Editing Money-Making/Calculations

The purpose of this page is to store calculations, scratch-work, and open questions related to the grinds described in [[Money-Making]] and [[Hinterland Scrip-Making]]. Ideally, EPAs in those guides should be explained here.

==University Laboratory Grinds==
{{GuideNeedsWork|With recent changes to the Lab, lab research is rather less predictable. For instance, having a Secret College is helpful, and being a Correspondent with a high Scholar of the Correspondence level can be quite helpful. Because cards are undiscardable, the laboratory is harder to control. Simulation analyses are requested for the below projects.}}

Requires access to the {{IL|University Laboratory}}

The following calculations currently weight University and Parabolan research equally. This is not accurate, as Parabolan research progresses more slowly. Users are expected to estimate their own research per action for each species of research. and calculate an expected action cost to achieve the target. Recall that research projects will attract an entry and exit action fee, which should be accounted for. 

===Forging {{IL|Infernal Sharpshooter's Rifle}}s===

Research required (start to finish): 1750 (in two stages: 100 and then 1650).

Echoes of value: 210 (plus any {{IL|Volume of Collated Research}}).

Echoes per research: 0.12.

Note: increases {{IL|Record of Successful Forgery}}.
===Studying {{IL|A Vial of Queenly Attar|Appearance=Queenly Attar}}===

Requires A Vial of Queenly Attar.

Research required (start to finish): 450 (UR) + 15 (PR). Parabolan research is 3.2% of the total.

Echoes of value: 62.5 (plus any {{IL|Volume of Collated Research}}).

Echoes of cost: 2 (non-Silverers) or 1 (Silverers).

Echoes per research: 0.130.
===Creating {{IL|Cartographer's Hoard}}s===

Requires Equipment for Scientific Experimentation 6.

Research required (start to finish): 2700.

Echoes of value: 312.5 (plus any {{IL|Volume of Collated Research}}).

Echoes per research: 0.116.
===Researching {{IL|Impossible Theorem}}s===

Requires Equipment for Scientific Experimentation 7.

Research required (start to finish): 13000 (UR) + 300 (PR). Parabolan research is 2.3% of the total.

Echoes of value: 1562.5 (plus any {{IL|Volume of Collated Research}}).

Echoes of cost: 2 (non-Silverers) or 1 (Silverers).

Echoes per research: 0.117. 

==Helicon House==
Calculations for various Helicon House grinds.

Any references to "free entry" mean any of the {{IL|A Pendant of Helicon Amber}}, {{IL|Oneiric Key}}, or {{IL|Location of an Underground Organ}}. All three of these methods allow entry into Helicon House without paying a cover charge, and additionally provide {{IL|Fitting in at Helicon House|2 x}} to start. The latter is often more important, as it saves actions.
===Helicon-Only Fate-Locked Casing Grind===
Run through Helicon House once, grinding {{IL|Casing...}} while inside, and grabbing {{IL|Crate of Incorruptible Biscuits}} on the way out. Then enter Helicon House a second time, immediately cashing in the {{IL|Casing...}} for Scrip. Requirements:
*{{FontFate}} {{IL|A Pendant of Helicon Amber}}
*A {{IL|Helicon House Companion}} that grants {{IL|Fitting in at Helicon House|Appearace=Fitting In}} on entry.

The {{IL|A Pendant of Helicon Amber}} saves an action on the first leg by entering at {{IL|Time Remaining at Helicon House}} 4 instead of 5. The second leg can be done in 2 actions by entering with {{IL|Fitting in at Helicon House|3 x}}, which requires 2 from any of the "free entry" methods plus 1 from the choice of {{IL|Helicon House Companion}}. While the Pendant can be used for the second leg, the {{IL|Oneiric Key}} is better because it provides {{IL|Romantic Notion|5 x}} and the different in {{IL|Time Remaining at Helicon House|Appearance = Time Remaining}} does not affect that leg.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Building Casing
|5
|1
|5
|N/A
|{{IL|Casing...|15 CP}}<br />
{{IL|Investigating...|15 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|5 x}}<br />
{{IL|Pot of Venison Marrow|4 x}}
|-
|Cashing in Casing
|2
|1
|2
|{{IL|Casing...|15 CP}}
|{{h}} 26<br />
{{IL|Moon-Pearl|25 x}}<br />
{{IL|Drop of Prisoner's Honey|10 x}}
|-
!Total
|
|
|7
|
|{{h}}55 (7.85 SPA)
{{e}}0.45 + {{e}}27.94 in Scrip (4.05 EPA)
|}

The payout can be increased by {{IL|Romantic Notion|5 x}} per cycle by entering with an {{IL|Oneiric Key}} the second time. While the {{IL|Investigating...}} does not have much value, the cycle could potentially build {{IL|Fascinating...}} at +5 CP per cycle based on the choice of {{IL|Helicon House Companion}} for the first leg.

