Monty Hall problem: Difference between revisions
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=={{header|BASIC}}==
==={{header|ANSI BASIC}}===
{{trans|
{{works with|Decimal BASIC}}
<syntaxhighlight lang="basic">
100 PROGRAM MontyHallProblem
110 DEF NGames = 10000
120 RANDOMIZE
130 LET NWins = 0
140 FOR Game = 0 TO NGames
150 IF IsGameWon(0) <> 0 THEN LET NWins = NWins + 1
160 NEXT Game
170 PRINT "NOT switching doors wins car in ";
180 PRINT USING "##.#": NWins / NGames * 100;
190 PRINT "% of games."
200 LET NWins = 0
210 FOR Game = 0 TO NGames
220 IF IsGameWon(1) <> 0 THEN LET NWins = NWins + 1
230 NEXT Game
240 PRINT "But switching doors wins car in ";
250 PRINT USING "##.#": NWins / NGames * 100;
260 PRINT "% of games."
270 END
280 REM ***
290 EXTERNAL FUNCTION IsGameWon(Sw)
300 REM Play one game.
310 REM Switching if and only if Sw <> 0.
320 REM Returns 1 if the game is won, 0 otherwise.
330 LET Car = INT(RND * 3) ! Randomly place car behind a door.
340 LET Player0 = INT(RND * 3) ! Player randomly chooses a door.
350 DO
360 LET Monty = INT(RND * 3) ! Monty opens door revealing a goat.
370 LOOP UNTIL (Monty <> Car) AND (Monty <> Player0)
380 IF Sw <> 0 THEN ! Player switches TO remaining door.
390 DO
400 LET Player = INT(RND * 3)
410 LOOP UNTIL (Player <> Player0) AND (Player <> Monty)
420 ELSE
430 LET Player = Player0 ! Player sticks with original door.
440 END IF
450 IF Player = Car THEN
460 LET IsGameWon = 1
470 ELSE
480 LET IsGameWon = 0
490 END IF
500 END FUNCTION
</syntaxhighlight>
{{out}}(example)
<pre>
NOT switching doors wins car in 32.3% of games.
But switching doors wins car in 67.3% of games.
</pre>
==={{header|BASIC256}}===
Line 569 ⟶ 595:
end
</syntaxhighlight>
==={{header|BBC BASIC}}===
<syntaxhighlight lang="bbcbasic"> total% = 10000
FOR trial% = 1 TO total%
prize_door% = RND(3) : REM. The prize is behind this door
guess_door% = RND(3) : REM. The contestant guesses this door
IF prize_door% = guess_door% THEN
REM. The contestant guessed right, reveal either of the others
reveal_door% = RND(2)
IF prize_door% = 1 reveal_door% += 1
IF prize_door% = 2 AND reveal_door% = 2 reveal_door% = 3
ELSE
REM. The contestant guessed wrong, so reveal the non-prize door
reveal_door% = prize_door% EOR guess_door%
ENDIF
stick_door% = guess_door% : REM. The sticker doesn't change his mind
swap_door% = guess_door% EOR reveal_door% : REM. but the swapper does
IF stick_door% = prize_door% sticker% += 1
IF swap_door% = prize_door% swapper% += 1
NEXT trial%
PRINT "After a total of ";total%;" trials,"
PRINT "The 'sticker' won ";sticker%;" times (";INT(sticker%/total%*100);"%)"
PRINT "The 'swapper' won ";swapper%;" times (";INT(swapper%/total%*100);"%)"</syntaxhighlight>
Output:
<pre>
After a total of 10000 trials,
The 'sticker' won 3379 times (33%)
The 'swapper' won 6621 times (66%)
</pre>
==={{header|Euphoria}}===
<syntaxhighlight lang="euphoria">integer switchWins, stayWins
switchWins = 0
stayWins = 0
integer winner, choice, shown
for plays = 1 to 10000 do
winner = rand(3)
choice = rand(3)
while 1 do
shown = rand(3)
if shown != winner and shown != choice then
exit
end if
end while
stayWins += choice = winner
switchWins += 6-choice-shown = winner
end for
printf(1, "Switching wins %d times.\n", switchWins)
printf(1, "Staying wins %d times.\n", stayWins)
</syntaxhighlight>
{{out}} (sample)
<pre>
Switching wins 6697 times.
