious|Andylicious]] 23:50, 28 February 2008 (CST)
*Excellent idea.  I'll be out (vacation) for a few days, but when I get back, I'll program that into my analyzer, have it figure out how many times the trailed monster occurred at adventure 1...39 after casting.--[[User:MindlessGames|MindlessGames]] 07:49, 29 February 2008 (CST)



===The Black Forest===
Well, even though it's already been spaded, I finished my 1000 adventures in the black forest. I trailed the Black Knight and got exactly 60%. Also, I reach a whole new level of geek by writing a program that analyzes my KolMafia logs for the adventure slot frequency, which I've also included here. I don't include my between-trail data here because I don't like counting that data as "non-trailed" as the sample size varies with the outcome. --[[User:Andylicious|Andylicious]] 14:26, 1 March 2008 (CST)
<pre>
1000 adventures On the Trail
Encounter Name            On the Trail     Percentage
Black Adder                    100            10.0%
Black Knight                   600            60.0%
Black Panther                   97             9.7%
Black Widow                    112            11.2%
Blackberry Bush                 91             9.1%

Total Trails Cast: 25
how many times did the trailed monster occur in each adventure after casting? (zero-based)
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     21  16  19  15  14  14  17  20  18  11  16  16  13  10  16  15  18  14  17  15    

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     15  11  16  17  16  13  10  14  16  13  14  15  13  14  17  14  16  14  15  12

</pre>

Here's some data for the Black Forest, an "N=5" case:
<pre>
347 Adventures
312 Adventures with On The Trail (Blackberry Bush)
Encounter name				No trail  Percentage  On the Trail Percentage
Blackberry Bush				8	  22.9%	      191	   61.2%
Black Adder				5	  14.3%	      29	   9.3%
Black Knight				5	  14.3%	      29	   9.3%
Black Panther				8	  22.9%	      32	   10.3%
Black Widow				9	  25.7%	      31	   9.9%
TOTAL					35	  100%	      312	   100.0%
</pre>
--[[User:Alomir|Alomir]] 15:30, 26 February 2008 (CST)


I was bored, and couldn't think of an awesome place to spade anything using On The Trail, so, I decided some Black Picnic Baskets were in order.
<pre>
1082 Adventures
975 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage  95% Conf Error 
Black Knight                            19        17.76       85           8.72        1.81           
black adder                             22        20.56       97           9.95        1.92           
black panther                           21        19.63       95           9.74        1.90           
black widow                             25        23.36       605          62.05       3.11           
blackberry bush                         20        18.69       93           9.54        1.88           
</pre>
added this to the combined table, under N=5
--[[User:MindlessGames|MindlessGames]] 10:31, 9 April 2008 (CDT)

===Misspelled Cemetary===
Misspelled Cemetary, Trailing corpulent zobmies:
{| border=1
!corp. zobmie !! gaunt ghuol !! gl. ghuol !! g. r. zmobie !! sen. lihc !! slick lihc !! spiny skel. !! toothy skel. !! #combat !! % trailed
|-
|14 || 2 || 5 || 5 || 2 || 4 || 3 || 3 || 38 || 36.8%
|-
|16 || 5 || 3 || 2 || 4 || 4 || 3 || 2 || 39 || 41%
|-
|21 || 3 || 2 || 2 || 3 || 4 || 2 || 2 || 39 || 53.9%
|-
|18 || 5 || 3 || 2 || 4 || 2 || 2 || 3 || 39 || 46.2%
|-
|16 || 3 || 2 || 3 || 1 || 3 || 7 || 4 || 39 || 41%
|-
|15 || 3 || 3 || 4 || 4 || 4 || 3 || 3 || 39 || 38.5%
|-
|17 || 4 || 4 || 2 || 2 || 5 || 2 || 3 || 39 || 43.6%
|-
|17 || 4 || 2 || 6 || 2 || 4 || 2 || 2 || 39 || 43.6%
|-
|22 || 0 || 3 || 4 || 2 || 3 || 3 || 2 || 39 || 56.4%
|-
| colspan=10 | total
|-
|156||29 ||27 ||30 ||24 ||33 ||27 ||24 ||350 || 44.6%
|}

===Knob Goblin Laboratory===
Lab, trailing Mad Scientists:
{| border=1
|Mad || 37 || 37 || 34 || 36 || 37 || 37 || 35 || 38
|-
|Very Mad || 2 || 2 || 4 || 3 || 2 || 2 || 4 || 1
|-
|#combat || 39 || 39 || 38 || 39 || 39 || 39 || 39 || 39
|-
|%trailed || 94.9%||94.9%||89.5%||92.3%||94.9%||94.9%||89.8% || 97.4%
|}

Weighted average: 93.6%.

Lab, trailing Very Mad Scientists:
{| border=1
|Mad ||9||10||6||7||5||8||7
|-
|Very Mad ||30||29||33||31||34||31||31
|-
|#combat ||39||39||39||38||39||39||
|-
|%trailed ||76.9%||74.4%||84.6%||81.6%||87.2%||79.5%||81.6%
|}

Weighted Average: 80.8%. --[[User:O 3 141592|O 3 141592]] 07:56, 3 March 2008 (CST)

here's data for trailing Very Mad Scientists. Updated from my March 19th data.
<pre>
1036 Adventures
935 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Knob Goblin Mad Scientist               77        76.24       183          19.57     
Knob Goblin Very Mad Scientist          24        23.76       752          80.43     
</pre>
I think that there's such a discrepancy in the non-trailing rates because every time the trail comes off, the queue is "supersaturated" with Very Mad Scientists (approximately 4/5 of the queue slots are Very Mad Scientists), and since they're supposed to have a lower rate anyway, the game waits a while to give you the next Very Mad Scientist.  Added this to the Current Combined table.
--[[User:MindlessGames|MindlessGames]] 00:35, 19 March 2008 (CDT), edited 4 April 2008

and here's some data for trailing Mad Scientists, same as before, not 1000 because O 3141592 already did some.
<pre>
856 Adventures
819 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Knob Goblin Mad Scientist               21        56.76       764          93.28     
Knob Goblin Very Mad Scientist          16        43.24       55           6.72      
</pre>
added this to the Combined Table.
--[[User:MindlessGames|MindlessGames]] 01:19, 23 March 2008 (CDT)

===Knob Kitchens===
Control data for Knob Goblin Kitchens. Definitely 66%/33% --[[User:Andylicious|Andylicious]] 20:59, 3 March 2008 (CST)
<pre>
966 Adventures
Knob Goblin Master Chef           323
Knob Goblin Chef                  643
</pre>

