[RPG] How much gold should be spent to optimally run this Tavern

dnd-5eeconomyoptimizationpublished-adventureswaterdeep-dragon-heist

The Waterdeep: Dragon Heist adventure gives the players the option to run a tavern. The "Tavern Keeping Expenses" sidebar (p. 41) specifies the regular running expenses and how to determine profit or loss. 60 gp is spent every tenday, and a d100 + 10 is rolled against the "Running a Business" table in the DMG (p. 129).

Rolling a 50, for example, means that players earned 60 gp for that period, and so matched the money spent in maintenance, earning no profits, but incurring no losses.

Combining this information, the tavern's profit or loss (based on the total of the roll) is as follows:

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

The sidebar also specifies that 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?

Best Answer

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. Here's a table of results, using the table and summary view:

Anydice table showing the mean result of various marketing spends

The results shown in anydice are a bit dense and impenetrable because it's checking for eighty different possible marketing spends, but by looking at the summary of mean results for each variation, we can see that the expected return on investment rises with diminishing returns for each gp spent on marketing to a peak of 19.25gp profit on a 30gp marketing investment; after that, expected profit declines. (The scale on the table is bizarre because this view also has minimum and maximum tables, so values are being graphed in relation to a minimum of -99 and a maximum of 150 off past the edge of my screencap.)

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.

Related Topic