Staying wins 3303 times.
</pre>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">
' version 19-01-2019
' compile with: fbc -s console
Const As Integer max = 1000000
Randomize Timer
Dim As UInteger i, car_door, chosen_door, montys_door, stay, switch
For i = 1 To max
car_door = Fix(Rnd * 3) + 1
chosen_door = Fix(Rnd * 3) + 1
If car_door <> chosen_door Then
montys_door = 6 - car_door - chosen_door
Else
Do
montys_door = Fix(Rnd * 3) + 1
Loop Until montys_door <> car_door
End If
'Print car_door,chosen_door,montys_door
' stay
If car_door = chosen_door Then stay += 1
' switch
If car_door = 6 - montys_door - chosen_door Then switch +=1
Next
Print Using "If you stick to your choice, you have a ##.## percent" _
+ " chance to win"; stay / max * 100
Print Using "If you switched, you have a ##.## percent chance to win"; _
switch / max * 100
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
</syntaxhighlight>
{{out}}
<pre>
If you stick to your choice, you have a 33.32 percent chance to win
If you switched, you have a 66.68 percent chance to win
</pre>
==={{header|IS-BASIC}}===
Line 586 ⟶ 713:
230 PRINT "Wins not changing doors:";NOTCHANGING,NOTCHANGING/NUMGAMES*100;"% of total."
240 PRINT "Wins changing doors:",CHANGING,CHANGING/NUMGAMES*100;"% of total."</syntaxhighlight>
==={{header|Liberty BASIC}}===
{{trans|Quick BASIC}}
{{works with|Just BASIC}}
<syntaxhighlight lang="lb">
DIM doors(3) '0 is a goat, 1 is a car
total = 10000 'set desired number of iterations
switchWins = 0
stayWins = 0
FOR plays = 1 TO total
winner = INT(RND(1) * 3) + 1
doors(winner) = 1'put a winner in a random door
choice = INT(RND(1) * 3) + 1'pick a door, any door
DO
shown = INT(RND(1) * 3) + 1
'don't show the winner or the choice
LOOP WHILE doors(shown) = 1 OR shown = choice
if doors(choice) = 1 then
stayWins = stayWins + 1 'if you won by staying, count it
else
switchWins = switchWins + 1'could have switched to win
end if
doors(winner) = 0 'clear the doors for the next test
NEXT
PRINT "Result for ";total;" games."
PRINT "Switching wins "; switchWins; " times."
PRINT "Staying wins "; stayWins; " times."
</syntaxhighlight>
{{out}} (example)
<pre>
Result for 10000 games.
Switching wins 6634 times.
