2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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@ -1,10 +1,16 @@
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[[File:Monte_Hall_problem.jpg|500px||right]]
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Run random simulations of the [[wp:Monty_Hall_problem|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.
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: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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice? ([http://www.usd.edu/~xtwang/Papers/MontyHallPaper.pdf Krauss and Wang 2003:10])
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Note that the player may initially choose any of the three doors (not just Door 1), that the host opens a different door revealing a goat (not necessarily Door 3), and that he gives the player a second choice between the two remaining unopened doors.
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;Task:
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Simulate at least a thousand games using three doors for each strategy <u>and show the results</u> in such a way as to make it easy to compare the effects of each strategy.
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;Reference:
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* [https://www.youtube.com/watch?v=4Lb-6rxZxx0 Monty Hall Problem - Numberphile]. (Video).
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<br><br>
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@ -1,6 +1,5 @@
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defmodule MontyHall do
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def simulate(n) do
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:random.seed(:os.timestamp)
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{stay, switch} = simulate(n, 0, 0)
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:io.format "Staying wins ~w times (~.3f%)~n", [stay, 100 * stay / n]
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:io.format "Switching wins ~w times (~.3f%)~n", [switch, 100 * switch / n]
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@ -9,7 +8,7 @@ defmodule MontyHall do
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defp simulate(0, stay, switch), do: {stay, switch}
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defp simulate(n, stay, switch) do
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doors = Enum.shuffle([:goat, :goat, :car])
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guess = :random.uniform(3) - 1
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guess = :rand.uniform(3) - 1
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[choice] = [0,1,2] -- [guess, shown(doors, guess)]
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if Enum.at(doors, choice) == :car, do: simulate(n-1, stay, switch+1),
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else: simulate(n-1, stay+1, switch)
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@ -5,7 +5,7 @@ simulate=:3 :0
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scenario=. ((pick@-.,])pick,pick) bind x
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stayWin=. =/@}.
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switchWin=. pick@(x -. }:) = {:
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r=.(stayWin,switchWin)@scenario"0 i.1000
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r=.(stayWin,switchWin)@scenario"0 i.y
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labels=. ];.2 'limit stay switch '
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smoutput labels,.":"0 y,+/r
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)
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50
Task/Monty-Hall-problem/Pascal/monty-hall-problem.pascal
Normal file
50
Task/Monty-Hall-problem/Pascal/monty-hall-problem.pascal
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@ -0,0 +1,50 @@
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program MontyHall;
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uses
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sysutils;
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const
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NumGames = 1000;
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{Randomly pick a door(a number between 0 and 2}
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function PickDoor(): Integer;
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begin
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Exit(Trunc(Random * 3));
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end;
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var
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i: Integer;
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PrizeDoor: Integer;
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ChosenDoor: Integer;
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WinsChangingDoors: Integer = 0;
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WinsNotChangingDoors: Integer = 0;
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begin
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Randomize;
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for i := 0 to NumGames - 1 do
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begin
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//randomly picks the prize door
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PrizeDoor := PickDoor;
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//randomly chooses a door
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ChosenDoor := PickDoor;
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//if the strategy is not changing doors the only way to win is if the chosen
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//door is the one with the prize
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if ChosenDoor = PrizeDoor then
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Inc(WinsNotChangingDoors);
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//if the strategy is changing doors the only way to win is if we choose one
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//of the two doors that hasn't the prize, because when we change we change to the prize door.
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//The opened door doesn't have a prize
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if ChosenDoor <> PrizeDoor then
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Inc(WinsChangingDoors);
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end;
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Writeln('Num of games:' + IntToStr(NumGames));
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Writeln('Wins not changing doors:' + IntToStr(WinsNotChangingDoors) + ', ' +
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FloatToStr((WinsNotChangingDoors / NumGames) * 100) + '% of total.');
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Writeln('Wins changing doors:' + IntToStr(WinsChangingDoors) + ', ' +
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FloatToStr((WinsChangingDoors / NumGames) * 100) + '% of total.');
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end.
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@ -1,14 +1,14 @@
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/*REXX program simulates a # of trials of the classic Monty Hall problem*/
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parse arg t .; if t=='' then t=1000000 /*Not specified? Then use default*/
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wins.=0 /*wins.0=stay; wins.1=switching.*/
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/*door values: 0=goat 1=car */
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do t /*perform this loop T times. */
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door.=0 /*set all doors to zero. */
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car=random(1,3); door.car=1 /*TV show hides a car randomly. */
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?=random(1,3) ; _=door.? /*contestant picks a random door.*/
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wins._=wins._+1 /*bump the type of win strategy. */
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end /*DO t*/
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say 'switching wins ' format(wins.0/t*100,,1)"% of the time."
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say ' staying wins ' format(wins.1/t*100,,1)"% of the time."; say
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say 'performed' t "times." /*stick a fork in it, we're done.*
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/*REXX program simulates a number of trials of the classic Monty Hall problem. */
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parse arg # d . /*obtain the optional args from the CL.*/
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if #=='' | #=="," then #=1000000 /*Not specified? Then use 1 million. */
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if d=='' | d=="," then d= 3 /* " " " " three doors.*/
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wins.=0 /*wins.0 ≡ stay, wins.1 ≡ switching.*/
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do #; door. =0 /*initialize all doors to a value of 0.*/
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car=random(1, d); door.car=1 /*the TV show hides a car randomly. */
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?=random(1, d); _=door.? /*the contestant picks a random door. */
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wins._ = wins._ + 1 /*bump the type of win strategy. */
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end /*#*/ /* [↑] perform the loop # times. */
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/* [↑] door values: 0≡goat 1≡car */
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say 'switching wins ' format(wins.0 / # * 100, , 1)"% of the time."
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say ' staying wins ' format(wins.1 / # * 100, , 1)"% of the time." ; say
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say 'performed ' # " times with " d ' doors.' /*stick a fork in it, we're all done. */
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