monty_hall.sh

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#!/bin/bash
##! Author:           Pieter van der Star (info@pietervanderstar.nl)
##! Modifications by: (unmodified)
##! 
##! This program is free software: you can redistribute it and/or modify
##! it under the terms of the GNU Affero General Public License as
##! published by the Free Software Foundation, either version 3 of the
##! License, or (at your option) any later version.
##! 
##! This program is distributed in the hope that it will be useful,
##! but WITHOUT ANY WARRANTY; without even the implied warranty of
##! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##! GNU Affero General Public License for more details.
##! 
##! You should have received a copy of the GNU Affero General Public License
##! along with this program.  If not, see <https://www.gnu.org/licenses/>.
 
#Changelog:
#┏━━━━━━━━━━━━━━━┯━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┯━━━━━━━━━━━━━━━━━━━━━━━━━━┓
#┃    3 jun 2022 │ Updated to work in bash                  │   Pieter van der Star    ┃
#┠───────────────┼──────────────────────────────────────────┼──────────────────────────┨
#┃    3 jun 2022 │ First release                            │   Pieter van der Star    ┃
#┠───────────────┼──────────────────────────────────────────┼──────────────────────────┨
#┃   21 feb 2024 │ Added doxygen documenation comments      │   Pieter van der Star    ┃
#┗━━━━━━━━━━━━━━━┷━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┷━━━━━━━━━━━━━━━━━━━━━━━━━━┛
 
##! @file
##! @brief This script simulates the Monty Hall problem to help decide on a strategy.
 
echo " __  __                   _               _   _           _   _ "
echo "|  \\/  |   ___    _ __   | |_   _   _    | | | |   __ _  | | | |"
echo "| |\\/| |  / _ \\  | '_ \\  | __| | | | |   | |_| |  / _\` | | | | |"
echo "| |  | | | (_) | | | | | | |_  | |_| |   |  _  | | (_| | | | | |"
echo "|_|  |_|  \\___/  |_| |_|  \\__|  \\__, |   |_| |_|  \\__,_| |_| |_|"
echo "                                |___/"
echo 
echo "                        _       _"
echo " _ __    _ __    ___   | |__   | |   ___   _ __ ___  "
echo "| '_ \\  | '__|  / _ \\  | '_ \\  | |  / _ \\ | '_ \` _ \\ "
echo "| |_) | | |    | (_) | | |_) | | | |  __/ | | | | | |"
echo "| .__/  |_|     \\___/  |_.__/  |_|  \\___| |_| |_| |_|"
echo "|_|"
 
 
 
 
echo "Behind one of the doors is a car you can win."
echo "Behind which door is the car?"
echo "  ___    ___    ___"
echo " |   |  |   |  |   |"
echo " | A |  | B |  | C |"
echo " |   |  |   |  |   |"
echo " |___|  |___|  |___|"
echo 
echo "You choose A."
echo "Let's open another door."
echo 
echo "  ___    ___    ___"
echo " |   |  |   | ||   |   )_)"
echo " | A |  | B | ||(\\_|__'\\_\\"
echo " |   |  |   | |||      | \""
echo " |___|  |___| |||\"\"\"\"\"\"|"
 
echo "Now do you want to switch?"
echo "Should you?"
echo "We can run this a couple of times, keep track of when we win if we"
echo "switch and if we don't and see what happens."
 
if [ $# -lt 1 ]; then
    echo "Running 100 times, you can change this by passing a number as first argument."
    numrounds=100;
else 
    numrounds=$1;
fi
if [ $# -lt 2 ]; then
    verbosity=0;
else 
    verbosity=$2;
fi
 
##! @brief Swap your choice from the chosen one to the other unrevealed door.
##! @param $arg1 Position of the prize.
##! @param $arg2 Position of the choice.
##! @returns New choice position.
function swap {
    prizepos=$1;
    guess=$2;
    opening=0;
    while [ $guess -eq $opening ] || [ $prizepos -eq $opening ]; do
        opening=$((opening + 1))
        opening=$((opening % 3))
    done
    if [ $verbosity -ge 2 ]; then
        echo "opening $opening"
    fi
    newchoice=$((guess+1));
    newchoice=$((newchoice % 3));
    while [ $newchoice -eq $opening ]; do
        newchoice=$((newchoice + 1));
        newchoice=$((newchoice % 3));
    done
    return $newchoice;
}
 
##! Number of wins for player A
winsa=0;
##! Number of wins for player B
winsb=0;
##! Position of the prize
prizepos=0;
##! Original guess
guess=0;
##! Counter for the number of rounds already done.
i=1;
##! Counts how often the random number was 0. Used for statistics at the end of the script.
rand[0]=0;
##! Counts how often the random number was 1. Used for statistics at the end of the script.
rand[1]=0;
##! Counts how often the random number was 2. Used for statistics at the end of the script.
rand[2]=0;
while [ $i -le $numrounds ]; do
    prizepos=$(($RANDOM % 3));
    rand[$prizepos]=$((rand[$prizepos]+1));
    guess=$(($RANDOM % 3));
    rand[$guess]=$((rand[$guess]+1));
    swap $prizepos $guess
    newguess=$?
    if [ $verbosity -ge 1 ]; then
        echo "prize: $prizepos a: $guess b: $newguess"
        echo "---------------------------------------"
    fi
    if [ $guess -eq $prizepos ]; then 
        winsa=$((winsa+1));
    fi
    if [ $newguess -eq $prizepos ]; then 
        winsb=$((winsb+1));
    fi
    if [[ $verbosity -ge 1 && $numrounds -lt 1000 ]]; then
        apercent=$((winsa*100/i))
        bpercent=$((winsb*100/i))
        echo "keep: $winsa $apercent% swap: $winsb $bpercent%";
    fi
    if [ $((i%1000)) -eq 0 ]; then
        apercent=$((winsa*100/i))
        bpercent=$((winsb*100/i))
        if [ $verbosity -ge 1 ]; then
            echo "keep: $winsa $apercent% swap: $winsb $bpercent%";
        fi
            print "progress: $(((i*1000/numrounds)/10)).$(((i*1000/numrounds)%10))%";
    fi
    ((i+=1))
done
 
    ((i-=1))
##! Percentage of wins for player A
apercent=$((winsa*100/i))
##! Percentage of wins for player B
bpercent=$((winsb*100/i))
printf "Let's look at the results. How often do you win:\n"
printf "                            |keep|swap|\n"
printf "                            |----|----|\n"
printf "                            |%4d|%4d|\n" $winsa $winsb
printf "                            |%3d%%|%3d%%|\n" $apercent $bpercent
echo "Assuming you ran this for enough tests, you see you should swap."
 
printf "Random number distribution:\n"
printf "                            |  0  |  1  |  2  |\n"
printf "                            |-----|-----|-----|\n"
printf "                            |%5d|%5d|%5d|\n" ${rand[0]} ${rand[1]} ${rand[2]}
printf "                            |%2d.%d%%|%2d.%d%%|%2d.%d%%|\n" $(((rand[0]*1000/(2*i)/10))) $(((rand[0]*1000/(2*i)%10))) $(((rand[1]*1000/(2*i)/10))) $(((rand[1]*1000/(2*i)%10))) $(((rand[2]*1000/(2*i)/10))) $(((rand[2]*1000/(2*i)%10)))