Problem 9 of Monte Carlo solutions to Fifty Challenging Problems...

(This is another part of the Fifty Problems series, a set of example applications of Monte Carlo methods. In each post, I present source code which answers a probabilistic question using simulated models of the underlying system.)

Problem 9: What are the odds of winning in Craps (using only Pass Line bets)?


#!/usr/bin/env ruby

# Modelling craps is weird.
# We roll two dice and sum them.
#
# if they're 7 or 11 => immediate win
#            2,3,12 => lose
# else, roll is the "point"
#       player keeps rolling until:
#         point => win
#             7 => lose
#
# So, what's the chance to win?

TRIALS=500000

def roll
	d1 = 1 + rand(6)
	d2 = 1 + rand(6)
	return d1+d2
end

def win()
	first_roll = roll()
	return true if (first_roll == 7 || first_roll == 11)
	return false if ([2,3,12].include?(first_roll))

	point = first_roll
	while (true) do
		next_roll = roll()
		return false if 7 == next_roll
		return true if next_roll == point
	end
end

wins = 0

TRIALS.times do
	wins += 1 if win()
end

puts "After #{TRIALS} games, won #{wins}"
puts "P(win) = #{wins.to_f/TRIALS.to_f}"

I've been coding my way through Fifty Challenging Problems in Statistics with Solutions. This post is a part of the Fifty Challenging Problems series.

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