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*Access to {{IL|The Waswood}}
 
*Access to {{IL|The Waswood}}
 
*That's it! No skills!
 
*That's it! No skills!
−
'''Expected EPA: 3.7125'''
+
'''Expected EPA: 3+'''
 
<div class="mw-collapsible mw-collapsed mw-collapsible-content">
 
<div class="mw-collapsible mw-collapsed mw-collapsible-content">
 
Repeatedly [[Reach towards the shore 2|Reach towards the shore with Airs 50+]]. Note that Airs can be shuffled at no action cost by leaving and returning to the Waswood, so it is not necessary to take the less profitable option.
 
Repeatedly [[Reach towards the shore 2|Reach towards the shore with Airs 50+]]. Note that Airs can be shuffled at no action cost by leaving and returning to the Waswood, so it is not necessary to take the less profitable option.
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Specifically, this stated EPA depends on the probability of rare success getting the [[Bottle of Fourth City Airag: Year of the Tortoise|Airag]]. Then we can calculate the expectation, so let's do the math!
 
Specifically, this stated EPA depends on the probability of rare success getting the [[Bottle of Fourth City Airag: Year of the Tortoise|Airag]]. Then we can calculate the expectation, so let's do the math!
  
−
Firstly, we assume that the probability of the normal failure and alternative failure are equal (25% each, for an overall failure rate of 50%), and also thusly that the game's stated overall failure/success probability of 50% is in fact true. We will also assume no value for Expertise of the 2nd/4th city ([[User:Druut|the writer]] pulls the old "leaving that as an exercise to the reader" trick), but they do have some value in the lab. Now, since the chance of a success becoming a rare success is 3%, we know the true probability of a rare success is half of that, or 1.5%, which makes the probability of a normal success 50% - 1.5% or 48.5%.
+
Firstly, we assume that the probability of the normal failure and alternative failure are equal (25% each, for an overall failure rate of 50%), and also thusly that the game's stated overall failure/success probability of 50% is in fact true. We will also assume no value for Expertise of the 2nd/4th city ([[User:Druut|the writer]] pulls the old "leaving that as an exercise to the reader" trick), but they do have some value in the lab. Now, since we don't know the true rate of rare success, we assign it the variable <math>x</math>, representing the percent chance of rare success (overall—NOT the probability that a given success will be rare [though that should in this case just be <math>2x</math>]), which makes the probability of a normal success (0.5 - <math>x</math>).
  
 
Now, we consider the values of each outcome by their sell values:
 
Now, we consider the values of each outcome by their sell values:
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*normal failure: 0.45 {{E}}, with a probability of 0.25
 
*normal failure: 0.45 {{E}}, with a probability of 0.25
 
*alt failure: 0.95 {{E}}, with a probability of 0.25
 
*alt failure: 0.95 {{E}}, with a probability of 0.25
−
* success: 5 {{E}}, with a probability of 0.485
+
*success: 5 {{E}}, with a probability of (0.5 - <math>x</math>)
−
*rare success: 62.5{{E}}, with a probability of 0.015
+
*rare success: 62.5{{E}}, with a probability of <math>x</math>
  
−
This gives us an expectation <math>EPA_{reach2}= (0.25)(0.45 E) + (0.25)(0.95 E) + (0.485)(5E) + (0.015)(62.5E)</math>
+
This gives us an expectation <math>EPA_{reach2}= (0.25)(0.45 E) + (0.25)(0.95 E) + (0.5-x)(5E) + x(62.5E)</math>
  
−
This gives an estimated EPA of 3.7125{{E}}.
+
If only there was a way to visualize how our EPA changed with different values of <math>x</math> numbers... Oh right, graphing! From [https://www.wolframalpha.com/input?i=plot+%280.5%29%280.53%29+%2B+%28x*62.5%29+%2B+%28.50-x%29%285%29+for+x%3D%5B0..0.05%5D this plot] we can see the following results:
 +
 
 +
*Without any Airag at all, this generates an expected 2.765 EPA
 +
*This hits 3 EPA at ~0.4% rare success rate.
 +
* At 1% rare success, we get 3.34 EPA.  At 2%, 3.915 EPA.  3%, 4.49 EPA! (These higher probabilities are likely not the case, however—more data is needed.)
  
 
It's important to note that it does cost an action to enter as well as 100/50 drops of honey, so when calculating your final EPA, you'll need to multiply by a factor of <math display="inline">\frac{N}{N+1}</math> where <math>N</math> is your actions spent reaching, then subtract your personal honey cost. You also don't have access to any cards, which can be significant depending on your goals and playstyle.  
 
