genesis
Posts: 924
4/8/2017
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[ETA: SIGNIFICANT REVISIONS HERE]
So I've been seeing recurring comments lately that Thieves' Cache expedition is better than Deep Blue Heaven. I ran an analysis on it and that's not what I am getting but perhaps I am missing something.
First some assumptions. 1) I assume we are comparing EPA over a long (statistically relevant) run and am ignoring opportunity costs etc, 2) I am assuming 1 action to get all the C:R for Eyeless Skull conversion (as I suspect it will cost 1 favour eventually), 3) I assume Humbug! is the most profitable way of caching in Criminal Favours, 4) Approximately 10% Eyeless Skull drop, 40% Souls drop (I know it is generally viewed that the drop rate is lower but these are the rates that I get from my data). It may be that it is precisely due to these assumptions that I reach a different conclusions and if that's the case then I am happy with that.
The two expeditions have different costs and different rewards so one would first need to establish the correct basis of comparison. Thieve's Caches costs half the supplies of DBH but also requires criminal favour. To my mind the correct basis of comparison is as follows:
1) 2 Thieves' Caches; versus
2) 1 Deep Blue Heaven + 2 Humbugs!
These two options both cost 20 Supplies and 2 Criminal favours, thus establishing parity to compare the value of rewards. Now you might say that Thieve's Cache starts with 1 progress whereas DBH has a rare success starting at 3. Well, I analysed all the ways of getting through the expedition (also accounting for A Sign?) and my figures are that the expected run for the Thieves' Cache requires 8.4 supplies (over 3 actions) and the expected run for DBH requires 16.74 supplies (over 6.46 actions). Thus we are comparing 16.8 supplies (for two Caches) and 16.74 supplies. These are sufficiently close that I think the parity of 2 Caches to 1 DBH remains.
Next I looked at the rewards from the unpredictable treasures, ignoring the warm amber (but not ignoring the venomous rubies). My figures give the following expected values:
- Thieves' Cache (UUT 1-80) - 16.19 echoes for 2 action
- DBH (excluding A tightly wrapped package; UUT 1-90, 100-160) (94.38%) - 54.09 echoes for 2 action
- DBH (A tightly wrapped package; UUT 91-99) (5.62%)- 65 echoes for 4 actions
(One action to complete the expedition and one action to play the unpredictable treasure; 2 actions to get F:TC and cash it in)
Taking account of the additional action needed to start the expedition, an action to play each Humbug! and 2 actions to cash in the Skull (one for Revolutionary "Favour" and one for Trade in), I get the following breakdown of options:
2 x Thieve's Cache
Glim 60%: 44.38 echoes for 16.8 supplies and 12 actions
Souls 40%: 56.38 echoes for 16.8 supplies and 12 actions
1 x DBH, 2 x Humbug!
Tightly wrapped package 5.06%: 73.8 echoes for 16.74 supplies and 13.46 actions
Other unpredictable treasures 84.94%: 62.09 echoes for 16.74 supplies and 11.46 actions
Eyeless Skull 10%: 74.8 echoes for 16.74 supplies and 12.46 actions
Assuming that the supply costs are sufficiently equal, this lets us compare the two expeditions in relative EPA terms:
Thieves' Cache: 4.10
DBH: 5.51
ETA: This is a relative comparison that shows that (with the assumptions above) DBH is more efficient. It does not say that your profit is at 4.61 since it doesn't include the cost of supplies
ETA2: Corrected DBH ETA from 4.61 to 5.51
edited by genesis on 4/9/2017
edited by genesis on 4/15/2017
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Keeping track of incomplete content and loose ends in Fallen London
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Optimatum
Posts: 3666
4/9/2017
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genesis wrote:
Humbug! has EPA of 4.4. That's vastly better than Beating the minister. Dov is right that one would have to account for the cases where you fail to draw Humbug! (which I partially have started doing in my last reply) but on pure EPA there is no doubt that Humbug is better
Humbug actually has an EPA of 2.2. The total profit is 4.4 E, yes, but it's spread across two actions - one for getting the Criminal Favours and one for spending it.
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rahv7
Posts: 294
4/10/2017
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Just wanted to say thank you for the detailed analysis.
Personally I'm a huge fan of DBH. One of its advantages not mentioned here is that you get resources that are otherwise difficult to obtain (Airag, Night Whispers, Enigmas, Skulls). Those are in my opinion worth more than the price tag suggests simply because there are no straightforward grinds.
I'm doing a lot of DBH runs and in my experience Skulls are rarer than your numbers suggest. But I'm not really keeping notes and maybe I'm just unlucky (or am I actually being lucky if I don't get skulls?  ). But even if you're are slightly off, I doubt the differences are large enough to make DBH less profitable than TC.
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Kaigen
Posts: 530
4/10/2017
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I agree with the other posters who are saying that you are likely underestimating the value of the Thieves' Cache Unpredictable Treasure. I'll be interested in seeing your numbers on that, but just with a quick look on the wiki, I see:
[spoiler]23.75% chance of An Instrument? for 14.5 echoes
22.5% chance of A Trophy? for 22.5 echoes
2.5% chance of An Amulet for 2 echoes
25% chance of A Wooden Mask? for 30.55 echoes (plus Warm Amber)
25% chance of The Seal of the Hooded Hawk for 40 echoes
1.25% chance of A fragile flake of vellum for 62.5 echoes[/spoiler]
When you factor in 60/40 glim/souls and the clues from the start, those numbers give me ~35.23, which is in the same neighborhood as Skinnyman's. How do your calculations differ such that you're getting a value that's less than half that?
