# The Fidgeting Writer - doing the maths (SPOILERS)

SPOILERS, do not read if you haven’t finished the content!

The Case of the Fidgeting Writer is a brilliant bit of content from Failbetter, just the sort of story I’m looking for in Echo Bazaar - a Lovecraftian peek behind the curtains at the horrors of the fallen cities. Absolutely wonderful stuff.

And not to be cynical about it or anything, but it also appears to be pretty lucrative, and that Overgoat ain’t getting any cheaper. I’m wondering if it could be a better deal than the current gold standard (the Velocipede Squad, rendering E1.23ish per action).

The difficulty is this. Each step you can trade your progress in for a guaranteed reward or take a chance on progressing further. The option to progress further carries a small(ish) item cost, win or lose. This makes the maths of the economics here pretty complicated (at least to me with my philosophy degree), particularly since we don’t know exactly what the odds are (most are “pretty good odds”, the last three are “could go either way”).

Here are the steps:

Step 1 (Tale of Terror!!):

Cost: 1xTale of Terror!! (E0.50)
Chance: Pretty good odds

Step 2 (Sense of Deja Vu):

Cost: 1xVision of the Surface (E0.50)
Chance: Pretty good odds

Step 3 (Glimpse of Something Larger):

Cost: 2xCorrespondence Plaques (E1.00 total)
Chance: Pretty good odds

Step 4 (Deal with a Devil):

Cost: 2xBrilliant Souls (E1.00 total)
Chance: Pretty good odds

Step 5 (Room Number at the Royal Beth):

Cost: 1xAn Identity Uncovered! (E2.50)
Chance: Could go either way

Step 6 (Last Hope of a Fidgeting Writer):

Cost: 1xExtraordinary Implication (E2.50)
Chance: Could go either way*

Step 7 (Lens of Black Glass):

Cost: 1xMourning Candle (E2.50)
Chance: Could go either way
Trade: 1xSearing Enigma, 1xPrimaeval Hint, 1xBazaar Permit, 1xComprehensive Bribe (E149.70 total)
Win: 1xCoruscating Soul (E312.50)

*A success here also increases your Wounds and Nightmares.

**This also has significant curiosity value, since currently the only other way to get a Night-Whisper is to trade with the Shivering Relicker, an option that requires Watchful 150 and is thus, I think, only available to those with Overgoats. (edit: I stand corrected on this last point, but it certainly is very difficult to get a Night-Whisper)

That’s a potential 302 Echoes from 7 actions. But of course, most times you won’t get all the way - if you fail on the last step, you’re out E10.5 worth of stuff. The question is, will you succeed often enough to make the failures worth it? To get an exact answer we’d need to know how good “pretty good odds” are, but we do know this: to get 302 Echoes from the Velocipede Squad storyline, you’d need to spend 245 actions. Maybe I’ve just gotten lucky, but I’m sure the average number of actions it takes for a successful Fidgeting Writer run is far smaller. Of course, you’ll occasionally have to replenish your stocks of Tales of Terror!!, Correspondence Plaques etc, but fortunately none of these are very hard to get.

Thoughts? Have I made obvious and terrible errors of judgement?
edited by SeanH on 3/2/2012

I ran the numbers after completing the line once myself; I’ll share them here.

Assuming a 66% chance on all “pretty good odds” and a 50% chance on “could go either way” odds, I came up with the following averages:

To get A:
Deja Vu: 1.52 turns, 0.76 echos cost, trade in for Extraordinary Implication (E2.50) (adding one extra turn)
Glimpse: 3.81 turns, 1.91 echos cost, trade in for Collated Research (E5.00 total) (adding one extra turn)
Deal: 7.29 turns, 4.4 echo cost, trade in for Brass Ring (E12.50) (adding one extra turn)
Room: 12.56 turns, 8.19 echos cost, trade in for 2xAntique Mysteries (E25.00 total) (adding one extra turn)
Last Hope: 27.12 turns, 21.37 echos cost, trade in for Night-Whisper (E62.50) (adding one extra turn)
Black Glass: 56.24 turns, 47.74 echos cost, trade in for 1xSearing Enigma, 1xPrimaeval Hint, 1xBazaar Permit, 1xComprehensive Bribe (E149.70 total) (adding one extra turn)
Soul: 114.47 turns, 100.48 echos cost, 1xCoruscating Soul (E312.50) to cash in (no extra turns this time)

Of course, the developers have stated that challenges with the same difficulty text may not have exactly the same odds of success - so there will be some variation from this. Also a lot of people like to assume 70% for “pretty good odds” which makes these numbers much better (I have those too; but in general it cuts about 15% off the time and 10% off the cost)

Unfortunately, to pin down those numbers to within a few %, with a 95% confidence, takes a couple thousand attempts… which is more than I’m willing to put into it. But this should give you a general picture.

Thanks, Dave! Your numbers are more pessimistic than my gut feeling, but still with the result that - if I’m reading it right - the expected return for a full run is a little over 1.85 Echoes/action, which is much better than the Velocipede Squad (and actually better than any opportunity card I’m aware of, except maybe “A presumptuous little opportunity” which can get you 4 Echoes/action, albeit with a prohibitive item cost).