If you do not have access to a Fitting In companion, then you must spend an extra action doing something in Helicon House that grants a point of Fitting In. Building Casing is one such action. Using this action means that the second leg takes 3 actions, but only uses up 10 net points of Casing.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Building Casing
|5
|2
|10
|N/A
|{{IL|Casing...|30 CP}}<br />
{{IL|Investigating...|30 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|10 x}}<br />
{{IL|Pot of Venison Marrow|8 x}}
|-
|Cashing in Casing
|3
|3
|9
|{{IL|Casing...|30 CP}}
|{{IL|Investigating...|15 CP}}<br />
{{h}} 78<br />
{{IL|Moon-Pearl|75 x}}<br />
{{IL|Drop of Prisoner's Honey|30 x}}
|-
!Total
|
|
|19
|
|{{h}}136 (7.16 SPA)
{{e}}1.35 + {{e}}69.08 in Scrip (3.71 EPA)
|}

===Helicon-Only, Fate-Locked, Spouse-Locked Casing Grind===
This grind generally resembles the one above, except that your choice of Companion for the first leg gives you additional Casing on entry. The amount of casing makes for very awkward numbers. Requirements:
*{{FontFate}} {{IL|A Pendant of Helicon Amber}}
*Your [[Spouse]] is the {{IL|Platonic Partner in Crime}}
*{{FontFate}} {{IL|Your Perpetually Festive Rubbery Friend}}, who is currently the only non-Spouse {{IL|Helicon House Companion}} who grants {{IL|Fitting in at Helicon House|Appearance=Fitting In}} on entry.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Building Casing
|5
|15
|75
|N/A
|{{IL|Casing...|285 CP}}<br />
{{IL|Investigating...|225 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|75 x}}<br />
{{IL|Pot of Venison Marrow|60 x}}
|-
|Cashing in Casing
|2
|19
|38
|{{IL|Casing...|285 CP}}
|{{h}} is 494<br />
{{IL|Moon-Pearl|475 x}}<br />
{{IL|Drop of Prisoner's Honey|190 x}}
|-
!Total
|
|
|113
|
|{{h}}929 (8.22 SPA)
{{e}}8.55 + {{e}}471.93 in Scrip (4.25 EPA)
|}

While this grind has the most exclusive requirements, it is the most profitable.

===Helicon-Only Fate-Free Casing Grind===

This works very similarly to the above grind, but you must spend an extra action in Helicon House grinding {{IL|Casing...}}. Because of this, the cycles don't line up neatly. The optimal exit while building {{IL|Casing...}} is now to acquire [[Forget the biscuits, take the Solacefruit|solacefruit]], as that yields {{h}} 29 (with a {{IL|Helicon House Companion}} that gives {{IL|Fitting in at Helicon House|Appearance=Fitting In}}; 7/2 = 3.5, which rounds to {{IL|Solacefruit| 4 x}}); this requires {{IL|Train Luxuries}} 4, of course. As cashing in {{IL|Casing...}} only requires 15 CP, this version of the grind is straightforward.

Requirements:
*Free entry into Helicon House
*A {{IL|Helicon House Companion}} that gives {{IL|Fitting in at Helicon House|Appearance=Fitting In}}