: Are you sure the Master Chefs are more common? It was the other way round according to the old data. --[[User:O 3 141592|O 3 141592]] 14:49, 4 March 2008 (CST)
: Oops, no it was the other way around. I fixed it. --[[User:Andylicious|Andylicious]] 14:38, 5 March 2008 (CST)

I have a [http://afh.s4.bizhat.com/viewtopic.php?t=1042&mforum=afh project] of my own on areas with unequal encounter probabilites and the first numbers are coming in:
<pre>
Knob Goblin Chef:             1277(63.85%) 
Knob Goblin Master Chef:       723(36.15%) 
total:                        2000(100%)
</pre>
As you can see, I'm pretty confident that the 67%/33% ratio you found was only an outlier. My results point to the actual appearance rates being 67%/33% which then get toned done by queue effects to 64%/36%.  --[[User:Narolf|Flolle]] 15:56, 12 March 2008 (CDT)

:actual rates of 67%/33% would lead to observed rates 61.7%/38.3%. 64%/36% observed is consistent with 70%/30% base.

Now the Kitchens are really starting to annoy me, nothing seems to be consistent. >.> 

Looking at the old (2006) data again I note that your ratio is very close to that from the day before the length-change was announced. Now solving my equations with the base rate unknown and Yiabs data as observed rate I get

 l=3: {chef -> 0.738297, masterchef -> 0.261703},
 l=5: {chef -> 0.700065, masterchef -> 0.299935}.

Now if this isn't a clear hint, than what is? Proposal: The queue-length was changed some time before the announcement and the base rate is 70%/30%. This even fits (well, roughly) the older data with length 3, where we get proposed base rates

 {chef -> 0.685068, masterchef -> 0.314932}.

Now all I have to do is find out, how the OtT-data fits in. --[[User:O 3 141592|O 3 141592]] 17:34, 12 March 2008 (CDT)

:Are you sure about that? My math (well, simulation by a program of mine) says that 70/30 appearance rates would get changed to roughly 67/33 and 67/33 would get changed to roughly 64/36, which is my observed rate.  --[[User:Narolf|Flolle]] 18:07, 12 March 2008 (CDT)
:: I am. Just recalculated some of the other numbers on this page to double-check I did not screw up my implementation, they come out as expected. I have to ramp up the Q-length to 7 or 8 to get your numbers. If you want to check my math, have a look at the "Advanced theory" section below. (It is intended to be understandable without a degree in maths, so feel free to ask questions, if I didn't achieve this goal.) --[[User:O 3 141592|O 3 141592]] 18:32, 12 March 2008 (CDT)
:::Well, I haven't looked at your math in detail yet (And I'm sure that the fact that I have yet to do my stochastics course will render me incapable of finding any possible errors anyway ;)). I try to work through it tomorrow since it's already in the middle of the night here. But I wanted to at least point this out: There are at least two different sources ([http://forums.jick-nerfed.us/viewtopic.php?p=30330#34930 1], [http://kol.coldfront.net/thekolwiki/index.php/Talk:Parseable_Area_Statistics#Several_zones_invalidated_by_NS13.3F 2]) which get the same results as I do. This is also the reason why I did in fact ask whether you were sure about your math; I remembered different results from other people. This doesn't necessaryly mean that you're wrong, as I said, I will look at your math or get someone who is better at math than I am to look it. --[[User:Narolf|Flolle]] 19:37, 12 March 2008 (CDT)


:::I checked O's calculations, and they all look fine to me.  However, I'm not convinced they're built upon a sound basis.  
:::O uses two sets of N equations:
:::*the first set relates the probability of seeing a given monster to the chance of it and other monsters being in the Q.  
:::*The second set relates the chance of a particular monster given in the Q to the chance of encountering it.
:::But obviously the true chance of encountering the monster on a given turn is not static, it depends on the state of the Q.  The chance of the monster being in the Q also depends on the past state of the Q.  O assumes that these sorts of effects flatten themselves out, and can be ignored when calculating the global frequencies of each monster, but I'm not very convinced that this is the case past the leading order.
:::Thus the very reason why I wrote a Q simulator myself, because I was concerned about these sorts of effects.  And my simulator agrees with Flolle above: when u={33%, 67%}, p={64.4%, 35.6%}.  That's with 1,000,000 trials, for an "experimental" uncertainty of 0.04%. --[[User:Starwed|Starwed]] 01:13, 13 March 2008 (CDT)

::::I agree, that my numbers are wrong. I don't see, ''why'' my method is flawed, though, as the idea of a static distribution ususally works fine for the analysis of [[Wikipedia:Markov_chain|Markov chains]]. I think I'll try to model the Q as a Markov chain explicitly. Might be a few days before I get around to this. --[[User:O 3 141592|O 3 141592]] 02:22, 14 March 2008 (CDT)
:::::Victory is mine!  I thought of a way to get exact predictions for the case of a two monster zone: For each monster, calculate the probability of it appearing exactly N times, then find the average string length.  That let's you calculate the theoretical frequency, and from a base rate of 33%/67% I got 35.612%, 64.388%, exactly in agreement with the Q simulator.
:::::The trick to this method is that, since there are exactly two monsters, the Q at the beginning of each string is always in a mixed state, which means you don't have to worry about the chance of a particular monster being in the Q.
:::::The exact result is a bit complicated, but basically the average Q length for each monster is:
::::::''<L<sub>i</sub>> = (1-r<sub>i</sub>)/r<sub>i</sub>&times;P<sub>4</sub>(r<sub>i</sub>) + r<sub>i</sub>^4&times;(1-s<sub>i</sub>)/s<sub>i</sub>^5&times;[P<sub>&infin;</sub>(s<sub>i</sub>)-P<sub>4</sub>(s<sub>i</sub>)]''
::::::''P<sub>N</sub>(a) &equiv; &sum;<sub>1 to N</sub> n*a^n'', P<sub>&infin;</sub>(a)=a/(1-a)^2
:::::and r,s are the chances of seeing a monster when the Q is mixed/only that monster. I can't quite see a way to generalize this to other types of zones, but I'll think about it a little bit more before I give up.  If anyone wants to see a more detailed explanation of how I got the above formula, let me know.  I've also got a maple worksheet which makes calculating stuff a bit easier.  --[[User:Starwed|Starwed]] 18:06, 15 March 2008 (CDT)
::::::I did not get your idea from your words. But I was able to extract it from the formulas. Also thinking about your method helped my to finally grok why mine doesn't work.
::::::I agree, that generalizing this will make it much more complex (as would fixing my approach). Basically in both cases one ends up with reinventing markov chains, which I wanted to try anyways. --[[User:O 3 141592|O 3 141592]] 15:04, 16 March 2008 (CDT)