I’ve been lucky so far and got two Coruscating Souls since yesterday. Naturally I’m keeping one on my mantlepiece, to provoke conversation and disorient burglars.

The Relickers suggest that there are three tiers of items above the current conversion cap- I suspect that eventually we’ll be able to convert Storm-Threnodies to Night-Whispers. I think Coruscating Soul’s the first tier 7 item that’s shown up, so the multiples of five seem to hold. So the tier 8 items will be worth 1562.5 Echoes? Wow.

(I suspect some of the other tier 6 items are the 62.50 connection-boosting items: Pulsating Amber’s at that slot in the hypothetical Rubbery conversion chain. But that might be a topic for another thread)

It is possible to reach Watchful 150 without the Overgoat, provided that you are otherwise wearing/wielding the best Bazaar-sold Watchful gear, are affiliated with a newspaper, and picked your Mysterious Benefactor and Constant Companion wisely.

That’s about what my calculations show - but in practice the result will be lower. That’s because the items necessary to “ante up” at each level can usually only be farmed at around 1 echo/action, and must often be converted (which is sometimes less than 1 echo/action.) Of course, if you already have a mountain of these items, and don’t mind spending them; it seems a good way to earn money. That is, provided that a) my numbers are right, and b) you don’t mind the risk, and c) you do this enough times that the averages actually matter.

That also fits with my numbers well; I had previously figured, based on the known item exchange prices, that each “scrap” was worth about half an echo (sell value.) As the top-tier item costs 3200 scraps, that’s pretty close to my ball park of 1600 echos. It’s also significantly less than an overgoat, which I find interesting.

That’s about what my calculations show - but in practice the result will be lower. That’s because the items necessary to “ante up” at each level can usually only be farmed at around 1 echo/action, and must often be converted (which is sometimes less than 1 echo/action.) Of course, if you already have a mountain of these items, and don’t mind spending them; it seems a good way to earn money. That is, provided that a) my numbers are right, and b) you don’t mind the risk, and c) you do this enough times that the averages actually matter. [/quote]

Yes, you’re right. But it does look like it’s at least as good as the Velocipede Squad, and much more interesting when you’re grinding for an Overgoat.

On a similar note, I’d like to note something I found out a few days back. The item crafting system is another thing that can be fairly lucrative. I put the following information up on the wikidot page for item conversions

Base item: Success gives ~30 pence, Rare Success gives one of the 250 pence items
~10 p item: Success gives ~40 pence, Rare Success gives one of the capstone items.
~50 p item: Success gives ~100 pence, Rare Success gives two capstone items
~250 p item: Success gives ~200 pence, Rare Success gives Connection Item

There are two things that lead to this being a lucrative venture. The first is that rare successes aren’t actually all that rare. 10% maybe? The second is that the two low end conversions can be done in bulk at 10x the normal rate. No rare success in that case, but you get a bit more of the main item: 50 pence more for the first conversion, and 250 pence more for the second.

The best method as far as I can tell, for people who’ve made a fair amount of progress in the game, is to do bulk conversion for the first two: 5 of the first conversion allows for one of the second, which then allows 2 conversions for the ~50 pence items. About every 2.5 runs of this allows for one of the final conversions. The main thing I’m aiming for in this case is a rare success while converting the ~50 pence items, as this offers up ~24 echoes worth of goods. Even the second stage offers ~12 echoes on a rare success, so one may be tempted to do normal conversions with that instead of bulk. It’s currently unknown if the final stage can offer a rare success, so it’s unknown what sort of item you would get.

Something of note: This system may actually be very nice for newbies: All the challenges are luck based, and even the success for the first two is a decent payout for someone with low stats. Though, they may have difficulty once the item chains require connections.

[quote=]and actually better than any opportunity card I’m aware of, except maybe “A presumptuous little opportunity” which can get you 4 Echoes/action, albeit with a prohibitive item cost[/quote]

How do you work the presumptuous little opportunity for Echoes? Maths isn’t my character’s strong point at this time of night. I’m currently grinding for an Overgoat and regretting burning my bridges with the Velocipede Squad, so new money-making ideas would be fantastic, even if they only come up occasionally. I can only do the Fidgeting Writer for so long before I start tearing my hair out and have to do something else.

Regarding rare successes on the final stage of item conversions, I just got a [color=#ffffff]Searing Enigma[/color] from turning Broken Giant 1844 into Cellars of Wine.
edited by the_antichris on 3/4/2012

“Perhap you’re interested in an exceptional vintage?” trades 50 echoes of 1879 for 60 echoes of broken giant.

“An alarming amount of Strangling Willow Absinthe” trades 40 echoes of Morelways for 48 echoes of strangling willow

“Ten cases of Morelways” trades 10 echoes of 1882 for 20 echoes of morelways.

“An improbable exchange” has you break even.

Obviously, the best choices in this example are trading for morelways and broken giant, as both earn you 10 echoes of profit. By the way, how much does that searing enigma sell for?