Staying wins 3366 times.</pre>
==={{header|Minimal BASIC}}===
{{trans|ANSI BASIC}}
{{works with|BASICA}}
<syntaxhighlight lang="basic">
10 REM Monty Hall problem
20 LET N = 10000
30 RANDOMIZE
40 LET W = 0
50 FOR G = 0 TO N
60 LET S = 0
70 GOSUB 230
80 IF V = 0 THEN 100
90 LET W = W+1
100 NEXT G
110 PRINT "NOT switching doors wins car in";
120 PRINT W/N*100; "per cent of games."
130 LET W = 0
140 FOR G = 0 TO N
150 LET S = 1
160 GOSUB 230
170 IF V = 0 THEN 190
180 LET W = W+1
190 NEXT G
200 PRINT "But switching doors wins car in";
210 PRINT W/N*100; "per cent of games."
220 END
230 REM ** Is game won?
240 REM Play one game.
250 REM Switching if and only if S <> 0.
260 REM Randomly place car behind a door.
270 LET C = INT(RND*3)
280 REM Player randomly chooses a door.
290 LET P0 = INT(RND*3)
300 REM Monty opens door revealing a goat.
310 LET M = INT(RND*3)
320 IF M = C THEN 310
330 IF M = P0 THEN 310
340 IF S = 0 THEN 410
350 REM Player switches to remaining door.
360 LET P = INT(RND*3)
370 IF P = P0 THEN 360
380 IF P = M THEN 360
390 GOTO 430
400 REM Player sticks with original door.
410 LET P = P0
420 REM Victory?
430 IF P <> C THEN 460
440 LET V = 1
450 RETURN
460 LET V = 0
470 RETURN
</syntaxhighlight>
==={{header|PureBasic}}===
<syntaxhighlight lang="purebasic">Structure wins
stay.i
redecide.i
EndStructure
#goat = 0
#car = 1
Procedure MontyHall(*results.wins)
Dim Doors(2)
Doors(Random(2)) = #car
player = Random(2)
Select Doors(player)
Case #car
*results\redecide + #goat
*results\stay + #car
Case #goat
*results\redecide + #car
*results\stay + #goat
EndSelect
EndProcedure
OpenConsole()
#Tries = 1000000
Define results.wins
For i = 1 To #Tries
MontyHall(@results)
Next
PrintN("Trial runs for each option: " + Str(#Tries))
PrintN("Wins when redeciding: " + Str(results\redecide) + " (" + StrD(results\redecide / #Tries * 100, 2) + "% chance)")
PrintN("Wins when sticking: " + Str(results\stay) + " (" + StrD(results\stay / #Tries * 100, 2) + "% chance)")
Input()</syntaxhighlight>
Output:<pre>Trial runs for each option: 1000000
Wins when redeciding: 666459 (66.65% chance)
Wins when sticking: 333541 (33.35% chance)</pre>
==={{header|QuickBASIC}}===
{{works with|QuickBasic|4.5}}
{{trans|Java}}
<syntaxhighlight lang="qbasic">RANDOMIZE TIMER
DIM doors(3) '0 is a goat, 1 is a car
CLS
switchWins = 0
stayWins = 0
FOR plays = 0 TO 32767
winner = INT(RND * 3) + 1
doors(winner) = 1'put a winner in a random door
choice = INT(RND * 3) + 1'pick a door, any door
DO
shown = INT(RND * 3) + 1
'don't show the winner or the choice
LOOP WHILE doors(shown) = 1 OR shown = choice
stayWins = stayWins + doors(choice) 'if you won by staying, count it
switchWins = switchWins + doors(3 - choice - shown) 'could have switched to win
doors(winner) = 0 'clear the doors for the next test
NEXT plays
PRINT "Switching wins"; switchWins; "times."
PRINT "Staying wins"; stayWins; "times."</syntaxhighlight>
Output:
<pre>Switching wins 21805 times.
Staying wins 10963 times.</pre>
==={{header|Run BASIC}}===
{{trans|Quick BASIC}}
{{works with|Just BASIC}}
<syntaxhighlight lang="runbasic">
input "Number of tries;";tries ' gimme the number of iterations
FOR plays = 1 TO tries
winner = INT(RND(1) * 3) + 1
doors(winner) = 1 'put a winner in a random door
choice = INT(RND(1) * 3) + 1 'pick a door please
[DO] shown = INT(RND(1) * 3) + 1
' ------------------------------------------
' don't show the winner or the choice
if doors(shown) = 1 then goto [DO]
if shown = choice then goto [DO]
if doors(choice) = 1 then
stayWins = stayWins + 1 ' if you won by staying, count it
else
switchWins = switchWins + 1 ' could have switched to win
end if
doors(winner) = 0 'clear the doors for the next test
NEXT
PRINT " Result for ";tries;" games."
PRINT "Switching wins ";switchWins; " times."
PRINT " Staying wins ";stayWins; " times."</syntaxhighlight>
==={{header|Sinclair ZX81 BASIC}}===
Line 615 ⟶ 922:
STICK SWITCH
341 659</pre>
==={{header|True BASIC}}===
<syntaxhighlight lang="
DIM puertas(3)
LET numTiradas = 1000000
FOR i =
LET pta_coche = INT(RND * 3) + 1
LET puertas(pta_coche) = 1
LET pta_elegida = INT(RND * 3) + 1
DO
LET pta_montys =
LOOP WHILE puertas(pta_montys) = 1 OR pta_montys = pta_elegida
IF puertas(pta_elegida) = 1 THEN
LET cambia = cambia + 1
ELSE
LET permanece = permanece + 1
END IF
LET puertas(pta_coche) = 0
NEXT i
PRINT "Cambiar gana el"; permanece / numTiradas * 100; "% de las veces."
PRINT "Mantenerse gana el"; cambia / numTiradas * 100; "% de las veces."