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout (Biscuits)
!Payout (Solacefruit)
|-
|Building Casing
|6
|1
|6
|N/A
|{{IL|Casing...|15 CP}}<br />
{{IL|Investigating...|20 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|4 x}}<br />
{{IL|Pot of Venison Marrow|5 x}}<br />
{{IL|Romantic Notion|5 x}}
|{{IL|Casing...|15 CP}}<br />
{{IL|Investigating...|20 CP}}<br />
{{IL|Hand-picked Peppercaps|25 x}}<br />
{{IL|Solacefruit|4 x}}<br />
{{IL|Romantic Notion|5 x}}
|-
|Cashing in Casing
|2
|1
|2
|{{IL|Casing...|15 CP}}
|{{h}} 26<br />
{{IL|Moon-Pearl|25 x}}<br />
{{IL|Drop of Prisoner's Honey|10 x}}<br />
{{IL|Romantic Notion|5 x}}
|{{h}} 26<br />
{{IL|Moon-Pearl|25 x}}<br />
{{IL|Drop of Prisoner's Honey|10 x}}<br />
{{IL|Romantic Notion|5 x}}
|-
!Total
|
|
|8
|
|{{h}}52 (6.5 SPA)<br />
{{e}}1.45 + {{e}}26.416 in Scrip ('''3.48 EPA''')
|{{h}}55 (6.875 SPA)<br />
{{e}}1.45 + {{e}}27.94 in Scrip ('''3.67 EPA''')
|}

The above assumes entering with the {{IL|Oneiric Key}}, which gives {{IL|Romantic Notion|5 x}}. The {{IL|Location of an Underground Organ}} gives {{IL|Nodule of Warm Amber}} instead, which is nominally worth the same but more difficult to spend.

(below updated to reflect 17 Jun 2021 changes to {{IL|Entrance Hall}} activities)

If you do not have access to a +Fitting In companion, then you must spend an extra action doing something in Helicon House that grants a point of Fitting In. Building Casing is one such action. Using this action means that the second leg takes 3 actions, and yields an extra 5 CP {{IL|Casing...}}. Thus, the building Casing and cashing-in cycles are in a 1:1 ratio.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout (Biscuits)
!Payout (Solacefruit)
|-
|Building Casing
|6
|1
|6
|N/A
|{{IL|Casing...|10 CP}}<br />
{{IL|Investigating...|20 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|4 x}}<br />
{{IL|Pot of Venison Marrow|5 x}}<br />
{{IL|Romantic Notion|5 x}}
|{{IL|Casing...|10 CP}}<br />
{{IL|Investigating...|20 CP}}<br />
{{IL|Hand-picked Peppercaps|6 x}}<br />
{{IL|Solacefruit|20 x}}<br />
{{IL|Romantic Notion|5 x}}
|-
|Cashing in Casing
|3
|1
|3
|{{IL|Casing...|15 CP}}<br />(includes 5 CP from this cycle)
|{{h}} 26<br />
{{IL|Moon-Pearl|25 x}}<br />
{{IL|Drop of Prisoner's Honey|10 x}}<br />
{{IL|Romantic Notion|5 x}}
|{{h}} 26<br />
{{IL|Moon-Pearl|25 x}}<br />
{{IL|Drop of Prisoner's Honey|10 x}}<br />
{{IL|Romantic Notion|5 x}}
|-
!Total
|
|
|9
|
|{{h}}51 (5.667 SPA)<br />
{{e}}1.45 + {{e}}25.908 in Scrip ('''3.040 EPA''')
|{{h}}52 (5.778 SPA)<br />
{{e}}1.45 + {{e}}26.416 in Scrip ('''3.096 EPA''')
|}

Additionally, if you've been gaining {{IL|Fascinating...}} upon entrance (default with no companion is +2 CP each time), then you can eventually make use of [[Attract a companion for the rest of the evening]], yielding {{e}} 70 in items at the cost of an extra 4 actions. Doing this after 105 cycles without a +Fitting In companion raises the overall payout to '''3.121 EPA''' (when using the [[Forget the biscuits, take the Solacefruit|solacefruit]] option).