Ok, looks like we've got some definitive results on the Kitchens. I was trailing the more-common Chefs this time. --[[User:Andylicious|Andylicious]] 00:43, 9 March 2008 (CST)
<pre>
1040 Adventures
Encounter Name                 On the Trail   Percentage
Knob Goblin Master Chef           81             7.8%
Knob Goblin Chef                  959           92.2%

Adventure slot frequency of the trailed monster, N=26
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     26  26  26  26  25  20  25  22  23  22  21  24  24  24  26  25  22  25  24  23    

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     24  26  24  24  26  21  24  25  24  24  22  22  24  24  25  26  25  23  25  22
</pre>

More data. I was trailing the less-common Master Chefs. --[[User:Andylicious|Andylicious]] 10:38, 12 March 2008 (CDT)
<pre>
1000 adventures
Encounter Name                 On the Trail   Percentage
Knob Goblin Master Chef           817           81.7%
Knob Goblin Chef                  183           18.3%

Adventure slot frequency of the trailed monster, N=25
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     19  21  18  23  23  24  21  18  22  15  21  22  24  22  17  20  17  20  23  20        

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     18  20  21  17  21  23  20  21  21  18  21  23  21  20  19  22  22  17  21  21
</pre>


*you state 1040 adventures, but only showing 724 adventure's worth of data here, and in the below table, you say you have 959 trailed Chefs.  Clerical error somewhere?--[[User:MindlessGames|MindlessGames]] 00:57, 9 March 2008 (CST)

: I gotta stop posting data late at night. Fixed it.--[[User:Andylicious|Andylicious]] 15:51, 9 March 2008 (CDT)

Doing some more data collection, because I have a hunch that if you have N=3, and an uneven encounter rate that is 33/66, then trailing on the 33% monster should bring back the same trailed percentage as N=3, but who knows, trying to test it out. The following trails Master Chefs.
<pre>
1167 Adventures
1083 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage  95% Conf Error 
Knob Goblin Chef                        56        66.67       193          17.82       2.33           
Knob Goblin Master Chef                 28        33.33       890          82.18       2.33           
</pre>
--[[User:MindlessGames|MindlessGames]] 00:24, 29 April 2008 (CDT)

===Icy Peak===
Trailing Yetis.
<pre>
1584 Adventures
1457 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Knott Yeti                              39        30.71       1167         80.10     
Snow Queen                              33        25.98       113          7.76      
upgraded ram                            55        43.31       177          12.15     

Total Trails Cast: 39
how many times did the trailed monster occur in each adventure after casting?
Adventure: 0   1   2   3   4   5   6   7   8   9   10  11  12  13  14  15  16  17  18  19  
Count:     0   32  34  30  33  25  28  30  32  30  27  31  29  30  33  29  27  31  32  32  

Adventure: 20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  
Count:     30  27  23  33  28  32  26  28  36  31  32  29  33  28  29  29  35  25  29  29  
</pre>
Fun stuff.. more than 1000 adventures because I went on vacation, didn't care to set to a new place.
--[[User:MindlessGames|MindlessGames]] 15:37, 4 March 2008 (CST)

: Note that the queen occurs only about half as often as the ram. Checking [[User:Yiab|Yiab]]'s data confirms that the base rate is about 2:1:2. --[[User:O 3 141592|O 3 141592]] 16:33, 4 March 2008 (CST)
: Yeah, I know that, kinda assumed everyone else knew that too..  Perhaps a bad assumption.--[[User:MindlessGames|MindlessGames]] 16:47, 4 March 2008 (CST)

===Whitey's Grove===
Here's my data for Whitey's Grove, I stopped at 700 figuring that we could combine this data with the current 300 (even though they're different locations, we believe them to be the same). I've combined my data in the below table, as well. I've also added rows for the chefs, even though they might be identical to the mad scientists. That's where I'm going next. --[[User:Andylicious|Andylicious]] 15:31, 5 March 2008 (CST)
: Chefs and Scientists aren't the same, see the control data. So they're a good place to spade. --[[User:O 3 141592|O 3 141592]] 15:52, 5 March 2008 (CST)
<pre>
774 combat adventures trailing Knight in White Satin
Encounter name                          On The Trail Percentage
white chocolate golem	                    81           10.5%
white lion	                            78           10.1%
Knight in White Satin	                   527           68.1%
whitesnake	                            88           11.4%
</pre>

===The Goatlet===
I've got this from before I started using mafia to keep track of all the adventures:<br>
D = dairy<br>
R = drunk<br>
S = sabre-toothed
<pre>
1  2  3  4  5  6  7  8  9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
D  DO DO DO DO DO SO DO DO DO DO DO SO DO RO DO DO DO DO DO DO DO SO DO DO DO DO DO DO RO DO DO DO DO DO DO DO DO SO RO
</pre>

39 with On The Trail, 32 dairy, 4 sabre-toothed, 3 drunk.<br>
I will be following this up in a day or two with 1000 or so On The Trail of dairy goats.--[[User:MindlessGames|MindlessGames]] 13:53, 8 March 2008 (CST)


<pre>
1134 Adventures
1051 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
dairy goat                              27        32.53       825          78.50     
drunk goat                              23        27.71       110          10.47     
sabre-toothed goat                      33        39.76       116          11.04     
</pre>
as promised, here's the followup data. Combining with the 39 trailed adventures just above, I get: 857/1090 = 78.62% dairy goats with On The Trail. Adding this in to the N=3 data in the Combined table.
--[[User:MindlessGames|MindlessGames]] 10:48, 10 March 2008 (CDT)

===The Inexplicable Door===
not quite 1000 adventures on the trail, it's very tedious making a character stick around in this area forever.  granted all the items are 100% drop without too much +item, but still, it's a horrible place to adventure :(
<pre>
1127 Adventures
975 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Blooper                                 25        16.45       425          43.59     
Bullet Bill                             21        13.82       79           8.10      
Buzzy Beetle                            22        14.47       78           8.00      
Keese                                   17        11.18       88           9.03      
Koopa Troopa                            18        11.84       72           7.38      
Octorok                                 16        10.53       80           8.21      
Tektite                                 15        9.87        81           8.31      
Zol                                     18        11.84       72           7.38      
</pre>
updated the table with this data.
--[[User:MindlessGames|MindlessGames]] 01:29, 16 March 2008 (CDT)