Searing Enigmas sell for 67.5 Echoes. They’re also (rarely and painfully) available at Hunter’s Keep towards the end of a cycle.

Ok. As all the rare successes of a given tier seem to sell for the same amount, I guess that means we can expect 67.5 echoes worth of goods (More or less) for rare successes for the other items.

62.5 Echoes for me. And it files under Mysteries, if anyone was wondering. I have a couple from Hunter’s Keep, so I sort of want to sell it, but as a completist I have a rule only to sell things I have a reliable source of. Waiting for the first one on the Keep was… painful.

Thanks for the info, Urthdigger! I’m off to collect wine.

Edit: My sock got a Fourth City Airag from one of the final-tier conversions (I wish I could remember what, but it might have been Touching Love Stories to Bazaar Permits - that’s what I’ve done the most of on that account), which is also 62.5 Echoes, so that supports your conclusion.
edited by the_antichris on 3/4/2012

Just looking at the wiki it seems that you actually break even on this trade as well, as it is 1000x 1882 selling at 2 pence for 200x Morelways selling at 10 pence. So they are 20 echoes each.

“Ten cases of Morelways” trades 10 echoes of 1882 for 20 echoes of morelways.

[/quote]

Just looking at the wiki it seems that you actually break even on this trade as well, as it is 1000x 1882 selling at 2 pence for 200x Morelways selling at 10 pence. So they are 20 echoes each.[/quote]
It might have changed, though, since that entry was penned.

“Ten cases of Morelways” trades 10 echoes of 1882 for 20 echoes of morelways.

[/quote]

Just looking at the wiki it seems that you actually break even on this trade as well, as it is 1000x 1882 selling at 2 pence for 200x Morelways selling at 10 pence. So they are 20 echoes each.[/quote]
It might have changed, though, since that entry was penned.[/quote]

I can’t recall for certain, but I think I tried that option just recently and received 240 Morelways; I remember vaguely it being ten dozen. That would be 4 echos profit, but at the cost of gathering 1882 when more profitable actions are available.

Unfortunately, statistics are statistics, i.e. they’re not really THAT useful. I’ve spent… 30? 40? actions already, and I only got to the room. Once. And failed. Even not counting the ~10 actions spent to make items neccessary to try again and again with the deja vu and glimpse, I am still way behind your approximate arrivals. For example, only 1 out of 5 times did the deal with the devil work for me. :(

By my estimates you should get to the room on average in 27 actions (not counting actions to gather materials!), so you’re actually right on track. It’s around 56 actions to get to the next step, and 114 actions to take the grand prize - again, on average. Of course, my estimates are considered “pessimistic” by some here; but they track reasonably well for me. “Statistics” are unfortunately only useful for large numbers of iterations - meaning if you are trying for the grand prize you could reasonably expect to get 50 in 5,700 actions; but your odds of getting one in 40 actions have a huge variability.

[quote=Dave ]
By my estimates you should get to the room on average in 27 actions (not counting actions to gather materials!), so you’re actually right on track. It’s around 56 actions to get to the next step, and 114 actions to take the grand prize - again, on average. Of course, my estimates are considered “pessimistic” by some here; but they track reasonably well for me. “Statistics” are unfortunately only useful for large numbers of iterations - meaning if you are trying for the grand prize you could reasonably expect to get 50 in 5,700 actions; but your odds of getting one in 40 actions have a huge variability.[/quote]

Hmm, I might be misreading something here…
“Room: 12.56 turns, 8.19 echos cost, trade in for 2xAntique Mysteries (E25.00 total) (adding one extra turn)
Last Hope: 27.12 turns, 21.37 echos cost, trade in for Night-Whisper (E62.50) (adding one extra turn)”
Doesn’t this mean that by turn 27 I should be around the Last Hope? [And BTW, did you calculate a standard deviation, too? ;)]

I’m grinding an overgoat too, and I’ve found that the most lucrative thing to do right now is this little story. Check my sig for my numbers. I’m currently at 18 brilliant Souls, having spent 1415 actions, and 1307 echoes worth of goods, for a total benefit/action of 3.05159010600707 echoes/action (2.19035176403603 echoes action once you take into account the actions needed to grind the materials, instead of their cost) [The link at my sig is constantly updated thanks to Google Docs magic]. With my percentages, it’s worth following the story until the end.

Current success percentages:

Tale of Terror->Sense of Deja Vu: 72.5738396624472%
Sense of Deja Vu->Glimpse of something larger: 72.6726726726727%
Glimpse of something larger->Deal with a Devil: 74.8936170212766%
Deal with a Devil->A Room Number at the Royal Beth: 61.9318181818182%
A Room Number at the Royal Beth->The Last Hope of a Fidgeting Writer: 50.4587155963303%
The Last Hope of a Fidgeting Writer->A Lens of Black Glass: 60%
A Lens of Black Glass-> Coruscating Soul: 54.5454545454545%

Given the data on my sig, could any armchair statistician calculate the confidence intervals and standard deviation for these percentages? Been a while for me.
edited by Vyrlokar on 4/8/2012