Snippet that simulates DnD 5e tavern marketing budget scenarios to determine optimal marketing budget from players

dnd-tavern-marketing-budget.js

/**
 * DnD 5e Waterdeep campaign includes a Tavern controlled by players, that for
 * every 10-day cycle, must have upkeep given but also can earn income from
 * the business. That net income is determined by dice roll. However, players
 * may opt to add a --marketing budget-- which adds on to the dice roll...
 * but at what (literal) cost?
 *
 * To answer the question of which amount of gold would grant best return on
 * investment, I wrote this to run scenarios to determine, over many iterations,
 * what the best choice of marketing budget would be.
 */

"use strict";

// Helper Functions
/**
 * Gets dice roll value based on variably sided die
 * @param {number} sides - Number of sides on the die
 * @returns {number} - Roll value
 */
function roll(sides) {
  return Math.floor(Math.random() * sides) + 1;
}

/**
 * Determines gross income based on dice roll
 * @param {number} value -
 * @returns {number}
 */
function getGrossIncome(value) {
  const scenario = Math.trunc((value - 1) * 0.1);

  if (scenario < 2) return -90;
  else if (scenario === 2) return -60;
  else if (scenario === 3) return -30;
  else if (scenario === 4 || scenario === 5) return 0;
  else if (scenario === 6 || scenario === 7) return 5 * roll(6);
  else if (scenario === 8) return 5 * (roll(8) + roll(8));
  else return 5 * (roll(10) + roll(10) + roll(10));
}

/**
 * Calculates net income for the week based on marketing budget
 * @param {number} budget - Total gold given by players as marketing budget
 * @returns {number} - Net income from 10-day cycle
 */
function getNetIncome(budget) {
  const value = roll(100) + 10 + budget;
  return getGrossIncome(value) - budget;
}

// MAIN FUNCTION
/**
 * Calculates the optimal marketing budget by running sample_size
 * trials. Marketing budgets checked from 0gp to 90gp as beyond
 * guarantees money lost.
 * @returns {{max_roi: number, budget: number, all_roi: number[]}}
 * max_roi: optimal return of interest
 * budget: optimal budget
 * all_roi: avg roi per budget
 */
function findOptimalMarketingBudget() {
  const sample_size = 1_000_000;

  // Indices correspond to marketing budget (arr[0] = 0gp; arr[90] = 90gp)
  const trial_sums = new Array(91).fill(0);

  // Run experiment sample_size times
  for (let i = 0; i < sample_size; i++) {
    // For each trial, add a cycle to arr[index] where the index is the marketing budget
    trial_sums.forEach(
      (_, budget) => (trial_sums[budget] += getNetIncome(budget))
    );
  }

  // Initialize variables for storing return of investment max and its corresponding budget
  let max_roi = -Infinity;
  let max_roi_budget;

  // Get mean averages and find max_roi and budget
  const all_roi = trial_sums.map((trial_sum, budget) => {
    const avg_roi = Number((trial_sum / sample_size).toFixed(2));
    if (avg_roi > max_roi) {
      max_roi = avg_roi;
      max_roi_budget = budget;
    }
    return avg_roi;
  });

  return {
    max_roi,
    budget: max_roi_budget,
    all_roi
  };
}

console.log(findOptimalMarketingBudget());