END</syntaxhighlight>
==={{header|Yabasic}}===
<syntaxhighlight lang="yabasic">
numTiradas = 1000000
for i = 1 to numTiradas
pta_coche = int(ran(3)) + 1
pta_elegida = int(ran(3)) + 1
if pta_coche <> pta_elegida then
pta_montys = 6 - pta_coche - pta_elegida
else
repeat
pta_montys = int(ran(3)) + 1
until pta_montys <> pta_coche
end if
// manteenr elección
if pta_coche = pta_elegida then permanece = permanece + 1 : fi
// cambiar elección
if pta_coche = 6 - pta_montys - pta_elegida then cambia = cambia + 1 : fi
next i
print "Si mantiene su eleccion, tiene un ", permanece / numTiradas * 100, "% de probabilidades de ganar."
print "Si cambia, tiene un ", cambia / numTiradas * 100, "% de probabilidades de ganar."
end
</syntaxhighlight>
=={{header|C}}==
<syntaxhighlight lang="c">//Evidence of the Monty Hall solution of marquinho1986 in C [github.com/marquinho1986]
Line 1,351 ⟶ 1,651:
=={{header|EasyLang}}==
{{trans|FreeBASIC}}
<syntaxhighlight
max = 1000000
for i = 1 to max
car_door =
chosen_door =
if car_door <> chosen_door
montys_door = 6 - car_door - chosen_door
else
repeat
montys_door =
until montys_door <> car_door
.
Line 1,852 ⟶ 2,152:
<pre>Switching wins 66595 times.
Staying wins 33405 times.</pre>
=={{header|F_Sharp|F#}}==
Line 2,065 ⟶ 2,339:
Chance of winning by not switching is 32.82%
Chance of winning by switching is 67.18%
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Monty_Hall_problem}}
Line 2,832 ⟶ 3,065:
(0.33241,0.66759)
</pre>
=={{header|K}}==
<syntaxhighlight lang="k">
montyhall:{t:,/ 1_ x {`prng@`t[];ch:1?3;pr:1?3;sw:1?2;$[sw;a:ch=pr;a:~(ch=pr)];a}\0N;("KEEP %";(+/t)%x;"SWAP %";(+/~t)%x)}
montyhall 100000
</syntaxhighlight>
=={{header|Kotlin}}==
Line 2,870 ⟶ 3,109:
Switching wins 666330 times
</pre>
=={{header|Lua}}==
Line 3,136 ⟶ 3,341:
<syntaxhighlight lang="maxscript">Stay strategy:33.77%
Switch strategy:66.84%</syntaxhighlight>
=={{header|Modula-2}}==
{{trans|XPL0|<code>CARDINAL</code> (unsigned integer) used instead of integer.}}
{{works with|ADW Modula-2|any (Compile with the linker option ''Console Application'').}}
<syntaxhighlight lang="modula2">
MODULE MontyHallProblem;
FROM STextIO IMPORT
WriteLn, WriteString;
FROM RandomNumbers IMPORT
Randomize, Rnd;
FROM SRealIO IMPORT
WriteFixed;
CONST
NGames = 10000; (* number of games simulated *)
VAR
NWins, Game: CARDINAL;
PROCEDURE IsGameWon(Sw: BOOLEAN): BOOLEAN;
(* Play one game. *)
VAR
Car, Player, Player0, Monty: CARDINAL;
BEGIN
Car := Rnd(3); (* Randomly place car behind a door. *)
Player0 := Rnd(3); (* Player randomly chooses a door. *)
REPEAT
Monty := Rnd(3); (* Monty opens door revealing a goat. *)
UNTIL (Monty <> Car) AND (Monty <> Player0);
IF Sw THEN
(* Player switches to remaining door. *)
REPEAT
Player := Rnd(3);
UNTIL (Player <> Player0) AND (Player <> Monty)
ELSE
Player := Player0 (* Player sticks with original door. *)
END;
RETURN (Player = Car);
END IsGameWon;
BEGIN
Randomize(0);
NWins := 0;
FOR Game := 0 TO NGames DO
IF IsGameWon(FALSE) THEN
NWins := NWins + 1
END
END;
WriteString('NOT switching doors wins car in ');
WriteFixed(FLOAT(NWins) / FLOAT(NGames) * 100.0, 1, 4);
WriteString('% of games.');
WriteLn;
NWins := 0;
FOR Game := 0 TO NGames DO
IF IsGameWon(TRUE) THEN
NWins := NWins + 1
END
END;
WriteString('But switching doors wins car in ');
WriteFixed(FLOAT(NWins) / FLOAT(NGames) * 100.0, 1, 4);
WriteString('% of games.');
WriteLn;
END MontyHallProblem.
