# Costs and probabilities for attaining toxins - My group, don't read!

So, my group has been told there is a pride of gryphons cruising around not far from the town they're in, and the king is offering good money for capture of any healthy, unharmed gryphons. (He might pay something for a slightly injured one).

One of the party is looking into using a paralysis toxin to subdue one.

The town is not particularly large, and the alchemist only had 1 dose each of carcass scavenger toxin, curare and Wolfsbane. The alchemist has said he can work to extract more if he is provided the raw materials (woohoo, a quest!) but that raises a few questions:

1. Assuming materials are provided, and given an alchemist charges 250gp/month, what is the cost for the alchemist to do the work? There has been a proposal for 62.5gp per attempt (1/4 of 250) given an attempt takes a week. (Realistically, I assume that a week to extract may not necessarily require an alchemist to be actively working on it the whole time (there might be some waiting involved), but I am inclined to overcharge rather than undercharge, as some of my players have a keen eye for exploitation opportunities). (And this is easily done given my players suggested it).

2. What should a curare plant (enough for 1 dose) cost? It's been noted Wolfsbane toxin is 350gp/dose while 1lb of Wolfsbane costs 10gp (noting there is nothing to suggest how much Wolfsbane plant is required to make 1 dose of toxin).

Trying to work backwards: A dose of curare is 1500gp, and assuming fresh plants (being generous), it's a 14+ (roughly 1/3 chance). So it takes 3 tries and 3 lots of curare plant to get 1 dose of the stuff, making each attempt theoretically worth 500gp. Going back to an alchemist's time being worth 62.5gp per week (and thus, per attempt), and that makes the materials worth 437.5gp. Again, it's probably the case that other materials are involved and they would be part of that material cost. Noting curare is a 20+ naturalism roll (once per week) of 20+, it appears very hard to find. My inclination is to assume it costs about 400gp for enough to attempt.

Another way of looking at it is that a naturalist is presumably a 1 proficiency NPC. Looking in Chapter 3, I see a basic Healer can heal 3 patients per day at 1gp/day/patient. This is a monthly (28 days for all months in my campaign, for simplicity) income of 84gp, or 21gp per week. Given a naturalist would spend 20 weeks (on average) to find a curare plant, you'd think he would charge 420gp for it. This is roughly in line with my 400gp above.

(If we do a comparison with Wolfsbane, again assuming fresh plants, 350gp per dose goes to ~120gp per attempt. Half that goes to the Alchemist, meaning ~60gp for materials. 1lb of Wolfsbane is 10gp, so I guess this means you need a fair bit of Wolfsbane to extract 1 dose of poison (say, 5lb)).

Summary:

Alchemist will charge 62.5gp per 1 week ATTEMPT to extract a poison, based on their 250gp monthly fee divided by 4.

Curare plant (enough to make a dose of curare poison) will cost 400gp (rounder figure than 420gp).

(I'm assuming in all of this that markup for profit is in the Alchemist's monthly rate. His "value add", so to speak)

Would welcome any thoughts on this, particularly any where I might be setting myself up for grief/exploitation later on.

Normally, for crafting, raw materials cost 25% of the value of the finished item. (It’s in D@W: Campaigns and also here: http://autarch.co/forums/ask-autarchs/crafting-proficiency-questions ).

So the plants required to make one dose of curare would cost 375 gp. The remaining 1125 GP would be alchemist’s fees normally.

I don’t have much else to add at the moment, perhaps more later!

Here is how the Cost of Poisons was calculated:

 Poison Costs # of Times Chance Cost of Net Cost Cost of Alchemy Target # of Times Cost of Chance Net Cost Cost of Naturalist Total Poison Save Chance Extraction to Fumble Fumble Fumble Alch Time Cost to Find to Find Fumble to Fumble Fumble Nat. Time Cost Cost Belladonna 0.35 2.86 14% 325 \$29 \$179 \$207 11 2.0 2000 9.75% \$127 \$13 \$139 \$347 Curare 0.25 2.86 14% 2000 \$204 \$179 \$383 20 20.0 2000 64.15% \$962 \$125 \$1,087 \$1,470 Foxglove 0.1 2.86 14% 325 \$40 \$179 \$218 14 2.9 325 13.63% \$40 \$18 \$58 \$276 Hellebore 0.35 2.86 14% 325 \$29 \$179 \$207 8 1.5 325 7.59% \$16 \$10 \$26 \$233 Hemlock 0.45 2.86 14% 325 \$24 \$179 \$203 8 1.5 325 7.59% \$14 \$10 \$23 \$226 Henbane 0.35 2.86 14% 325 \$29 \$179 \$207 8 1.5 325 7.59% \$16 \$10 \$26 \$233 Wolfsbane 0.35 2.86 14% 325 \$29 \$179 \$207 11 2.0 2000 9.75% \$127 \$13 \$139 \$347 Yew 0.45 2.86 14% 325 \$24 \$179 \$203 4 1.2 325 5.86% \$10 \$7 \$18 \$221 Chance of Extraction 35% Average Number of Attempts to Extract 2.857143

The "# Of Times" column is based on a 35% chance of extraction.