===Helicon+London Fate-Free Casing Grind===

The overall reduction in {{IL|Casing...}} gain as compared to {{IL|Investigating...}} gain from the 17 Jun 2021 update now means that periodically returning to London for use in [[The Heights of Chicanery]] slightly boosts the EPA of the above grind (at the cost of somewhat increasing the complexity of the grind; on the other hand, this grants more frequent access to the main London opportunity deck). Note that another station beyond Ealing Gardens is needed in order to make this variant worthwhile (as travel back to London from Ealing Gardens does '''not''' yield a {{IL|Rumour of the Upper River}}). Here, 2 building-casing-cash-in cycles are used in between each roundtrip to London.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout (Biscuits)
!Payout (Solacefruit)
|-
|Building Casing
|6
|2
|12
|N/A
|{{IL|Casing...|20 CP}}<br />
{{IL|Investigating...|40 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|8 x}}<br />
{{IL|Pot of Venison Marrow|10 x}}<br />
{{IL|Romantic Notion|10 x}}
|{{IL|Casing...|20 CP}}<br />
{{IL|Investigating...|40 CP}}<br />
{{IL|Hand-picked Peppercaps|12 x}}<br />
{{IL|Solacefruit|40 x}}<br />
{{IL|Romantic Notion|10 x}}
|-
|Cashing in Casing
|3
|2
|6
|{{IL|Casing...|30 CP}}<br />(includes 10 CP from the 2 cycles)
|{{h}} 52<br />
{{IL|Moon-Pearl|50 x}}<br />
{{IL|Drop of Prisoner's Honey|20 x}}<br />
{{IL|Romantic Notion|10 x}}
|{{h}} 52<br />
{{IL|Moon-Pearl|50 x}}<br />
{{IL|Drop of Prisoner's Honey|20 x}}<br />
{{IL|Romantic Notion|10 x}}
|-
|Chicanery in the Flit
|4
|1
|4
|{{IL|Investigating...|36 CP}}<br />(excess CP removed)
|{{IL|Rumour of the Upper River|3 x}}<br />
{{IL|Cryptic Clue|260 x}} or {{IL|Rostygold|540 x}}
|{{IL|Rumour of the Upper River|3 x}}<br />
{{IL|Cryptic Clue|260 x}} or {{IL|Rostygold|540 x}}
|-
!Total
|
|
|22
|
|{{h}}102 (4.636 SPA)<br />
{{e}}15.8 + {{e}}51.816 in Scrip ('''3.073 EPA''')
|{{h}}104 (4.727 SPA)<br />
{{e}}15.8 + {{e}}52.832 in Scrip ('''3.120 EPA''')
|}

Using [[Attract a companion for the rest of the evening]] after 53 complete cycles bumps the payouts to '''3.122 EPA''' and '''3.170 EPA'''.

===Parabolan Casing grind (Obsolete)===
{{Wiki Note|This source of Casing was nerfed 13 Jan 2021. This contained is retained for historical archives. Updated HPA/EPA are included at the bottom}}.

Grind {{IL|Casing...}} in Parabola, and then spend in Helicon House. Requirements:
*Free entry, ideally {{IL|Oneiric Key}} (Bohemian 40 Renown reward). The {{IL|Location of an Underground Organ}} or {{IL|A Pendant of Helicon Amber}} reduce the Echo value of the pay-out, but do not impact the Scrip or number of actions.
*A {{IL|Helicon House Companion}} that grants {{IL|Fitting in at Helicon House|Appearace=Fitting In}} on entry.
*{{IL|Shadowy Gains}} 6.

Building {{IL|Casing...}} from [[Find the weakness in an opponent's defences]] takes 4 actions on average if you have ''either'' {{IL|Shadowy|285}} or {{IL|Glasswork|12}}. With only a single-stage hunt, the value of [[Apply your own knowledge]] is reduced. Choosing to [[sneak forward]] will usually take fewer actions, although it will also incur {{IL|Nightmares}}.

Cashing in via [[Lay claim to any left-behind items]] can be done immediately upon entry if you can enter [[Helicon House]] with {{IL|Fitting in at Helicon House|3 x}}, which is possible by combining 2 points from any "free entry" option with a {{IL|Helicon House Companion}} that grants a third point. While the {{IL|A Pendant of Helicon Amber}} will work for this, it's not the best option. The {{IL|Oneiric Key}} grants {{IL|Romantic Notion|5 x}} on entry, and the difference in {{IL|Time Remaining at Helicon House}} does not effect the grind.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Grind Casing in Parabola
|4
|3
|12
|N/A
|{{IL|Casing...|150 CP}}
|-
|Rob Dreamers in Helicon
|2
|10
|20
|{{IL|Casing...|150 CP}}
|{{h}}260<br />
{{IL|Romantic Notion|50 x}}<br />
{{IL|Moon-Pearl|250 x}}<br />
{{IL|Drop of Prisoner's Honey|100 x}}
|-
!Total
|
|
|32
|
|{{h}} 260 (8.125 SPA)
{{e}}9.5 + {{e}}132 of scrip (4.42 EPA)
|}

The {{IL|Moon-Pearl}} and {{IL|Drop of Prisoner's Honey}} outcomes are averages. The above calculations ignore travel cost. Every round of travel will cost 4 actions, costing {{IL|Drop of Prisoner's Honey|100 x}} but providing {{IL|Rumour of the Upper River|Appearance = Rumours of the Upper River|3 x}} ([[An Unattended Mirror]] may reduce the actions and Rumours by 1 each, and being a [[Silverer]] will halve the honey cost).

