Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -5,7 +5,7 @@ Behind one door is a car; behind the others, goats.
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The car and the goats were placed randomly behind the doors before the show.
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;Rules of the game:
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;Rules of the game<nowiki>:</nowiki>
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After you have chosen a door, the door remains closed for the time being.
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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.
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@ -19,21 +19,21 @@ Imagine that you chose Door 1 and the host opens Door 3, which has a goat.
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He then asks you "Do you want to switch to Door Number 2?"
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;The question:
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;The question<nowiki>:</nowiki>
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Is it to your advantage to change your choice?
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;Note:
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;Note<nowiki>:</nowiki>
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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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;Task<nowiki>:</nowiki>
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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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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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;References:
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;References<nowiki>:</nowiki>
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:* Stefan Krauss, X. T. Wang, "The psychology of the Monty Hall problem: Discovering psychological mechanisms for solving a tenacious brain teaser.", Journal of Experimental Psychology: General, Vol 132(1), Mar 2003, 3-22 [https://doi.org/10.1037/0096-3445.132.1.3 DOI: 10.1037/0096-3445.132.1.3]
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:* A YouTube video: [https://www.youtube.com/watch?v=4Lb-6rxZxx0 Monty Hall Problem - Numberphile].
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<br><br>
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@ -2,14 +2,14 @@
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110 DEF NGames = 10000
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120 RANDOMIZE
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130 LET NWins = 0
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140 FOR Game = 0 TO NGames
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140 FOR Game = 1 TO NGames
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150 IF IsGameWon(0) <> 0 THEN LET NWins = NWins + 1
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160 NEXT Game
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170 PRINT "NOT switching doors wins car in ";
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180 PRINT USING "##.#": NWins / NGames * 100;
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190 PRINT "% of games."
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200 LET NWins = 0
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210 FOR Game = 0 TO NGames
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210 FOR Game = 1 TO NGames
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220 IF IsGameWon(1) <> 0 THEN LET NWins = NWins + 1
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230 NEXT Game
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240 PRINT "But switching doors wins car in ";
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@ -1,76 +0,0 @@
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-- Monty Hall Game
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with Ada.Text_Io; use Ada.Text_Io;
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with Ada.Float_Text_Io; use Ada.Float_Text_Io;
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with ada.Numerics.Discrete_Random;
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procedure Monty_Stats is
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Num_Iterations : Positive := 100000;
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type Action_Type is (Stay, Switch);
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type Prize_Type is (Goat, Pig, Car);
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type Door_Index is range 1..3;
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package Random_Prize is new Ada.Numerics.Discrete_Random(Door_Index);
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use Random_Prize;
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Seed : Generator;
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Doors : array(Door_Index) of Prize_Type;
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procedure Set_Prizes is
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Prize_Index : Door_Index;
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Booby_Prize : Prize_Type := Goat;
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begin
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Reset(Seed);
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Prize_Index := Random(Seed);
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Doors(Prize_Index) := Car;
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for I in Doors'range loop
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if I /= Prize_Index then
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Doors(I) := Booby_Prize;
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Booby_Prize := Prize_Type'Succ(Booby_Prize);
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end if;
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end loop;
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end Set_Prizes;
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function Play(Action : Action_Type) return Prize_Type is
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Chosen : Door_Index := Random(Seed);
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Monty : Door_Index;
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begin
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Set_Prizes;
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for I in Doors'range loop
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if I /= Chosen and Doors(I) /= Car then
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Monty := I;
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end if;
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end loop;
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if Action = Switch then
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for I in Doors'range loop
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if I /= Monty and I /= Chosen then
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Chosen := I;
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exit;
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end if;
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end loop;
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end if;
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return Doors(Chosen);
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end Play;
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Winners : Natural;
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Pct : Float;
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begin
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Winners := 0;
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for I in 1..Num_Iterations loop
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if Play(Stay) = Car then
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Winners := Winners + 1;
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end if;
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end loop;
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Put("Stay : count" & Natural'Image(Winners) & " = ");
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Pct := Float(Winners * 100) / Float(Num_Iterations);
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Put(Item => Pct, Aft => 2, Exp => 0);
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Put_Line("%");
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Winners := 0;
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for I in 1..Num_Iterations loop
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if Play(Switch) = Car then
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Winners := Winners + 1;
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end if;
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end loop;
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Put("Switch : count" & Natural'Image(Winners) & " = ");
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Pct := Float(Winners * 100) / Float(Num_Iterations);
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Put(Item => Pct, Aft => 2, Exp => 0);
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Put_Line("%");
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end Monty_Stats;
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@ -2,7 +2,7 @@ stay: 0
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swit: 0
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loop 1..1000 'i [
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lst: shuffle new [1 0 0]
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lst: shuffle [1 0 0]
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rand: random 0 2
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user: lst\[rand]
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remove 'lst rand
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@ -1,89 +0,0 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. monty-hall.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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78 Num-Games VALUE 1000000.
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*> These are needed so the values are passed to
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*> get-rand-int correctly.