The "Chance to Fumble" is based on a 5% chance of fumbling per attempt, using the formula
(1-((1-0.05)^(# of Times))

Cost of Fumble is the cost of a Neutralize Poison (325gp) or a Raise Dead (2000gp). The idea is that unless the poison takes effect instantly, the alchemist will have time to neutralize it before he dies.

Net Cost of Fumble is the cost of a fumble times the chance to fumble.

Cost of Alchemical Time is equal to 250gp/month / 4 weeks per month x # of Times.

Alchemy Cost is the sum of Net Cost of Fumble + Cost of Alchemy Time.

***

Target to Find is the target value required to find the toxin.

# of Times to Find is calculated as 1/((21-Target)*5/100)

Cost of Fumble is again either the cost of Neutralize Poison or Raise Dead. Since finding poisons takes place out in the wild, I assumed that it would take more than 10 minutes to get to a cleric, so poisons that are instant or 1 turn or less onset are priced as Raise Dead. However, Henbane is priced at 325gp (Neutralize) even though it has a low onset time, since it is so low-damage and unlikely to kill.

Chance to Fumble is, again, (1-((1-0.05)^(# of Times)))

Net Cost of Fumble is equal to Cost of Fumble times Chance to Fumble.

Cost of Naturalist Time is equal to 25gp per month / 4 weeks per month x # of Times.

Natural Cost is equal to Net Cost of Fumble plus Cost of Naturalist Time.

Total Cost is equal to Alchemy Cost + Naturalist Cost.

Henbane's price was adjusted upward in play because Feeblemind is so powerful an effect.

I think part of the reason I love this table so much is the idea that, in ACKS, you can in fact put an actual GP value on risking your life. It’s the cost of a Raise Dead.

So I think I understand most of this. One question I have is:

If a naturalist were to charge per ATTEMPT to find a particular plant, how would you calculate that?

I've done it by assuming 6.25gp for a week of his time, added to (chance to fumble)x(cost to fumble), in order to cover himself against mistakes. Given my players are interested in Wolfsbane and Curare, which both require Raise Dead as cover, and it's 1/20 to fumble on ANY GIVEN ATTEMPT, giving 100gp as cover, so I get a total of 106.25gp per ATTEMPT.

For the alchemist charging per attempt, 62.5gp per week for the guy's time. Then, for curare, same cost to mitigate death, so total cost per attempt is 162.5gp. For Wolfsbane, which gives time to get a Neutralise Poison, mitigation cost is 1/20 x 325gp = 16.25gp, giving total cost per ATTEMPT as 78.75gp.

Have I done anything dumb?

EDIT:

I took this to players, and one of them asked a valid question. Using Curare as an example:

As an alchemist, it takes you 2.86 tries, on average to successfully extract the toxin and make a dose. That means you use 2.86 plants for 1 dose. Presumably the alchemist is purchasing the recovered plants at 1087gp per viable plant (the naturalist's cost to recover a plant), then the process and sell the extract. Shouldn't that mean that in addition to the alchemy cost for 383gp based on time and Raise Dead, a commercial toxin-dealing alchemist should also be charging 2.86 x 1087 = 3108.82gp to cover the number of plants he actually goes through to get the dose? So a dose of curare SHOULD cost 3108.82 (total cost of materials, including naturalist's Raise Dead) + 383 (alchemist's time and Raise Dead) = 3491.82gp?

Silent Tempest - that would be correct IF the rules said that the raw plant was consumed on a failed extraction, but they don't say that. If you fail the roll but don't get a natural 1, you simply try again the following week.

Heh, an excellent point I had overlooked. I had indeed been assuming the plant was lost on failed extraction. It does feel a little wierd to me that it isn't, as I would have thought most failed processing attempts to turn one thing into another would generally destroy or damage-beyond-usefulness the raw material, but I'll run with it, if nothing else for simplicity and ability to use the numbers already generated :D

Thanks Alex!