EU4 Gold Mine Development Calculations

#!/usr/bin/env ruby
require "rational"

# Game shows in tooltip:
# Base | Change per year
# 1      0.00%
# 2      0.01%
# 5      0.12%
# 10     0.49%
# 15     1.12%
# 20     1.99%
# Best fit says there's extra digit 0.5 missing,
# so it's really
def fail_chance(base)
  return 0 if base <= 1
  Rational(base**2-1, 20000)
end

def lerp(ratio, a, b)
  ratio = 0 if ratio <= 0
  ratio = 1 if ratio >= 1
  ratio * a + (1-ratio) * b
end

# Depletion keeps fractional development, so 61 depletes to 30.5
# For simplicity/performance round to two decimal places
$base_after_depletion = {}
def base_after_depletion(base)
  Rational((base*50).floor, 100)
end

$expected_gold = {}
def expected_gold_income(base, years)
  $expected_gold[[base, years]] ||= begin
    if years == 0
      0
    else
      # Assume depletion only happens on annual tick, since we don't know any better
      current_year_income = 8 * base
      chance = fail_chance(base)
      depleted = base_after_depletion(base)
      current_year_income + lerp(chance, expected_gold_income(depleted, years-1), expected_gold_income(base, years-1))
    end
  end
end

def value_of_button_press(base, year)
  expected_gold_income(base+1, year) - expected_gold_income(base, year)
end


puts "Expected Total Income By Dev [100/200/300/400 years]"
(1..50).each do |base|
  puts ["*",
    base,
    "-",
    expected_gold_income(base, 100).round,
    expected_gold_income(base, 200).round,
    expected_gold_income(base, 300).round,
    expected_gold_income(base, 400).round,
  ].join(" ")
end

puts "Expected Total Gold Value Of Pressing Dev Button [100/200/300/400 years]"
(1..50).each do |base|
  puts ["*",
    base,
    "-",
    value_of_button_press(base, 100).round,
    value_of_button_press(base, 200).round,
    value_of_button_press(base, 300).round,
    value_of_button_press(base, 400).round,
  ].join(" ")
end