Keno Monte Carlo

keno.js

/*
Output:
Pick 1 winnings per game: -0.499308
Pick 2 winnings per game: -0.39711
Pick 3 winnings per game: -0.377799
Pick 4 winnings per game: -0.387787
Pick 5 winnings per game: -0.381384
Pick 6 winnings per game: -0.430624
Pick 7 winnings per game: -0.440436
Pick 8 winnings per game: -0.407179
Pick 9 winnings per game: -0.441691
Pick 10 winnings per game: -0.404874
/*


const _ = require('lodash')

const numGames = 1000000

const numbers = _.range(1, 81)

let bank = 0

const payoffs = {
  1: {
    1: 2
  },
  2: {
    2: 10
  },
  3: {
    2: 2,
    3: 25
  },
  4: {
    2: 1,
    3: 5,
    4: 60
  },
  5: {
    3: 2,
    4: 20,
    5: 330
  },
  6: {
    3: 1,
    4: 6,
    5: 55,
    6: 1000
  },
  7: {
    3: 1,
    4: 2,
    5: 15,
    6: 100,
    7: 5000
  },
  8: {
    4: 2,
    5: 6,
    6: 75,
    7: 550,
    8: 10000
  },
  9: {
    4: 1,
    5: 5,
    6: 20,
    7: 125,
    8: 3000,
    9: 30000
  },
  10: {
    0: 5,
    5: 2,
    6: 10,
    7: 45,
    8: 300,
    9: 5000,
    10: 100000
  },
}

for (let pickN = 1; pickN <= 10; pickN++) {
  bank = 0
  for (let i = 0; i < numGames; i++) {
    bank -= 1
    const guesses = _.sampleSize(numbers, pickN)
    const picks = _.sampleSize(numbers, 20)
    const numMatches = _.intersection(guesses, picks).length
    const winnings = payoffs[pickN][numMatches] || 0
    bank += winnings
  }
  console.log(`Pick ${pickN} winnings per game: ${bank / numGames}`)
}