===Cobb's Menagerie Level 3===
what can I say, I wanted some booze bottles...
<pre>
1013 Adventures
936 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Booze Giant                             24        31.17       732          78.21     
Portly Abomination                      20        25.97       105          11.22     
Spectral Jellyfish                      33        42.86       99           10.58     
</pre>
by the by, I got 1738 bottles of various booze, ~300 of each :)
added to Combined table under N=3
--[[User:MindlessGames|MindlessGames]] 00:04, 27 March 2008 (CDT)

<pre>
4019 Adventures
3705 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf    On The Trail Percentage  95% Conf Error 
Spectral Jellyfish                      95        30.25       5.18        2870         77.46       1.37           
Portly Abomination                      109       34.71       5.37        426          11.5        1.05           
Booze Giant                             110       35.03       5.38        409          11.04       1.03           
</pre>
some more N=3 stuff.. yay spectral jelly.--[[User:MindlessGames|MindlessGames]] 21:56, 21 March 2009 (UTC)

===Degrassi Knoll===
<pre>
1203 Adventures
1028 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage
Gnollish Crossdresser                   18        10.29       54           5.25      
Gnollish Flyslayer                      23        13.14       59           5.74      
Gnollish Gearhead                       32        18.29       571          55.54     
Gnollish Piebaker                       17        9.71        55           5.35      
Gnollish Plungermaster                  16        9.14        56           5.45      
Gnollish Tirejuggler                    18        10.29       58           5.64      
Gnollish War Chef                       19        10.86       54           5.25      
Guard Bugbear                           16        9.14        70           6.81      
one-eyed Gnoll                          16        9.14        51           4.96      
</pre>
--[[User:MindlessGames|MindlessGames]] 11:39, 3 April 2008 (CDT)

===Ninja Snowmen Lair===
<pre>
1140 Adventures
1013 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage  95% Conf Error 
Ninja Snowman                           72        56.69       302          29.81       2.87           
Ninja Snowman Janitor                   29        22.83       88           8.69        1.77           
Ninja Snowman Weaponmaster              26        20.47       623          61.50       3.06           
</pre>
This is an interesting area, since it is in fact N=5, and not uneven, just the three different "Ninja Snowman" monsters are the same name, mafia can't seem to tell the difference.  Added this in under N=5 in the table.
--[[User:MindlessGames|MindlessGames]] 10:59, 14 April 2008 (CDT)

===The Upper Chamber===
<pre>
1121 Adventures
1014 Adventures with On The Trail
Encounter name                          No Trail  Percentage  On The Trail Percentage  95% Conf Error 
tomb asp                                43        40.19       116          11.44       2.00           
tomb rat                                26        24.30       787          77.61       2.62           
tomb servant                            38        35.51       111          10.95       1.96           
</pre>
some tomb rat trailings, for even more N=3
--[[User:MindlessGames|MindlessGames]] 00:31, 24 April 2008 (CDT)

<pre>
7649 Adventures
7098 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf    On The Trail Percentage  95% Conf Error 
tomb asp                                185       33.58       4.02        806          11.36       0.75           
tomb rat                                182       33.03       4.01        5482         77.23       1.00           
tomb servant                            184       33.39       4.02        810          11.41       0.75           
</pre>
Good Lord. I must have been seriously bored. 
On the plus side, i'm fairly confident that N=3 has a rate of 77%, with off rates of 11.5%
--[[User:MindlessGames|MindlessGames]] 00:34, 3 June 2008 (CDT)

<pre>
5652 Adventures
5187 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf    On The Trail Percentage  95% Conf Error 
tomb rat                                165       35.48       4.44        4040         77.89       1.15           
tomb asp                                154       33.12       4.37        578          11.14       0.87           
tomb servant                            146       31.4        4.3         569          10.97       0.87           
</pre>
Even more boredom.. sure there are areas which need tighter confidence intervals, buuuutt.. oh well.
--[[User:MindlessGames|MindlessGames]] 08:05, 18 November 2008 (UTC)

<pre>
7194 Adventures
6613 Adventures with On The Trail
Encounter name                          No Trail  Percentage  95% Conf    On The Trail Percentage  95% Conf Error 
tomb asp                                209       35.97       3.98        756          11.43       0.78           
tomb rat                                169       29.09       3.77        5104         77.18       1.03           
tomb servant                            203       34.94       3.96        753          11.39       0.78           
</pre>
more fiddling around in N=3 areas. --[[User:MindlessGames|MindlessGames]] 21:55, 21 March 2009 (UTC)

===Current Combined Data===
All the data on this page gives the following data:<br>
N=2, Spookyraven Cellar<br>
N=3, The Goatlet, Menagerie Level 3, The Upper Chamber<br>
N=4, Whitey's Grove, The Oasis<br>
N=5, Black Forest<br>
N=6, Castle in the Sky, The F'c'le<br>
N=7, Copse of the Deep Fat Friars<br>
N=8, Misspelled Cemetary, The Inexplicable Door<br>
{| cellpadding="3" cellspacing="0" border="1px" style="text-align:center" align="center"
|-
!N / monster !! #combats !! #trailed !! obs. rate !! 95% C.I. !! predicted rate !! collecting more data
|-
|2 || 2028 || 1799 || 0.887 || 0.014 || 0.87 || none needed atm
|-
|3 || 25643 || 19872 || 0.775 || 0.005 || 0.76 || none needed atm
|-
|4 || 1064 || 724 || 0.680 || 0.029 || 0.67 || none needed atm
|-
|5 || 3300 || 2019 || 0.611 || 0.017 || 0.60 || none needed atm
|-
|6 || 1074 || 583 || 0.543 || 0.030 || 0.54 || none needed atm
|-
|7 || 1028 || 514 || 0.500 || 0.031 || 0.50 || none needed atm
|-
|8 || 1325 || 581 || 0.438 || 0.027 || 0.46 || none needed atm
|-
|colspan="6"  | ''Nonequal chances''
|-
| Astronomer || 2106 || 854 || 0.405 || 0.021 || 0.41 || none needed atm
|-
| Mad Scientist || 1130 || 1055 || 0.934 || 0.015 || 0.88 v 0.95 v 0.92 || none needed atm
|-
| Very Mad Scientist || 1206 || 971 || 0.805 || 0.023 || 0.72 v 0.86 v 0.80 || none needed atm
|-
| Knob Goblin Chef || 1040 || 959 || 0.922 || 0.017 || 0.88 v 0.94 || none needed atm
|-
| Knob Goblin Master Chef || 2083 || 1707 || 0.819 || 0.017 || 0.76 v 0.86 || none needed atm  
|-
| Yeti || 1457 || 1167 || 0.800 || 0.021 || 0.80 || none needed atm
|-
| Gnollish Gearhead || 1028 || 571 || 0.555 || 0.031 || ? || none needed atm
|-
|colspan="6" | ''Control data'' (non-trailing)
|-
| Astronomer || 4392 || 537 || 0.122 || 0.010 || 0.13 ||
|-
| Lab || >8000 || colspan="2" | 71% vs. 29% || || 72% vs. 28% || none neded atm
|-
| Kitchen || 966 || colspan="2"| 67% vs. 33% || || 68% vs. 32% || none needed atm
|-
| Peak || 6577 || colspan="2" | Y/Q/R=38/23/39 || || 38/25/38 || none needed atm
|}
[http://chart.apis.google.com/chart?cht=s&chxt=x,y&chs=280x140&chtt=Rate%20vs.%20N&chd=s:MSYflrx,2vpmhfX&chxl=0:|0|1|2|3|4|5|6|7|8|9|10|1:|0|1 Image of rate vs. N]