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01 One PIC 9 VALUE 1.
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01 Three PIC 9 VALUE 3.
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01 doors-area.
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03 doors PIC 9 OCCURS 3 TIMES.
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01 choice PIC 9.
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01 shown PIC 9.
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01 winner PIC 9.
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01 switch-wins PIC 9(7).
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01 stay-wins PIC 9(7).
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01 stay-wins-percent PIC Z9.99.
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01 switch-wins-percent PIC Z9.99.
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PROCEDURE DIVISION.
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PERFORM Num-Games TIMES
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MOVE 0 TO doors (winner)
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CALL "get-rand-int" USING CONTENT One, Three,
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REFERENCE winner
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MOVE 1 TO doors (winner)
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CALL "get-rand-int" USING CONTENT One, Three,
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REFERENCE choice
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PERFORM WITH TEST AFTER
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UNTIL NOT(shown = winner OR choice)
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CALL "get-rand-int" USING CONTENT One, Three,
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REFERENCE shown
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END-PERFORM
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ADD doors (choice) TO stay-wins
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ADD doors (6 - choice - shown) TO switch-wins
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END-PERFORM
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COMPUTE stay-wins-percent ROUNDED =
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stay-wins / Num-Games * 100
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COMPUTE switch-wins-percent ROUNDED =
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switch-wins / Num-Games * 100
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DISPLAY "Staying wins " stay-wins " times ("
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stay-wins-percent "%)."
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DISPLAY "Switching wins " switch-wins " times ("
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switch-wins-percent "%)."
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.
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IDENTIFICATION DIVISION.
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PROGRAM-ID. get-rand-int.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 call-flag PIC X VALUE "Y".
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88 first-call VALUE "Y", FALSE "N".
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01 num-range PIC 9.
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LINKAGE SECTION.
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01 min-num PIC 9.
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01 max-num PIC 9.
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01 ret PIC 9.
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PROCEDURE DIVISION USING min-num, max-num, ret.
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*> Seed RANDOM once.
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IF first-call
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MOVE FUNCTION RANDOM(FUNCTION CURRENT-DATE (9:8))
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TO num-range
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SET first-call TO FALSE
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END-IF
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COMPUTE num-range = max-num - min-num + 1
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COMPUTE ret =
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FUNCTION MOD(FUNCTION RANDOM * 100000, num-range)
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+ min-num
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.
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END PROGRAM get-rand-int.
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END PROGRAM monty-hall.
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@ -1,51 +0,0 @@
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use Random;
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param doors: int = 3;
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config const games: int = 1000;
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config const maxTasks = 32;
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var numTasks = 1;
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while( games / numTasks > 1000000 && numTasks < maxTasks ) do numTasks += 1;
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const tasks = 1..#numTasks;
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const games_per_task = games / numTasks ;
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const remaining_games = games % numTasks ;
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var wins_by_stay: [tasks] int;
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coforall task in tasks {
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var rand = new RandomStream();
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for game in 1..#games_per_task {
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var player_door = (rand.getNext() * 1000): int % doors ;
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var winning_door = (rand.getNext() * 1000): int % doors ;
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if player_door == winning_door then
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wins_by_stay[ task ] += 1;
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}
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if task == tasks.last then {
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for game in 1..#remaining_games {
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var player_door = (rand.getNext() * 1000): int % doors ;
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var winning_door = (rand.getNext() * 1000): int % doors ;
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if player_door == winning_door then
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wins_by_stay[ task ] += 1;
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}
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}
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}
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var total_by_stay = + reduce wins_by_stay;
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var total_by_switch = games - total_by_stay;
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var percent_by_stay = ((total_by_stay: real) / games) * 100;
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var percent_by_switch = ((total_by_switch: real) / games) * 100;
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writeln( "Wins by staying: ", total_by_stay, " or ", percent_by_stay, "%" );
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writeln( "Wins by switching: ", total_by_switch, " or ", percent_by_switch, "%" );
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if ( total_by_stay > total_by_switch ){
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writeln( "Staying is the superior method." );
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} else if( total_by_stay < total_by_switch ){
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writeln( "Switching is the superior method." );
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} else {
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writeln( "Both methods are equal." );
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}
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@ -1,21 +0,0 @@
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use Random;
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config const numGames = 100_000_000;
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var switch, stick: uint;
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// have a separate RNG for each task; add together the results at the end
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forall i in 1..numGames
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with (var rand = new RandomStream(uint, parSafe = false), + reduce stick)
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{
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var chosen_door = rand.getNext() % 3;
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var winner_door = rand.getNext() % 3;
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if chosen_door == winner_door then
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stick += 1;
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}
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// if you lost by sticking it means you would have won by switching
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switch = numGames - stick;
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writeln("Over ", numGames, " games:\n - switching wins ",
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100.0*switch / numGames, "% of the time and\n - sticking wins ",
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100.0*stick / numGames, "% of the time");
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@ -1,15 +0,0 @@
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(defun montyhall (keep)
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(let ((prize (random 3))
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(choice (random 3)))
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(if keep (= prize choice)
