Editing Khaganian Intrigue (Guide)/Opportunity cycles

This is a list of interesting [https://en.wikipedia.org/wiki/Cycle_(graph_theory) cycles] in  {{IL|An Opportunity in the Khanate}}. <ref>The starting case of zero, which is functionally identical to 1, but can not be reached again once left will not be regarded here. </ref>

Here is a [https://gist.github.com/klenze/50fe0349379569914a8d58080d6e3cc0 gist] of the python networkx code used to do the following analysis/plot. 

[[File:Opportunity graph.png|thumb|Red edges yield local currency <br/>
Green either local or echoes <br/>
Other colours yield echoes only.  <br/>
Pink gives Hillmover, <br/>
Blue gives Faction Favours. <br/>
]]

Moving along a node is assumed to take 12 actions: one to start the intrigue, ten to grind, and one to finish it. It also takes one {{IL|Emetic Revelation}}, which cuts into profits a bit. (For simplicity, we will assume that the player character has a surplus of these they would otherwise sell for 12.5E, if they have to be grinded, I would first have to get the [https://github.com/klenze/emissary/ Emissary] running again.)

For brevity, cycles are given as a list of nodes/vertices, <math>(n_0, n_1, n_2, \ldots, n_N)</math>. This means: ''go from <math>n_0</math> to <math>n_1</math>, then from <math>n_1</math> to <math>n_2</math>, ..., and finally return from <math>n_N</math> to <math>n_0</math>''. 

Note that {{IL|Bottle of Fourth City Airag: Year of the Tortoise|1 x|Appearance=Bottle of Airag}}, {{IL|Salt Steppe Atlas|1 x}}, {{IL|Much-Needed Gap}}, and {{IL|Oneiric Pearl|1 x}} are considered better than {{IL|Assortment of Khaganian Coinage|125 x|Appearance=Khaganian Coins}}, as they can all be sold for that. 

Also, {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins}} (and  {{IL|Oneiric Pearl}}, {{IL|Much-Needed Gap}}) can not be traded for {{e}} Echoes efficiently without spending actions. The best route is probably [[Purchase a box of lightbulbs]] and [[Sell lightbulbs to Londoners]], but the action cost of these options lowers the efficiency from 4.16EPA to just 3.3EPA. On the other hand, this is one of the few reliable ways to grind {{IL|Emetic Revelation}}s which fuel the opportunities. 

Some options yield Favours for Hell, Society or Revolutionaries and only 60E worth of items. However, none of them are in good cycles. The shortest cycle for [[Warn the Eagle]] (Hell) is (1, 2, 4, 11), the shortest for [[Warn the Revolutionaries]] is (5, 7, 9, 6) and the shortest for [[Leak their identities to the Khagan]] (Society) is (1, 3, 9, 10). All of these are of length 4, so you will spend some 48 actions per favour gained. Furthermore, all of these cycles pay out a suboptimal mixture of {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins}} and Bazaar-sellable items. 

== (3, 5, 4): Echo Grind ==
[[Obtain the codebook, and sell it]] for 62.45E, <br/>
[[Distract the Navy's investigators]] for 62.5E,<br/>
[[Snap him out of his daze]] for one Oneiromantic Revelation (or also 62.5E)<br/>

A reasonable simple Echo grind. 

== (2, 8, 6): Echo Grind with a hint of Hillmovers ==
{{IL|Bottle of Fourth City Airag: Year of the Tortoise|1 x|Appearance=Bottle of Airag}}<br/>

{{IL|Vital Intelligence|1 x}}<br/>
{{IL|Hillmover|1 x}}<br/>
{{IL|Perfumed Gunpowder|5 x}}<br/>
{{IL|Correspondence Plaque|25 x}}<br/>
{{IL|Mourning Candle|5 x}} <br/>

{{IL|Searing Enigma|1 x}}

You miss out on 25E, but gain a Hillmover plus some Gunpowder. Given that a Hillmover otherwise takes six actions in Parabola (which you could spend to earn some 31E here), this looks like a winner if you need huge quantities of coins and the odd Hillmover for some reason. 

== (2, 4, 3, 9, 6): Longish Echo Grind ==
{{IL|Salt Steppe Atlas|1 x}}

{{IL|Bottle of Fourth City Airag: Year of the Tortoise|1 x|Appearance=Bottle of Airag}}

{{IL|Parabola-Linen Scrap|1 x}}

[[Distract the Navy's investigators]]:<br />
{{IL|Vital Intelligence|3 x}}<br />{{IL|Extraordinary Implication|5 x}}<br />{{IL|Vienna Opening|5 x}}

[[Leak this information to the Tortoise]]:<br />
{{IL|Vital Intelligence|1 x}}<br />{{IL|Hillmover|1 x}}<br />{{IL|Perfumed Gunpowder|5 x}}<br />{{IL|Correspondence Plaque|25 x}}<br />{{IL|Mourning Candle|5 x}}

If you want to diversify a lot, this might be the way to go. 