Data for one of N=4,5, and 7 would be good, as 3 solid points can fit about any model.  :)  It would also be interesting to see how the regular scientists in the lab behave.  --[[User:Starwed|Starwed]] 02:07, 15 February 2008 (CST)

: Completely revamped to reflect current state of spading. - Tried my best to not make it too wide.--[[User:O 3 141592|O 3 141592]] 16:11, 4 March 2008 (CST)

* Added Andylicious' and my data. --[[User:O 3 141592|O 3 141592]] 05:02, 25 February 2008 (CST)
** And I deleted your data again, note that Astronomers have (or at least had) another chance to encounter then the other monsters in that area. I just removed your findings in the table, because we don't know how to work with that yet. --[[User:Mercantilia|Mercantilia]] 12:13, 25 February 2008 (CST)
*** According to a trivial update on 11 February they are equally likely now. Also Mindless Games' data suggests equal rates. (The higher observed rate is due to the fact that each non-trail sequence had to contain one astrononmer despite them being shorter than 9 adventures - the N=6 datasets show the same phenomenon. If Astronomers were more likely the difference should've been even greater.) --[[User:O 3 141592|O 3 141592]] 16:43, 25 February 2008 (CST)
**** Yesterday I found a [http://forums.kingdomofloathing.com:8080/vb/showpost.php?p=2721815&postcount=15 forum post by Hellion] stating that the astronomer is still 1.5 times as likely, only the mechanic has changed. Looks like I was wrong. Getting exact figures would however still be useful as it seems that the rates for zones with unequal encounter chances might have changed with NS13 (see my post on [[Talk:Parseable Area Statistics]] for details). --[[User:O 3 141592|O 3 141592]] 01:41, 29 February 2008 (CST)

* Any suggestions for good spots for 4, 5 and/or 7 monster spading?--[[User:Alomir|Alomir]] 13:45, 25 February 2008 (CST) 
:EDIT: how about -
:* 4: [[Whitey's Grove]] or [[Oasis]]
:* 5: [[Lair of the Ninja Snowmen]] or [[The Black Forest]]
:* 7: [[The Palindome]] or [[The Deep Fat Friars' Gate]]
:Anyone know if these areas have even occurrence rates among the monsters there?--[[User:Alomir|Alomir]] 14:12, 25 February 2008 (CST)

I think Andilicious' data from the Friars is enough for N=7 at the moment. Additional data from the [[8-Bit Realm]] (are there other N=8 locations?) and non-trailing [[HitS]]-data would be useful, however. And of course N=4/5. --[[User:O 3 141592|O 3 141592]] 16:43, 25 February 2008 (CST)

Currently, for monsters which appear w/ a rate of 1/N, the new rate seems very linear: approximately 1.05-.08*N.  Probably that's just a first-order approximation to the true mechanism.  Info from the astronomers, and the (regular) Mad Scientists, might shed light on what's going on.  But the base freq. of astronomers is needed to determine what's up there.  (The freq used to be 3/21, but it should be respaded in light of the changes to the zone.) --[[User:Starwed|Starwed]] 04:20, 26 February 2008 (CST)

I'll work on the Black Forest for N=5 for the next few days. Takes me about 5 or 6 days for 1000 adventures.--[[User:Andylicious|Andylicious]] 12:25, 26 February 2008 (CST)

I'm hitting the Black Forest too - sorry, spent the turns before seeing your post. First set of turns is posted above, along with some HitS control data. --[[User:Alomir|Alomir]] 15:30, 26 February 2008 (CST)

No biggie, Alomir. Little replication never hurt no one. :) I'm also using a multi to spade the N=7 Friar's off the trail - so far they're evenly split. --[[User:Andylicious|Andylicious]] 21:21, 26 February 2008 (CST)
:Most zones already have the freq. spaded: check out [[Parseable Area Statistics]].  It's just the HitS which might need rechecking, since they recently changed something about how it worked.  That said, the data above indicates that the HitS hasn't changed; assuming everything but the astronomer appears with equal probability, you get a rate of 9.7%, when the previous was 9.5%.  --[[User:Starwed|Starwed]] 01:48, 27 February 2008 (CST)

The ''most'' useful place right now to spade would probably be N=8, and in the kitchens.  (Where the monsters are distributed 40%/60%) --[[User:Starwed|Starwed]] 06:11, 28 February 2008 (CST)
: I agree and want to add Mad Scientists. I've started gathering data at the cemetary (N=8) today. I'm planning on doing 2 days of spading there and then switching to lab or kitchen. --[[User:O 3 141592|O 3 141592]] 11:17, 28 February 2008 (CST)
: One more point: The kitchen being (exactly) 60%/40% should be rechecked. I just found that post-NS13 the lab is no longer exactly 66%/33%. (Already mentioned this on [[Talk:Parseable Area Statistics]]) --[[User:O 3 141592|O 3 141592]] 16:29, 28 February 2008 (CST)

