Gamblers Fallacy

gamblers-fallacy.js

/* 
Models flip-a-coin game with variative chance of "heads" and "tails". Chance depends on betWinPayoutRatio.
For 2 it's 50% like you wold expect and for 10 it's 1/10th

Once you copy paste this code to Chrome's console, run 

main({
  gamesToPlay: 100,
  timesToPlayEachGame: 1000000,
  chainLenghtToWaitFor: 5,
  betWinPayoutRatio: 10,
})

and tweak self-explanatory parametrs

The most interesting one is "chainLenghtToWaitFor" which represents how long a player should wait for a give number of tails in a row
before placing a bet to heads. For 5 a player would wait for 5 tails in a row and only then place a bet on heads.

starting money for each player is 1000
each bet is equal to 1

I CHALLANGE YOU to find parameters where avgMoneyLeft doubles =)

*/

function main({
    gamesToPlay = 10,
    timesToPlayEachGame = 10,
    chainLenghtToWaitFor = 5,
    betWinPayoutRatio = 2
  }) {
  console.clear()
  const log = console.log

  log(...arguments)

  function rnd(min, max) {
    min = Math.ceil(min);
    max = Math.floor(max);
    return Math.floor(Math.random() * (max - min + 1)) + min;
  }

  // const flipCoin = () => (Math.random() >= 0.5 ? 'heads' : 'tails')
  const flipCoin = () => (rnd(1, betWinPayoutRatio) === 1 ? 'tails' : 'heads')
  const winningBet = coinSide => (coinSide === 'tails')

  class Player {
    constructor({startingMoney, winGoal}) {
      this.money = startingMoney
      this.betsPlaced = 0
      this.betPlaced = false
      this.betAmount = 0
      this.winGoalAchived = false
    }

    placeBet(betAmount) {
      const remainingMoney = this.money - betAmount

      this.betPlaced = true
      this.betsPlaced++
      this.betAmount = betAmount
      this.money -= betAmount
    }

    collectWinnings({payoutRatio}) {
      this.money += (this.betAmount * payoutRatio)
      this.betPlaced = false
      this.betAmount = 0

      if (this.money >= this.winGoal) {
        this.winGoalAchieved = true
        log(`Win goal achieved, player's balance: ${this.money}`)
      }
    }

    feelDisappointed() {
      this.betPlaced = false
      this.betAmount = 0
    }
  }

  function playAGame({sameSideChainLength = 5, timesToPlay = 1000}) {
    let headsInARow = 0
    let previousFlipWasHeads = false
    const player = new Player({startingMoney: 1000, winGoal: 2000})

    for(let i = 0; i < timesToPlay; i++) {
      let coinSide = flipCoin()

      if (player.betPlaced) {
        if (winningBet(coinSide)) {
          player.collectWinnings({payoutRatio: betWinPayoutRatio})
          // log('collected winnings')
        } else {
          player.feelDisappointed()
        }
      }

      if (coinSide === 'heads') {
        if (previousFlipWasHeads) {
          headsInARow++
        } else {
          headsInARow = 1
        }
        previousFlipWasHeads = true
      } else {
        previousFlipWasHeads = false
        headsInARow = 0
      }

      if (headsInARow === sameSideChainLength) {
        player.placeBet(1)
      }
    }

//     log(player.money)
//     log(`Bets placed: ${player.betsPlaced}`)
    return {
      moneyLeft: player.money,
      betsPlaced: player.betsPlaced
    }
  }

  const game = () => playAGame({sameSideChainLength: chainLenghtToWaitFor, timesToPlay: timesToPlayEachGame})
  
  const playGameNTimes = (game, times) => {
    let results = []

    for (let i = 0; i < times; i++) {
      results.push(game())
    }

    return results
  }

  const gamesResults = playGameNTimes(game, gamesToPlay)
  const stats = gamesResults
    .reduce((a, b) => {
      a.moneyLeft += b.moneyLeft
      a.betsPlaced += b.betsPlaced
      return a
    }, {moneyLeft: 0, betsPlaced: 0})

  log('--- last N games results ---')
  gamesResults.slice(gamesToPlay - 10).map(x => {
    log(x)
    return x
  })

  log('Total bankrupt players: ')
  log(gamesResults.filter(x => x.moneyLeft < 0).length)

  console.info({
    avgMoneyLeft: stats.moneyLeft / gamesToPlay,
    avgBetsPlaced: stats.betsPlaced / gamesToPlay
  })

  //1234
}

main({
  gamesToPlay: 100,
  timesToPlayEachGame: 1000000,
  chainLenghtToWaitFor: 5,
  betWinPayoutRatio: 10,
})