== (5, 7, 9, 6): Imperfect {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins}} Grind ==

This will yield one Airag and one Oneiric Pearl, which can be sold for {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins}}, plus {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins|125 x}}. You will also pass [[Warn the Revolutionaries]] once, earning you 60E of items not sellable in the Khanate.

Warning: following this path [[Advancing the Liberation of Night|advances the Liberation of Night]].

== (1, 2, 4, 3, 9, 10, 11): {{IL|Hinterland Scrip}} Grind==

This yields {{h}}757.7 for 85.9 actions (8.7 SPA), assuming use of [[The Rat Market (Area)|the Rat Market]]. The rewards consist of the following:

* Items that can be directly sold for {{h}}345 on the [[Upper River Exchange]]
** {{IL|Vital Intelligence|12 x}}
** {{IL|Vienna Opening|5 x}}
** {{IL|Moves in the Great Game|20 x}}
* Items that can be sold for {{IL|Rat-Shillings|3301 x}} at [[The Rat Market (Bazaar)]]
** {{IL|Parabola-Linen Scrap|1 x}} 
** {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins|125 x}}
** {{IL|Salt Steppe Atlas|1 x}}
** {{IL|Much-Needed Gap|1 x}}
* Rewards that cannot easily be converted into Scrip: {{IL|Extraordinary Implication|2 x}}, {{IL|Favours: Society|1 x}} and {{IL|Favours: Hell|1 x}}

The {{IL|Parabola-Linen Scrap}} can be sold at the Rat Market for Rat-Shillings during the right season. The {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins}}, {{IL|Salt Steppe Atlas}}, and {{IL|Much-Needed Gap}} can exchanged at the [[Khaganian Markets]] for a {{IL|Crackling Device}}, which can be exchanged at the Rat-Market during different seasons. {{IL|Rat-Shillings}} can then be used to purchase {{IL|Solacefruit}} from the {{IL|Extramurine Trading Company}}, which can be sold for Scrip on the [[Upper River Exchange]]. This chain of arbitrage ends up with an overall loss of about 20%.

== (5, 7, 9, 6): {{IL|Advancing the Liberation of Night:|Appearance=Advancing the Liberation of Night}} Grind==

If you need to grind {{IL|Advancing the Liberation of Night:|Appearance=Advancing the Liberation of Night}}, perhaps for RP or Paramount Presence reasons, this is a pretty good grind for it. It yields 16 CP/Cycle or 0.33 CP/Action.

5. [[Leave him in his state]]: {{IL|Oneiric Pearl|1 x}}

7. [[Proceed as planned; let the Bazaar have these books]]: {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins|125 x}}

9. [[Vouch for the Foppish Revolutionary]]: {{IL|Bottle of Fourth City Airag: Year of the Tortoise|Appearance=Bottle of Airag|1 x}}

6. [[Warn the Revolutionaries]]: {{IL|Vital Intelligence|2 x}}, {{IL|Blackmail Material|2 x}}, {{IL|An Identity Uncovered!|4 x}}, {{IL|Favours: Revolutionaries|1 x}}

This yields {{IL|Assortment of Khaganian Coinage|Appearance=Khaganian Coins|250 x}}, 122.5{{e}} and {{IL|Favours: Revolutionaries|1 x}} per cycle of 48 actions.

== Closing Remarks ==

There is no [https://en.wikipedia.org/wiki/Hamiltonian_path Hamiltonian cycle] for {{IL|An Opportunity in the Khanate}}. The longest cycles have length 10, (1, 3, 9, 6, 5, 4, 11, 8, 7, 10) is one of those.

As all of the nodes have even in-degrees and out-degrees (both are two for every node), and FBG thankfully made the graph strongly connected as well, the existence of an [https://en.wikipedia.org/wiki/Eulerian_path Euler circuit] is guaranteed. Visiting the vertices (1, 3, 5, 7, 10, 11, 8, 7, 9, 6, 2, 8, 6, 5, 4, 3, 9, 10, 1, 2, 4, 11) in that order is an example of such. It should take 264 actions to traverse, longer than writing the initial version of this article did.