</syntaxhighlight>
{{out}}(example)
<pre>
NOT switching doors wins car in 33.4% of games.
But switching doors wins car in 66.5% of games.
</pre>
=={{header|NetRexx}}==
Line 3,703 ⟶ 3,978:
Staying wins 332 out of 1000.
</pre>
=={{header|Python}}==
Line 4,243 ⟶ 4,477:
<pre>Staying wins 33.84% of the time.
Switching wins 66.16% of the time.</pre>
=={{header|Rust}}==
Line 4,495 ⟶ 4,705:
Staying wins 3346 times
</pre>
=={{header|SETL}}==
<syntaxhighlight lang="setl">program monty_hall;
setrandom(0);
n_simulations := 100000;
print('Chance to win:');
print('When switching doors:', win_chance(true, n_simulations) * 100, '%');
print('When not switching doors:', win_chance(false, n_simulations) * 100, '%');
proc win_chance(switch, n_simulations);
wins := 0;
loop for i in [1..n_simulations] do
wins +:= if simulate(switch) then 1 else 0 end;
end loop;
return wins / n_simulations;
end proc;
proc simulate(switch);
doors := {1, 2, 3};
car := random doors;
goats := doors less car;
choice := random doors;
opened := random (goats less choice);
if switch then
choice := arb (doors less choice less opened);
end if;
return choice = car;
end proc;
end program;</syntaxhighlight>
{{out}}
<pre>Chance to win:
When switching doors: 66.584 %
When not switching doors: 33.093 %</pre>
=={{header|Sidef}}==
Line 5,009 ⟶ 5,254:
=={{header|Vedit macro language}}==
{{trans|
Vedit macro language does not have random number generator, so one is implemented in subroutine RANDOM (the algorithm was taken from ANSI C library).
Line 5,161 ⟶ 5,406:
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">def
int Game,
include c:\cxpl\codes;
int Switch;
int Car, Player, Player0, Monty;
Line 5,176 ⟶ 5,421:
until Player # Player0 and Player # Monty
else Player:= Player0; \player sticks with original door
];
[Format(2,1);
NWins:= 0;
for Game:= 0 to NGames-1 do
if IsGameWon(false) then NWins:= NWins+1;
Text(0, "NOT switching doors wins car in ");
RlOut(0, float(NWins)/float(NGames)*100.0);
Text(0, "% of games.^M^J");
NWins:= 0;
for Game:= 0 to NGames-1 do
if IsGameWon(true) then NWins:= NWins+1;
Text(0, "But switching doors wins car in ");
RlOut(0, float(NWins)/float(NGames)*100.0);
Text(0, "% of games.^M^J");
]</syntaxhighlight>
Line 5,195 ⟶ 5,442:
Example output:
<pre>
But switching doors wins car in 66.7% of games.
</pre>
=={{header|Zig}}==
<syntaxhighlight lang="zig">const std = @import("std");
const number_of_simulations: u32 = 10_000_000;
pub fn main() !void {
var stick_wins: u32 = 0;
var switch_wins: u32 = 0;
var doors = [3]bool{ true, false, false };
var t = std.rand.DefaultPrng.init(42);
const r = t.random();
var guess: u8 = undefined;
var door_shown: u8 = undefined;
for (0..number_of_simulations) |_| {
std.rand.Random.shuffle(r, bool, &doors);
guess = r.intRangeAtMost(u8, 0, 2);
door_shown = r.intRangeAtMost(u8, 0, 2);
while (!doors[door_shown] and door_shown != guess) door_shown = r.intRangeAtMost(u8, 0, 2);
if (doors[guess]) {
stick_wins += 1;
} else {
switch_wins += 1;
}
}
std.debug.print("After {} simulations:\nStick wins: {}\nSwitch wins: {}\n", .{ number_of_simulations, stick_wins, switch_wins });
}</syntaxhighlight>
| |||