Monty Hall problem

Monty Hall problem
You are encouraged to solve this task according to the task description, using any language you may know.

Run random simulations of the Monty Hall game. Show the effects of a strategy of the contestant always keeping his first guess so it can be contrasted with the strategy of the contestant always switching his guess.

A well-known statement of the problem was published in Parade magazine:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? (Whitaker 1990)

Simulate at least a thousand games using three doors for each strategy and show the results in such a way as to make it easy to compare the effects of each strategy.

AWK

#!/bin/gawk -f 

# Monty Hall problem

BEGIN {
	srand()
	doors = 3
	iterations = 10000
	# Behind a door: 
	EMPTY = "empty"; PRIZE = "prize"
	# Algorithm used
  KEEP = "keep"; SWITCH="switch"; RAND="random"; 
  #
}
function monty_hall( choice, algorithm ) {
  # Set up doors
  for ( i=0; i<doors; i++ ) {
		door[i] = EMPTY
	}
  # One door with prize
	door[int(rand()*doors)] = PRIZE

  chosen = door[choice]
  del door[choice]

  #if you didn't choose the prize first time around then
  # that will be the alternative
	alternative = (chosen == PRIZE) ? EMPTY : PRIZE 

	if( algorithm == KEEP) {
		return chosen
	} 
	if( algorithm == SWITCH) {
		return alternative
	} 
	return rand() <0.5 ? chosen : alternative

}
function simulate(algo){
	prizecount = 0
	for(j=0; j< iterations; j++){
		if( monty_hall( int(rand()*doors), algo) == PRIZE) { 
			prizecount ++ 
		}
	}
	printf "  Algorithm %7s: prize count = %i, = %6.2f%%\n", \
		algo, prizecount,prizecount*100/iterations

}

BEGIN {
	print "\nMonty Hall problem simulation:"
	print doors, "doors,", iterations, "iterations.\n"
	simulate(KEEP)
	simulate(SWITCH)
	simulate(RAND)
		
}

Sample output:

bash$ ./monty_hall.awk

Monty Hall problem simulation:
3 doors, 10000 iterations.

  Algorithm    keep: prize count = 3411, =  34.11%
  Algorithm  switch: prize count = 6655, =  66.55%
  Algorithm  random: prize count = 4991, =  49.91%
bash$

Python

<python> I could understand the explanation of the Monty Hall problem but needed some more evidence

References:

 http://www.bbc.co.uk/dna/h2g2/A1054306
 http://en.wikipedia.org/wiki/Monty_Hall_problem especially:
 http://en.wikipedia.org/wiki/Monty_Hall_problem#Increasing_the_number_of_doors

from random import randrange, shuffle

doors, iterations = 3,100000 # could try 100,1000

def monty_hall(choice, switch=False, doorCount=doors):

 # Set up doors
 door = [False]*doorCount
 # One door with prize
 door[randrange(0, doorCount)] = True

 chosen = door[choice]

 unpicked = door
 del unpicked[choice]

 # Out of those unpicked, the alterantive is either:
 #   the prize door, or
 #   an empty door if the initial choice is actually the prize.
 alternative = True in unpicked

 if switch:
   return alternative
 else:
   return chosen

print "\nMonty Hall problem simulation:" print doors, "doors,", iterations, "iterations.\n"

print "Not switching allows you to win", print [monty_hall(randrange(3), switch=False)

       for x in range(iterations)].count(True),

print "out of", iterations, "times." print "Switching allows you to win", print [monty_hall(randrange(3), switch=True)

       for x in range(iterations)].count(True),

print "out of", iterations, "times.\n" </python> Sample output:

Monty Hall problem simulation:
3 doors, 100000 iterations.

Not switching allows you to win 33337 out of 100000 times.
Switching allows you to win 66529 out of 100000 times.