: I've got a multi doing the control on the Knob Goblin Kitchens - looks 66%/33% after about 500 adventures. I'll post the data in two days once I hit 1000. In the meantime, what should be done next? Should we be trailing master chefs and non-master chefs in the kitchens to see if/how they're different? I feel like we need a signup table so we don't double-spade. I'll be working on the Grove (N=4) next --[[User:Andylicious|Andylicious]] 15:02, 1 March 2008 (CST)

In case anyone's wondering: I stopped collecting data for the moment bacause
# I think it's better if a theory is checked by other people than those that came up with it and
# I want to farm some meat to afford a hatrack (and some older IotMs, though that is more of a long term project). --[[User:O 3 141592|O 3 141592]] 16:11, 4 March 2008 (CST)

Ok, so all the HCO forum data should be removed from the table above, for two reasons:
#It was collected in 40-turn bursts using odor extractors, which might produce a different bias than the 1000+ turn blocks being taken with Olfaction.
#I think the N=3 data was including either kitchen or lab data, whichever was previously pegged at 66/33 on the wiki.  
I don't have time this minute, but I will resort all the data somtime if no one gets to it first.  --[[User:Starwed|Starwed]] 17:05, 28 March 2008 (CDT)  
#
*I have changed the table per your request, feel free to check it over and see if I missed anything (or more importantly, if I made a mistake!), I did not change anything about the Control Data section.--[[User:MindlessGames|MindlessGames]] 18:28, 28 March 2008 (CDT)

== Advanced theory ==

I think I figured it out: On the Trail adds 15 copies of the trailed monster to the zone in question. The observed rate will however be lower due to the [[Adventure Queue]].

'''The numbers in this section are flawed''' due to a yet unidentified error. Lab and Kitchens are completely wrong, all (or at least most of) the other predictions appear to be within 1% of the numbers a Q simulator gives. --[[User:O 3 141592|O 3 141592]] 02:26, 14 March 2008 (CDT)

===Details/Formulas===

Throughout this section I will use the following notation:

 p<sub>i</sub>:   Probability of observing monster i (after adventure queue etc.).
 u<sub>i</sub>:   Probability that monster i is chosen (before adventure queue etc.).
 q<sub>i</sub>:   Probability that monster i is in the queue.
 r  :   Probability of a reroll, if the chosen monster is in the queue.
 l  :   Queue length.
 N  :   Number of monsters in the zone.
 X  :   Number of copies added by OTT.

For the following I will assume a "swung in" state, that is OTT is active for some adventures and the probabilities are no longer influenced by pre-OTT-queue-state. In this case we find the following equation:

 p<sub>i</sub> = u<sub>i</sub> &times; (1 - q<sub>i</sub>&times;r) + p<sub>i</sub> &times; &sum;<sub>j=1..N</sub> (u<sub>j</sub>&times;q<sub >j</sub>&times;r).

Explanation: There are three ways how monster i may be observed:
# It is chosen and not in the queue. Probability: u<sub>i</sub>&times;(1-q<sub>i</sub>).
# It is chosen, in the queue, but kept anyway. Probability: u<sub>i</sub>&times;q<sub>i</sub>&times;(1-r).
# Any monster in the queue is chosen and rejected. Probability: &sum;<sub>j=1..N</sub> (u<sub>j</sub>&times;q<sub>j</sub>&times;r). Now the situation is the same as before drawing. Thus the probability of choosing and keeping monster i after redrawing is p<sub>i</sub>.

The equation is obtained by adding the 3 cases and simplifying.

Now q<sub>i</sub> simply is 1 minus the chance of not choosing monster i l times in a row:

 q<sub>i</sub> = 1 - (1 - p<sub>i</sub>)<sup>l</sup>.

:This formula is wrong. It uses the (arithmetic) mean insted of the actual values which works fine as long as you add these values. But here they are multiplied and so using the mean will estimate the q<sub>i</sub> too high, which is consistent with observed errors. --[[User:O 3 141592|O 3 141592]] 15:14, 16 March 2008 (CDT)

This gives us a set of 2&times;N equations which can be used to determine the vales of p<sub>i</sub> and q<sub>i</sub>, assuming l,r and q<sub>i</sub> are known.

In the special case of u<sub>i</sub> = 1/N for every i (=N equally likely monsters) we find that p<sub>i</sub> = 1/n independent of r and l, ie. in this case the queue does not affect the ratios in the long run.

====How to determine r and l====

Have a look at the Wine Cellar results posted at the beginning of the data section: Analysing the length of runs of consecutive Sommeliers (and only taking into account runs that end with OTT active, i.e. are terminated by a WO) we find that runs of length 4 or less are very rare while length 5 is the most common. From there the frequency slowly goes down with increasing run length. This can easily be explained by a queue of length 5: After 5 consecutive Sommeliers the last Wine Rack is dropped from the queue and they immediately get more likely. Thus:

 l = 5.

This is the officially announced pre-NS13-queue-length adds to the plausibility.

Concerning r, we could also use the data above, determining the ratio of runs with length equal to k to runs with length > k (k>=5). However, as this only came to my mind during writing I have chosen a different way:

I made 2 assumptions:

# OTT uses a roulette wheel mechanic, i.e. adds X copies of the trailed monster. (Reason: easy to implement)
# l is a fraction of small integers. (Reason: Every mechanic in KoL I know about uses only integers as random numbers and there is no obvious reason here to deviate from this.)

Now for a zone with N equally likely monsters we get u_trailed = (1+X)/(N+X) and u_untrailed = 1/(N+X). I generated tables for 1/2<=l<1, l being a fraction of 2 integers <=10, 2<=N<=9 and 1<=X<=20. The best match was for l=3/4 and X=15:

{| border=1
|N:|| 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9
|-
|p_trailed: || 0.87 || 0.76 || 0.67 || 0.60 || 0.54 || 0.50 || 0.46 || 0.43
|-
|observed: || 0.89 || 0.77 || 0.68 || 0.60* || 0.54 || 0.50 || 0.38?
|}

(*) for N=5 I used Andylicious' 1000 Adventures in the Black Forest instead of the data currently in the table.

As you can see the prediction fits extremely well, except for N=8, where the observed data is based on a small sample (I will add more data tomorrow) and N=2,3,4, where the prediction is slightly low. However these mispredictions can be explained: At the beginning of the OTT-run the chance of having untrailed monsters in the queue is higher than during the run (~1 vs. ~0.5 for N=2). Thus the first few adventures of each run are less likely to contain untrailed monsters, resulting in a slightly higher rate of the trailed monster overall. For larger N this effect is weaker as the monsters have a higher probability of not being in the queue out of OTT.

