Monty Hall problem: Difference between revisions
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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. |
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. |
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=={{header|AWK}}== |
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<pre> |
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#!/bin/gawk -f |
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# Monty Hall problem |
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BEGIN { |
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srand() |
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doors = 3 |
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iterations = 10000 |
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# Behind a door: |
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EMPTY = "empty"; PRIZE = "prize" |
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# Algorithm used |
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KEEP = "keep"; SWITCH="switch"; RAND="random"; |
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# |
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} |
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function monty_hall( choice, algorithm ) { |
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# Set up doors |
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for ( i=0; i<doors; i++ ) { |
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door[i] = EMPTY |
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} |
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# One door with prize |
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door[int(rand()*doors)] = PRIZE |
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chosen = door[choice] |
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del door[choice] |
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#if you didn't choose the prize first time around then |
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# that will be the alternative |
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alternative = (chosen == PRIZE) ? EMPTY : PRIZE |
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if( algorithm == KEEP) { |
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return chosen |
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} |
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if( algorithm == SWITCH) { |
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return alternative |
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} |
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return rand() <0.5 ? chosen : alternative |
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} |
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function simulate(algo){ |
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prizecount = 0 |
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for(j=0; j< iterations; j++){ |
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if( monty_hall( int(rand()*doors), algo) == PRIZE) { |
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prizecount ++ |
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} |
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} |
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printf " Algorithm %7s: prize count = %i, = %6.2f%%\n", \ |
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algo, prizecount,prizecount*100/iterations |
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} |
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BEGIN { |
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print "\nMonty Hall problem simulation:" |
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print doors, "doors,", iterations, "iterations.\n" |
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simulate(KEEP) |
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simulate(SWITCH) |
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simulate(RAND) |
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} |
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</pre> |
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Sample output: |
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<pre> |
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bash$ ./monty_hall.awk |
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Monty Hall problem simulation: |
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3 doors, 10000 iterations. |
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Algorithm keep: prize count = 3411, = 34.11% |
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Algorithm switch: prize count = 6655, = 66.55% |
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Algorithm random: prize count = 4991, = 49.91% |
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bash$ |
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</pre> |
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=={{header|Python}}== |
=={{header|Python}}== |
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<python> |
<python> |
Revision as of 12:59, 10 August 2008
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.