Arjen Markus (21 june 2017) Here is a small program to simulate the so-called
Monty Hall problem
, one of those fascinating counter-intuitive results in statistics and probabilistics. While it is not really difficult to describe the set-up, simulating it turned out to be a trifle tricky. But the outcome is in agreement with the theoretical results.
Note: it could be done in fewer lines as well.
# threedoors.tcl --
# Simulate a classical game show problem:
# - Three doors are shown, one gives access to the prize
# - You chose a door
# - The game show host shows that one of the other doors
# does NOT contain the prize and asks you if you want
# to change your mind
#
# The statistically correct answer is: you should change your
# mind. It is counter-intuitive though that this should matter.
#
# This is a demonstration of the situation.
#
set trials 10000
#set trials 3
set otherDoorWins 0
set firstDoorWins 0
for {set i 0} {$i < $trials} {incr i} {
# Determine the winning door
set winning [expr {int(3 * rand())}]
# Select a door
set selected [expr {int(3 * rand())}]
# Now exclude a non-winning door
set excludables {}
foreach door {0 1 2} {
if { $door != $selected } {
lappend excludables $door
}
}
#puts "Selected: $selected"
#puts "Winning: $winning"
#puts "Excluding: $excludables"
set excludedIndex [expr {int(2 * rand())}]
if { [lindex $excludables $excludedIndex] == $winning } {
set excludedIndex [expr {1 - $excludedIndex}]
}
set remaining [lindex $excludables [expr {1 - $excludedIndex}]]
#puts "Remaining: $remaining"
# Check if we have won the prize or if the remaining door is the one
if { $winning == $remaining } {
incr otherDoorWins
}
if { $winning == $selected } {
incr firstDoorWins
}
}
puts "Total number of trials: $trials"
puts "First door wins: $firstDoorWins - [expr {$firstDoorWins/double($trials)}]"
puts "Other door wins: $otherDoorWins - [expr {$otherDoorWins/double($trials)}]"