This choice of r and X is plausible for other reasons too:

* r = 3/4 was also the value before NS13.
* X = 15 is divisible by 5, a natural choice for a human. Plus it is 1.5 times the largest N in KoL.

===Zones with unequal encounter rates===

The first question is: How are these unequal rates implemented, as this influences the effect of OTT. Considering the simple case of 2 monsters m1 and m2, m1 being k times as likely, I see 4 resp. 5 possible implementations:

# There are k internally distinguishable (i.e. if copy 1 is in the queue, this will not affect copies 2-k) copies of m1.
# There are k internally indistinguishable copies of m1 or m1 is chosen with probability k/(k+1). (Both versions will behave exactly the same in all circumstances.)
# If m2 is chosen it is rejected with probability 1/k before being added to the queue.
# If m2 is chosen it is rejected with probability 1/k after being added to the queue.
# Some combinbation of the above to get non-integral ratios.

Cases 1 and 4 will result in the observed ratio being exactly k:1. Looking at the data on the monster talk pages we find for the lab (other locations are similar) ratios of 67.2% (10-Feb-06) and 71.1% (14-Aug-07) for the Mad Scientists. While the first figure could be explained by k=2 and RNG the second figure (based on >8000 adventures) does not fit into this model.

They can however be explained by cases 2 and 3, when taking into account that on 10-Feb-06 the queue was still 3 adventures long. (It took me a while until I found this explanation for the changed ratio.) Using u_mad = 4/5, u_verymad = 1/5 and l=3, the above equations give p_mad = 68.8% and for l=5 we find p_mad = 71.9%. Both values are reasonably close to the observed rates.

Now cases 2 and 3 cannot be distinguished with this data, they can however be distinguished with OTT-data: In case 2 the 15 copies added will have the same probability as m2, in case 3 they will have the same probability as m1.

====Laboratory====
The formulas predict:

{| border=1
! !! Case 2, trailing Very Mads !! Case 2, trailing Mads !! Case 3, trailing Very Mads !! Case 3, trailing Mads
|-
| u_mad || 4/20 || 19/20 || 4/65 || 64/65
|-
| u_verymad || 16/20 || 1/20 || 61/65 || 1/65
|-
| p_mad || 28.1% || 88.0% || 13.8% || 95.1%
|-
| p_verymad || 71.9% || 12.0% || 86.2% || 4.9%
|}

Observed ratios: Trailing Mads: p_mad = 93%; Trailing Very Mads: p_mad = 19.3%.

I'd say there is a trend towards case 3 but more data is needed to give a definitive answer. (A mixed case of Mads being double probability plus Very Mads being rejected 50% of the time comes quite close to the observed data, predicting p_mad_trailed=92%, p_verymad_trailed=79.8%. Seems implausible to be actually implemented but should be kept in mind.)

====Harem====
Current data (which is only one one pair of encounter numbers on the monster talk pages from l=3 times) suggests that the same values as in the lab are used.

====Kitchens====
Data: 
* (17-May-06) p_chef = 60.7%, p_masterchef = 39.3%
* (5-Sep-06) p_chef = 64.2%, p_masterchef = 35.8%

This is interesting once again. The May-data easily fits with l=3, u_chef=2/3, u_masterchef=1/3. But the September data doesn't fit l=5, u<sub>i</sub> unchanged. Digging the archives yields: The queue length was changed from 3 to 5 on 6-Sep-06, that is, the day after the second set of data was taken. Looks like the base rate was changed somewhere in 2006. l=3, u_chef=3/4, u_masterchef=1/4 fits once again. Now l=5, u_chef=3/4, u_masterchef=1/4 yields the prediction p_chef=67.9%, p_masterchef=32.1% for todays kitchen without OTT.

With OTT we get the following table:

{| border=1
! !! Case 2, trailing Master Chefs !! Case 2, trailing Chefs !! Case 3, trailing Master Chefs !! Case 3, trailing Chefs
|-
| u_chef || 3/19 || 18/19 || 3/49 || 48/49
|-
| u_masterchef || 16/19 || 1/19 || 46/49 || 1/49
|-
| p_chef || 24.5% || 87.6% || 13.7% || 93.8%
|-
| p_masterchef || 75.5% || 12.4% || 86.3% || 6.2%
|}

Unless I overlooked something, there is no data yet.

====HitS====

Here it is reasonable to assume (and supported by Hellions forum post) that the ratio of the genitals is the base ratio with the astronomer showing up 1.5 times as often. This gives u_astronomer=3/21, u_genitals=2/21 leading to p_astronomer=12.9% and p_genitals=9.7%, which fits well with Alomir's data.

For trailing astronomers we get u_astronomer=33/51 and u_genitals=2/51, leading to p_astronomer=41.3% and p_genitals=6.5%. Again this fits with MindlessGames' data.

Trailing one of the genitals we get u_astronomer=3/51, u_untrailedg=2/51 and u_trailedg=32/51. This yields (after finding and working around a bug in Mathematica 6) p_astronomer=9.8%, p_untrailedg=6.4%, p_trailedg=40.0%.

====Airship====

I haven't looked into the data yet.

====Icy Peak====

Without OTT: u_yeti=u_ram=2/5, u_queen=1/5 → p_yeti=p_ram=0.375, p_queen=0.25.

Trailing Yetis: u_yeti=32/35, u_queen=1/35, u_ram=2/35 → p_yeti=0.80, p_queen=0.08, p_ram=0.13.

Trailing Queens: u_yeti=u_ram=2/35, u_queen=31/35 → p_yeti=p_ram=0.12, p_queen=0.75.

====Other areas====

Are there any?

===Other ideas===

Some ideas I had during developing above theory:

* Base probability is multiplied by 16 instead of adding 15 copies. -> Didn't fit data for unequal base rates.
* One copy which is 15 times as likely instead of 15 copies. -> Perfectly possible, cannot be distinguished from the above theory (like the 2 possibilities in case 2 of unequal base chances).
* (In case 3 of unequal base chances) 15 new copies are also rejected with probability 1/k. -> Didn't fit data.