It's important to note that it does cost an action to enter as well as 100/50 drops of honey, so when calculating your final EPA, you'll need to multiply by a factor of <math display="inline">\frac{N}{N+1}</math> where <math>N</math> is your actions spent reaching, then subtract your personal honey cost. You also don't have access to any cards, which can be significant depending on your goals and playstyle.  
 +
 +
Ultimately, we really need a large sample size to determine the small mystery probability and until that data is collected, it's hard to say just how profitable this should be. It's important to remember that even with an expectation of some EPA, it is just that—an expectation: while one <i>can</i> expect to approach that number if you try enough times, it can take a very long (technically infinitely long) to reach it. This is ultimately still an RNG grind, and some will be luckier than others. So while this analysis was prompted by my annoyance at the vagueness of the stated "3+" expected EPA, I now believe that it's possibly in fact the best way to succinctly present the results. Go figure.
 +
 +
Still, this has the potential to be a very simple, very profitable grind especially for those like [[User:Druut|me]] who have very middling stats (low 100s), unlocked parabola quickly before anything else, and are basically flat broke.
 +
 +
'''Below is WIP testing, please feel free to add data, do not expect good formatting until we get a solid amount of data'''
 +
 +
Samples (please feel free to do some testing and add a line for any data you add):
 +
{{#vardefine:regular|0}}
 +
{{#vardefine:rare|0}}
 +
{| class="wikitable"
 +
|+
 +
!Username
 +
!Successes ({{IL|Carved Ball of Stygian Ivory}} + {{IL|Unprovenanced Artefact}})
 +
!Rare successes ({{IL|Bottle of Fourth City Airag: Year of the Tortoise}})
 +
|-
 +
|[[User:JmeJuniper]]
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 41 }}}} 41
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|[[User:Tirerim]]
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 45 }}}} 45
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 4 }}}} 4
 +
|-
 +
|Taila Catz
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 97 }}}} 97
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 4 }}}} 4
 +
|-
 +
|Honey
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 12 }}}} 12
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 0 }}}} 0
 +
|-
 +
|jaidenthebear
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 29 }}}} 29
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 0 }}}} 0
 +
|-
 +
|gloomie
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 31 }}}} 31
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|Vanilla Plots
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 126 }}}} 126
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 7 }}}} 7
 +
|-
 +
|unfortunate_weeval
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 2 }}}} 2
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 0 }}}} 0
 +
|-
 +
|contra_cyn_cretize
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 58 }}}} 58
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|Taylor Catz
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 17 }}}} 17
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 4 }}}} 4
 +
|-
 +
|Simon Catz
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 46 }}}} 46
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|Silas Sterling
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 11 }}}} 19
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 2 }}}} 1
 +
|-
 +
|Bernard Porter
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 72 }}}} 72
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|MuSlime
 +
|{{#vardefine:regular|{{#expr:{{#var:regular}}+ 13 }}}} 13
 +
|{{#vardefine:rare|{{#expr:{{#var:rare}}+ 1 }}}} 1
 +
|-
 +
|'''Totals:'''
 +
|{{#var:regular}}
 +
|{{#var:rare}}
 +
|-
 +
| colspan="3" |If you add a row, you can just copy an existing row and change the values (+ the variables), and the probability statistics will update automatically.
 +
|}
 +
 +
{{#vardefine:rareprob|{{#expr:({{#var:rare}}/({{#var:rare}}+{{#var:regular}}))*0.5}}}}
 +
Probability statatistics, wip: including failures, the probability of receiving Airag based on current data is {{#expr:{{#var:rareprob}}*100 round 2}}%.<br />
 +
This would make the expected EPA {{#expr:0.25*0.45 + 0.25*0.95 + (0.5-{{#var:rareprob}})*5.0 + {{#var:rareprob}}*62.5 round 2}}{{E}}.
 
</div>
 
</div>
 
{{clear}}
 
{{clear}}
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==Tied to the Rat Market==
 
==Tied to the Rat Market==
−
===Mr Chimes' Grand Clearing-Out Unveiled activities (Rat Market)===
+
=== Mr Chimes' Grand Clearing-Out Unveiled activities (Rat Market)===
 
Expected EPA (mid-game): Up to '''3.54''' at midgame levels.
 
Expected EPA (mid-game): Up to '''3.54''' at midgame levels.
 
*Source of {{IL|Captivating Ballad}}s, {{IL|Parabola-Linen Scrap}}s and {{IL|Crackling Device}}s.
 
*Source of {{IL|Captivating Ballad}}s, {{IL|Parabola-Linen Scrap}}s and {{IL|Crackling Device}}s.
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*Underclay can produce:
 
*Underclay can produce:
 
**With [[Send an Unfinished Man to Mahogany Hall]] - {{IL|Captivating Ballad|1 x}} for 23 actions, using [[Stage an introduction]] (requires {{IL|Shadowy}} 209 for 100%). Additional action to [[Sell a Captivating Ballad for 850 Rat-Shillings]], turning Ballad into 85 {{e}}. 24 actions for 85 {{e}} - '''3.54 EPA'''.
 
