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Dragon Heist gives the players the option to run a tavern where 60gp are spent every tenday and a d100+10 is rolled against the Running a Business table in the DMG. Rolling a 50, for example, means that players earned 60gp for that period, and so matched the money spent in maintenance, earning no profits, but incurring no losses.

  • 20- Loss of 90g.
  • 21-30 Loss of 60g.
  • 31-40 Loss of 30g.
  • 41-60 No profit, no losses.
  • 61-80 Profits 1d6×5gp.
  • 81-90 Profits 2d8×5gp.
  • 91+ Profits 3d10×5gp.

Players can spend gold on marketing, adding 1 to the roll for each 1 gp they spend. What is the optimal amount of gold to spend in marketing to optimize the profits earned? Or is it not even worth to run the tavern?

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  • \$\begingroup\$ I actually worked this out in a comment on this answer to another question - pretty sure I just wrote some anydice looping to calculate it. I'll try to recreate and post as a proper answer to this question. \$\endgroup\$ – Carcer Sep 7 at 16:45
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Spend 30gp/tenday

Using this anydice program, I've calculated the expected profit based on how much money you spend on marketing. I've defined a function for calculating the profit or loss of a business as per the DMG's rules, and then run it in a loop to compare the result of differing marketing spends when used to run Trollskull Manor.

function: profit ROLL:n MAINT:n {
  if ROLL <= 20 { result: -(MAINT * 15) / 10 }
  if ROLL <= 30 { result: -MAINT }
  if ROLL <= 40 { result: -MAINT / 2 }
  if ROLL <= 60 { result: 0 }
  if ROLL <= 80 { result: 1d6 * 5 }
  if ROLL <= 90 { result: 2d8 * 5 }
  if ROLL >= 91 { result: 3d10 * 5 }
}

output [profit 1d100+10 60] named "Trollskull: No Marketing"

loop X over {1..80} {
  output [profit 1d100+10+X 60] - X named "Trollskull: [X]gp Marketing"
}

We're only going as high as 80gp on marketing spend, since at 80gp we have already guaranteed the result will be the best possible, and any extra money we throw at it will go to waste. The awkward -(MAINT * 15) / 10 is there because anydice can only do integers, so can't tell it directly to multiply by 1.5. I have also assumed (as in this answer) that the profit roll described by the rules in the DMG is a single amount for an entire operating period (30 days in a normal downtime activity, 10 days in the special case of the Trollskull Manor's rules) rather than being daily profits.

The results shown in anydice are a bit dense and impenetrable because it's checking for eighty different possible marketing spends and tabulates each individually but if you skim through the average expected result for spends, which is what we're interested in, you'll see that the expected return on investment rises steadily for each gp spent on marketing to a peak of 19.25gp profit on a 30gp marketing investment; after that, expected profit declines.

I note, with some trepidation, that this answer is entirely different to the analysis I previously offered in a comment on this answer to another question. However, very importantly, the analysis in this post was done just now and so I am absolutely convinced of its correctness, whereas I don't remember exactly what I did for that previous comment and probably mucked it up somehow.

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    \$\begingroup\$ @Medix2 worth noting, the function does expect the maintenance cost for the entire period, which you may need to extrapolate up to the appropriate time period from the daily maintenance costs described for other properties in the DMG. \$\endgroup\$ – Carcer Sep 7 at 17:39
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    \$\begingroup\$ @Medix2 the maintenance costs and profits are independent; the DMG's rules always have it so that you either have to pay some proportion of the maintenance cost, or the business makes enough to support itself and make might make a few gp extra. Trollskull's a special case because it allows you spend extra money outside that system in order to influence the roll. \$\endgroup\$ – Carcer Sep 7 at 17:41
  • \$\begingroup\$ Worth noting that any amount of marketing not over 80 gp will average a positive amount of profit-- the inn makes money on average regardless of how you run it, until you spend 82.5 gp on marketing. Also worth noting that this is with the profits monthly rather than profits daily interpretation (which is the interpretation the OP is going with, based on the 50 example)-- in the latter you want to spend all the marketing all the time. \$\endgroup\$ – the dark wanderer Sep 7 at 18:44
  • \$\begingroup\$ @thedarkwanderer The profits should be calculated every tenday, according to the Water Deep book, for this tavern. \$\endgroup\$ – BlueMoon93 Sep 7 at 19:34

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