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(/= prize choice))))
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(let ((cnt 0))
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(dotimes (i 10000)
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(and (montyhall t) (setq cnt (1+ cnt))))
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(message "Strategy keep: %.3f%%" (/ cnt 100.0)))
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(let ((cnt 0))
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(dotimes (i 10000)
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(and (montyhall nil) (setq cnt (1+ cnt))))
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(message "Strategy switch: %.3f%%" (/ cnt 100.0)))
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@ -1,20 +0,0 @@
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integer switchWins, stayWins
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switchWins = 0
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stayWins = 0
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integer winner, choice, shown
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for plays = 1 to 10000 do
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winner = rand(3)
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choice = rand(3)
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while 1 do
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shown = rand(3)
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if shown != winner and shown != choice then
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exit
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end if
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end while
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stayWins += choice = winner
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switchWins += 6-choice-shown = winner
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end for
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printf(1, "Switching wins %d times.\n", switchWins)
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printf(1, "Staying wins %d times.\n", stayWins)
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@ -40,17 +40,17 @@ _NGames = 10000
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float NWins = 0
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short Game
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FOR Game = 0 TO _NGames
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FOR Game = 1 TO _NGames
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IF fn IsGameWon(0) <> 0 THEN NWins = NWins + 1
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NEXT Game
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PRINT "NOT switching doors wins car in ";
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PRINT USING "##.##" ; NWins / 100 ;
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PRINT USING "##.##" ; NWins / _NGames * 100 ;
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PRINT " % of games."
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NWins = 0
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FOR Game = 0 TO _NGames
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FOR Game = 1 TO _NGames
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IF fn IsGameWon(1) <> 0 THEN NWins = NWins + 1
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NEXT Game
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PRINT "But switching doors wins car in ";
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@ -2,7 +2,7 @@
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20 LET N = 10000
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30 RANDOMIZE
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40 LET W = 0
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50 FOR G = 0 TO N
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50 FOR G = 1 TO N
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60 LET S = 0
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70 GOSUB 230
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80 IF V = 0 THEN 100
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@ -11,7 +11,7 @@
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110 PRINT "NOT switching doors wins car in";
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120 PRINT W/N*100; "per cent of games."
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130 LET W = 0
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140 FOR G = 0 TO N
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140 FOR G = 1 TO N
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150 LET S = 1
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160 GOSUB 230
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170 IF V = 0 THEN 190
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@ -36,7 +36,7 @@ END IsGameWon;
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BEGIN
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Randomize(0);
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NWins := 0;
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FOR Game := 0 TO NGames DO
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FOR Game := 1 TO NGames DO
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IF IsGameWon(FALSE) THEN
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NWins := NWins + 1
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END
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@ -46,7 +46,7 @@ BEGIN
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WriteString('% of games.');
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WriteLn;
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NWins := 0;
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FOR Game := 0 TO NGames DO
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FOR Game := 1 TO NGames DO
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IF IsGameWon(TRUE) THEN
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NWins := NWins + 1
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END
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@ -1,54 +0,0 @@
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#Declaring variables
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$intIterations = 10000
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$intKept = 0
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$intSwitched = 0
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#Creating a function
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Function Play-MontyHall()
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{
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#Using a .NET object for randomization
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$objRandom = New-Object -TypeName System.Random
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#Generating the winning door number
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$intWin = $objRandom.Next(1,4)
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#Generating the chosen door
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$intChoice = $objRandom.Next(1,4)
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#Generating the excluded number
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#Because there is no method to exclude a number from a range,
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#I let it re-generate in case it equals the winning number or
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#in case it equals the chosen door.
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$intLose = $objRandom.Next(1,4)
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While (($intLose -EQ $intWin) -OR ($intLose -EQ $intChoice))
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{$intLose = $objRandom.Next(1,4)}
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#Generating the 'other' door
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#Same logic applies as for the chosen door: it cannot be equal
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#to the winning door nor to the chosen door.
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$intSwitch = $objRandom.Next(1,4)
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While (($intSwitch -EQ $intLose) -OR ($intSwitch -EQ $intChoice))
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{$intSwitch = $objRandom.Next(1,4)}
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#Simple counters per win for both categories
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#Because a child scope cannot change variables in the parent
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#scope, the scope of the counters is expanded script-wide.
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If ($intChoice -EQ $intWin)
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{$script:intKept++}
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If ($intSwitch -EQ $intWin)
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{$script:intSwitched++}
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}
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#Looping the Monty Hall function for $intIterations times
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While ($intIterationCount -LT $intIterations)
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{
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Play-MontyHall
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$intIterationCount++
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}
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#Output
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Write-Host "Results through $intIterations iterations:"
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Write-Host "Keep : $intKept ($($intKept/$intIterations*100)%)"
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Write-Host "Switch: $intSwitched ($($intSwitched/$intIterations*100)%)"
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Write-Host ""
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