**With [[Send an Unfinished Man to Mahogany Hall]] - {{IL|Captivating Ballad|1 x}} for 23 actions, using [[Stage an introduction]] (requires {{IL|Shadowy}} 209 for 100%). Additional action to [[Sell a Captivating Ballad for 850 Rat-Shillings]], turning Ballad into 85 {{e}}. 24 actions for 85 {{e}} - '''3.54 EPA'''.
−
** With [[Send the Unfinished Man to teach Third City history]] - {{IL|Storm-Threnody|1 x}} and {{IL|Shard of Glim|200 x}} for 7 actions, combining [[Extract confessions from the Calcified Men]] (requires {{IL|Persuasive}} 209 to 100%) with [[Stage an introduction]] (requires {{IL|Shadowy}} 209 for 100%). Additional action to [[Sell a Storm-Threnody for 200 Rat-Shillings]], turning the Threnody into 20 {{e}}. 8 actions for 22 {{e}} - '''2.75 EPA'''.
+
**With [[Send the Unfinished Man to teach Third City history]] - {{IL|Storm-Threnody|1 x}} and {{IL|Shard of Glim|200 x}} for 7 actions, combining [[Extract confessions from the Calcified Men]] (requires {{IL|Persuasive}} 209 to 100%) with [[Stage an introduction]] (requires {{IL|Shadowy}} 209 for 100%). Additional action to [[Sell a Storm-Threnody for 200 Rat-Shillings]], turning the Threnody into 20 {{e}}. 8 actions for 22 {{e}} - '''2.75 EPA'''.
 
*Spider Symposium with [[Accept some of the finest linen]] can produce {{IL|Parabola-Linen Scrap|1 x}} for ~29 actions (using [[Pass the floor to a spider inadequately prepared for debate]] and [[Posit that language makes reality]], requires {{IL|Persuasive}} 225 for 76%). Additional action to [[Sell a Parabola-Linen Scrap for 850 Rat-Shillings]], turning Scrap into 85 {{e}}. ~30 actions for ~85 {{e}} - '''2.83 EPA'''.
 
*Spider Symposium with [[Accept some of the finest linen]] can produce {{IL|Parabola-Linen Scrap|1 x}} for ~29 actions (using [[Pass the floor to a spider inadequately prepared for debate]] and [[Posit that language makes reality]], requires {{IL|Persuasive}} 225 for 76%). Additional action to [[Sell a Parabola-Linen Scrap for 850 Rat-Shillings]], turning Scrap into 85 {{e}}. ~30 actions for ~85 {{e}} - '''2.83 EPA'''.
−
* L.B. Industries can produce:<!--Other rewards are too inefficient at shadowy 225 to reach 2.5 EPA and are as such not included-->
+
*L.B. Industries can produce:<!--Other rewards are too inefficient at shadowy 225 to reach 2.5 EPA and are as such not included-->
−
**With [[Ask for a Crackling Device as payment]] - {{IL|Crackling Device|1 x}}  for 28.29 actions (using [[Assist with assembly]], requires {{IL|Shadowy}} 225 to 75%). Additional action to [[Sell a Crackling Device for 850 Rat-Shillings]], turning Device into 85 {{e}}. ~30 actions for 85 {{e}} - '''2.83 EPA'''.
+
** With [[Ask for a Crackling Device as payment]] - {{IL|Crackling Device|1 x}}  for 28.29 actions (using [[Assist with assembly]], requires {{IL|Shadowy}} 225 to 75%). Additional action to [[Sell a Crackling Device for 850 Rat-Shillings]], turning Device into 85 {{e}}. ~30 actions for 85 {{e}} - '''2.83 EPA'''.
 
</div>
 
</div>
 
{{clear}}
 
{{clear}}
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----
 
----
  
−
===Using up Bone Market Exhaustion===
+
===Using up Bone Market Exhaustion ===
 
Using up Exhaustion is hard in the mid-game, but also profitable. Exhaustion in itself is around 200 {{e}} per week. If you have {{IL|A Custom-Engraved Skull}} from {{FontRose}}, you should use those most weeks, leading to a net gain of 160 {{e}} for 2 skulls. The exception to the rule is when the Phantasist is around - then you may be able to spend all your exhaustion through other means.
 
Using up Exhaustion is hard in the mid-game, but also profitable. Exhaustion in itself is around 200 {{e}} per week. If you have {{IL|A Custom-Engraved Skull}} from {{FontRose}}, you should use those most weeks, leading to a net gain of 160 {{e}} for 2 skulls. The exception to the rule is when the Phantasist is around - then you may be able to spend all your exhaustion through other means.
 
----
 
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