Rahv7 does raise a good point in that if you are trying to achieve other goals that pure echoes (Master's Blood, Noman Tattoo, etc.) then Deep Blue Heaven has its benefits. Personally, one of the fringe benefits of Thieves' Caches for me is that Warm Amber a quarter of the time, which helps me get Rubbery Favours without having to worry about Scandal cures.
edited by Kaigen on 4/10/2017
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Optimatum
Posts: 3666
4/10/2017
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While the Warm Amber can't be sold directly, I find it is worth a decent amount, thanks to all the actions saved by getting Rubbery Favours without scandal.
edited by Optimatum on 4/10/2017
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Optimatum, a ruthless and merciful gentleman. No plant battles, Affluent Photographer requests, or healing offers; all other social actions welcome.
Want a sip of Cider? Just say hi!
PM me for information enigmatic or Fated. Though the forum please, not FL itself.
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genesis
Posts: 924
4/15/2017
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Ok, so this was more complex than I anticipated. Apologies for the delay. My original plan/hope was to provide a *comparison* between the two expeditions without committing myself to an explicit EPA computation (which depends on lots of variable inputs). But as the above discussion has shown that's trickier than I had assumed. In the end I had to commit myself to explicit EPA computation in order to give a meaningful comparison.
In trying to address the concerns raised above, I've come up with the following spreadsheet.
Assuming there are no mistakes, the idea is that you can enter your own assumptions about the chances of rare successes, the action costs of criminal favours and supplies and the echo value of criminal favour trade in. Then the spread sheet calculates the EPA for both expeditions and (subject to a caveat below) the Spirifer approach to Thieves' Cache.
Caveats:
1. The spreadsheet wouldn't be able to calculate accurately scenarios where you cash in criminal favours in bulk. You can still use it if you want to have approximation of course but the maths behind it assumes that you cash in one favour at a time.
2. The Spirifer strategy is an approximation. The accurate calculation would have been unfeasibly complicated, I think. Broadly it calculates the EPA of the non-Soul component of the strategy and "souls per action". Then it computes how many actions it would take to get to 1000 souls using that rate and approximates the total echo rate from there.
From quick playing around with figures it still looks to me that DBH is more efficient than the Cache, although the difference is quite a bit less stark than I had imagined. Assuming the trade-in with Humbugs!, DBH is also more efficient for Spirifers although fore most other trade-ins Spirifers are better off doing Caches.
This has already gotten a bit long but if anyone wants to discuss the nitty gritty of the spreadsheet, I'd be happy to.
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Optimatum
Posts: 3666
4/9/2017
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Kaijyuu wrote:
Humbug has the additional cost of not earning another favor. That's opportunity cost, which is hard to calculate, but considering the small difference between Humbug and Catch a Glimpse of the Notorious Smuggler, it's quite certainly better to spend singular favors on the latter (barring certain combinations of card draws where you need to drop a favor quick but don't have Implausible Penance available).
For Spirifers, it's actually better to spend favours on One Stone in a Thousand instead. It takes 6.25 favours for the necessary 1000 Souls for the efficient trade-in option, making 13.5 actions. With 30.30 echoes profit, it's 2.24 EPA compared to Try to Glimpse a Notorious Smuggler's 2.14 EPA. As the Spirifer trade-in also gives 30 CP of C: Hell, two more actions to cash it in for another 4.80 echoes in the FQ brings us up to 15.5 actions and 35.10 echoes, for a total of 2.26 EPA.
genesis wrote:
A very fair point! I should have qualified it as "conditional EPA". In the sense that the point of the exercise is to compare the efficacy of the two expeditions *once* you have the necessary supplies and favours. In other words, controlling for the input, to see how the output differs.
That doesn't make any sense. The input for all situations is actions, and we control for the input by calculating the profits relative to actions. Ignoring some of the actions entirely because of where they fall along the grinding process doesn't make those actions unnecessary, so it can throw off the math entirely. For example, using your math on the example earlier in my post:
- Spirifers can spend 6.25 favours (in as many actions) on An Implausible Penance for 1000 Souls. In one action those 1000 Souls become 30.30 echoes and 30 CP C: Hell. That 30 CP becomes 4.80 echoes in two actions. Overall that's 35.10 echoes in 9.25 actions, for 3.79 EPA.
- Non-Spirifers would spend 1 favour on An Implausible Penance for 4.28 echoes and a pittance of C: Constables. That is 4.28 EPA.
Using this math the Spirifage method has a lower EPA than the other method, even though my earlier math shows the opposite.
edited by Optimatum on 4/9/2017
--
Optimatum, a ruthless and merciful gentleman. No plant battles, Affluent Photographer requests, or healing offers; all other social actions welcome.
Want a sip of Cider? Just say hi!
PM me for information enigmatic or Fated. Though the forum please, not FL itself.
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