So that's my theory. Feel free to comment, criticize, support or disprove with new data, etc. If it holds up I will probably add my imagination of how the actual code looks like, including interaction with champagne poppers etc., which I will try to spade next. --[[User:O 3 141592|O 3 141592]] 06:57, 3 March 2008 (CST)

Holy crap that's a huge post. I like this model a lot - very intuitive and seems to fit the data quite well. I've been working on Whitey's Grove N=4 - do we still need data for that? Otherwise I can still spade one of the unequal zones. --[[User:Andylicious|Andylicious]] 20:15, 3 March 2008 (CST)

: N=4 is based on only 324 adventures right now. This is not all that much but the data fits well with the other equal data. Thus unequal rates would be more useful now, I think. --[[User:O 3 141592|O 3 141592]] 15:04, 4 March 2008 (CST)

I agree, I like this idea a lot.  I am currently working on The Icy Peak trailing Yetis, I have had a.. minor.. setback, and I'm on vacation right now, I'll be posting my results here in a day or two.  I think that we should make a table with the following columns: username, Monster being Trailed, control percent, and trailed percent. Maybe even toss on Predicted percent?--[[User:MindlessGames|MindlessGames]] 22:01, 3 March 2008 (CST)

: I think we can add this data to the existing table. I'll revamp it after posting this. --[[User:O 3 141592|O 3 141592]] 15:04, 4 March 2008 (CST)

Re areas with unequal encounter rates: I believe that Degrassi Knoll is another one of those areas. To be more exact: The Gnollish Gearhead appears more often than the other combats in that area. I think numbers on the Knoll are needed first though since Yiab's spading dates back to the 3 item queue days.  --[[User:Narolf|Flolle]] 21:27, 7 March 2008 (CST)

== Random facts ==

* You can not get rid of the trailed monster using a [[Divine champagne popper]] (tried myself), [[Creepy Grin]] (stated on [[Talk:Creepy Grin]]) or [[Harold's bell]] (stated in the HCO forum thread mentioned in the Theories section). --[[User:O 3 141592|O 3 141592]] 12:58, 3 March 2008 (CST) edited --[[User:O 3 141592|O 3 141592]] 14:24, 4 March 2008 (CST)
**Eeenteresting. Anyone happen to know if this applies to ''all'' [[Adventure Queue#NS13 Queue Manipulation|queue-clearing items]]? Trinket/napkin tricks on the pirate boat aren't listed above. --[[User:Bagatelle|Bagatelle]] 17:37, 5 March 2008 (CST)
**This is a little misleading. On the trail does seem to trump scare away effects when determining which monster you will fight next, however you CAN escape combat vs a monster you have on the trail. If you then remove the "on the trail" effect after escaping combat you should expect the popper/bell/grin effect to work as per normal. I have only tried this a few times in the HitS vs astronomers and have not encountered an astronomer after poppering it while on the trail and removing the trail directly after combat. Spading needed to confirm it's not just rng, but seems logical and I have seen no spading to prove otherwise. --[[User:Darkness|Darkness]] 07:56, 15 June 2008 (CDT)
* Sniffing a Monster you got from a choice adventure will put you on the trail of that monster (tested on a Mech from [[Random Lack of an Encounter]]). I will check the jilted mistress too. --[[User:O 3 141592|O 3 141592]] 12:58, 3 March 2008 (CST)

:* Sniffing the jilted mistress will activate the effect but has no apparent effect at all. Neither the ratio of combats nor that of noncombats is changed. Also the jilted mistress does not appear as a regular combat. This will probably be the same for all monsters that only occur as a choice in a noncombat. --[[User:O 3 141592|O 3 141592]] 14:13, 3 March 2008 (CST)
::*Confirmed for the wolf knight. --[[User:O 3 141592|O 3 141592]] 06:19, 18 March 2008 (CDT)

* On the Trail does not work properly on the Island War Battlefield. It does work on some monsters though. (source: same HCO forum thread as above). --[[User:O 3 141592|O 3 141592]] 14:24, 4 March 2008 (CST)

* OtT works at the Hidden City (HCO again) --[[User:O 3 141592|O 3 141592]] 14:24, 4 March 2008 (CST)

* Monsters occuring in several zones will appear more frequently in all zones. (Tested on a tomb servant, sniffed in the upper chamber then encountered 8 out of 9 adventures in the middle chamber.) --[[User:O 3 141592|O 3 141592]] 06:19, 18 March 2008 (CDT)

== Current Analysis (April 19) ==

So, I used my simulator to generate predictions, using a model where N copies of a monster are added to a zone with M monsters, with initial encounter rates all equal.  I compared the simulated data to that gathered above.  I find that only N=15, N=16 are favored by the current data.  I'd give a slight edge to N=15, but I haven't done a proper statistical analysis to see which is more probable.  (Pretty much, N=15 agrees better for large M, N=16 a bit better for small M.)  The simulation ran trials of 100,000 data points, with a margin of error of ~0.2%.--[[User:Starwed|Starwed]] 08:29, 19 April 2008 (CDT)

*For an explanation of how the regular monster selection process works, see: http://alliancefromhell.com/forum/viewtopic.php?t=1042 --[[User:Hellion|Hellion]] 04:09, 26 February 2009 (UTC)

== Same Monster, Different Zone ==

Is a monster considered the same monster in multiple zones?  For instance, if I Olfact a [[Hellion]] in [[The Dark Neck of the Woods]], then go to [[The Deep Fat Friars' Gate]], will I get the increased encounter rate on [[Hellion]]s still? --[[User:DoctorWorm|DoctorWorm]] 22:34, 28 April 2009 (UTC)
* Whoops, didn't read above, apparently the answer is yes.--[[User:DoctorWorm|DoctorWorm]] 22:41, 28 April 2009 (UTC)

== discrepancy in main page table ==

In the data on the talk it lists icy peak snow queens as a 1/5th encounter rate and the other combats as 2/5 each. Yet in the table the values are different... anyone know which is correct? anyone want to double check the rest? [[User:Judge Omega|Judge Omega]] 18:19, 21 May 2010 (UTC)
*The page is correct.  Due to the way the queue works, it's not 1/5, 2/5, 2/5, even though that's the way the area is set up, the Queue takes over and the actual observed rates are a bit different.  It's the same thing for anywhere that has multiple copies of one monster and a different number of copies of another monster.  It's slightly different from what you might think, due to the Queue. --[[User:MindlessGames|RoyalTonberry]] 20:52, 21 May 2010 (UTC)
**See also [[Adventure Queue]].  The game is set up to make it less likely to see an encounter that has occurred recently, loosely speaking.  --[[User:Flargen|Flargen]] 23:41, 21 May 2010 (UTC)