If you do not have access to a Fitting In companion, then you must spend an extra action doing something in Helicon House that grants a point of Fitting In. Building Casing is one such action. Using this action means that each run through Helicon House takes 3 actions, but only uses up 10 net points of Casing.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Grind Casing in Parabola
|4
|1
|4
|N/A
|{{IL|Casing...|50 CP}}
|-
|Rob Dreamers in Helicon
|3
|5
|15
|{{IL|Casing...|50 CP}}
|{{h}}130<br />
{{IL|Romantic Notion|25 x}}<br />
{{IL|Moon-Pearl|125 x}}<br />
{{IL|Drop of Prisoner's Honey|50 x}}
{{IL|Investigating...|25 CP}}
|-
!Total
|
|
|19
|
|{{h}} 130 (6.84 SPA)
{{e}}4.75 + {{e}}66 of scrip (3.72 EPA)
|}
As building Casing takes only a small number of actions and more time is spent cashing it out, an extra action here significantly impacts the efficiency of the grind.

===='''Post-Nerf'''====
{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Grind Casing in Parabola
|4
|15
|60
|N/A
|{{IL|Casing...|420 CP}}
|-
|Rob Dreamers in Helicon
|2
|28
|56
|{{IL|Casing...|420 CP}}
|{{h}}728<br />
{{IL|Romantic Notion|140 x}}<br />
{{IL|Moon-Pearl|700 x}}<br />
{{IL|Drop of Prisoner's Honey|280 x}}
|-
!Total
|
|
|116
|
|{{h}} 728 (6.28 SPA)
{{e}}26.60 + {{e}}370 of scrip (3.41 EPA)
|}

===With the Rubbery Cat===
The option to [[deploy your Morally and Physically Flexible Rubbery Cat]], earns more Casing per Action, but must be supplied with {{IL|Hand-picked Peppercaps}}. Peppercaps can be obtained by occasionally swiping Solacefruit instead of Biscuits, with payout worth only 1 scrip less (free entry plus the Casing options will earn {{IL|Fitting in at Helicon House|6 x|Appearance=Fitting In}}).

However, it seems that cost of using up the Peppercaps is not worth the additional Casing provided. The table below assumes the Pendant and a Fitting In companion, but earns lower SPA than the cat-free grind above with similar requirements. From an aesthetic view, the different legs of this grind fail to line up in spectacular fashion: Peppercaps are earned in batches of 25 and spent in batches of 3, while Casing is earned in batches of 17 and spent in batches of 15.

{|class="article-table"
!Stage in the Grind
!Actions per Cycle
!Cycles
!Total Actions
!Cost
!Payout
|-
|Build Casing while Napping Biscuits
|5
|66
|330
|{{IL|Hand-picked Peppercaps|198 x}}
|{{IL|Casing...|1122 CP}}<br />
{{IL|Investigating...|660 CP}}<br />
{{IL|Crate of Incorruptible Biscuits|330 x}}<br />
{{IL|Pot of Venison Marrow|264 x}}
|-
|Build Casing and Restock Peppercaps
|5
|9
|45
|{{IL|Hand-picked Peppercaps|27 x}}
|{{IL|Casing...|153 CP}}<br />
{{IL|Investigating...|90 CP}}<br />
{{IL|Hand-picked Peppercaps|225 x}}<br />
{{IL|Solacefruit|27 x}}
|-
|Rob Dreamers in Helicon
|2
|85
|170
|{{IL|Casing...|1275 CP}}
|{{h}}2210<br />
{{IL|Romantic Notion|425 x}}<br />
{{IL|Moon-Pearl|2125 x}}<br />
{{IL|Drop of Prisoner's Honey|850 x}}<br />
{{IL|Investigating...|660 CP}}
|-
!Total
|
|
|545
|
|{{h}} 4151 (7.62 SPA)
{{e}}80.75 + {{e}}2108 of scrip (4.02 EPA)
|}
[[Category:Guides]]