Monty Hall problem: Difference between revisions
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Line 47:
{{trans|Python}}
<
V sw = 0
Line 71:
print(‘Stay = ’stay)
print(‘Switch = ’sw)</
=={{header|8086 Assembly}}==
<
puts: equ 9 ; MS-DOS syscall to print a string
cpu 8086
Line 153:
nsw: db 'When not switching doors: $'
db '*****'
number: db 13,10,'$'</
{{out}}
Line 161:
=={{header|ActionScript}}==
<
import flash.display.Sprite;
Line 192:
}
}
}</
Output:
<pre>Switching wins 18788 times. (62.626666666666665%)
Line 198:
=={{header|Ada}}==
<
with Ada.Text_Io; use Ada.Text_Io;
Line 273:
Put_Line("%");
end Monty_Stats;</
Results
<pre>Stay : count 34308 = 34.31%
Line 284:
{{works with|ALGOL 68G|Any - tested with release mk15-0.8b.fc9.i386}}
{{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386}}
<
PROC brand = (INT n)INT: 1 + ENTIER (n * random);
Line 337:
print(("Changing: ", percent(change winning), new line ));
print(("New random choice: ", percent(random winning), new line ))
)</
Sample output:
<pre>
Line 346:
=={{header|APL}}==
<
[1] ⍝0: Monthy Hall problem
[2] ⍝1: http://rosettacode.org/wiki/Monty_Hall_problem
Line 360:
[12] ⎕←'Swap: ',(2⍕100×(swap÷runs)),'% it''s a car'
[13] ⎕←'Stay: ',(2⍕100×(stay÷runs)),'% it''s a car'
∇</
<pre>
Run 100000
Line 371:
{{trans|Nim}}
<
swit: 0
Line 394:
print ["Stay:" stay]
print ["Switch:" swit]</
{{out}}
Line 402:
=={{header|AutoHotkey}}==
<
Iterations = 1000
Loop, %Iterations%
Line 435:
Mode := Mode = 2 ? 2*rand - 1: Mode
Return, Mode = 1 ? 6 - guess - show = actual : guess = actual
}</
Sample output:
<pre>
Line 448:
=={{header|AWK}}==
<
# Monty Hall problem
Line 504:
simulate(RAND)
}</
Sample output:
<
Monty Hall problem simulation:
Line 514:
Algorithm switch: prize count = 6655, = 66.55%
Algorithm random: prize count = 4991, = 49.91%
bash$</
=={{header|BASIC}}==
{{works with|QuickBasic|4.5}}
{{trans|Java}}
<
DIM doors(3) '0 is a goat, 1 is a car
CLS
Line 537:
NEXT plays
PRINT "Switching wins"; switchWins; "times."
PRINT "Staying wins"; stayWins; "times."</
Output:
<pre>Switching wins 21805 times.
Line 544:
==={{header|BASIC256}}===
<syntaxhighlight lang="basic256">
numTiradas = 1000000
permanece = 0
Line 568:
print "Si cambia, tiene un "; cambia / numTiradas * 100; "% de probabilidades de ganar."
end
</syntaxhighlight>
==={{header|IS-BASIC}}===
<
110 RANDOMIZE
120 LET NUMGAMES=1000
Line 585:
220 PRINT "Num of games:";NUMGAMES
230 PRINT "Wins not changing doors:";NOTCHANGING,NOTCHANGING/NUMGAMES*100;"% of total."
240 PRINT "Wins changing doors:",CHANGING,CHANGING/NUMGAMES*100;"% of total."</
==={{header|Sinclair ZX81 BASIC}}===
Line 596:
switcher wins;</pre>
but I take it that the point is to demonstrate the outcome to people who may <i>not</i> see that that's what is going on. I have therefore written the program in a deliberately naïve style, not assuming anything.
<
20 PRINT "STICK","SWITCH"
30 LET STICK=0
Line 610:
130 IF NEWGUESS=CAR THEN LET SWITCH=SWITCH+1
140 NEXT I
150 PRINT AT 2,0;STICK,SWITCH</
{{out}}
<pre> WINS IF YOU
Line 618:
==={{header|True BASIC}}===
<
LET numTiradas = 1000000
Line 640:
PRINT "Mantenerse gana el"; cambia / numTiradas * 100; "% de las veces."
END
</syntaxhighlight>
=={{header|BBC BASIC}}==
<
FOR trial% = 1 TO total%
prize_door% = RND(3) : REM. The prize is behind this door
Line 664:
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);"%)"</
Output:
<pre>
Line 674:
=={{header|C}}==
<
#include <stdio.h>
Line 697:
printf("\nAfter %u games, I won %u by switching. That is %f%%. ", GAMES, winsbyswitch, (float)winsbyswitch*100.0/(float)i);
}
</syntaxhighlight>
Output of one run:
Line 705:
=={{header|C sharp|C#}}==
{{trans|Java}}
<
class Program
Line 740:
Console.Out.WriteLine("Switching wins " + switchWins + " times.");
}
}</
Sample output:
<pre>
Line 748:
=={{header|C++}}==
<
#include <cstdlib>
#include <ctime>
Line 804:
int wins_change = check(games, true);
std::cout << "staying: " << 100.0*wins_stay/games << "%, changing: " << 100.0*wins_change/games << "%\n";
}</
Sample output:
staying: 33.73%, changing: 66.9%
=={{header|Chapel}}==
<
param doors: int = 3;
Line 860:
writeln( "Both methods are equal." );
}
</syntaxhighlight>
Sample output:
<pre>
Line 869:
=={{header|Clojure}}==
<
(:use [clojure.contrib.seq :only (shuffle)]))
Line 884:
(range times))]
(str "wins " wins " times out of " times)))
</syntaxhighlight>
<
staying: wins 337 times out of 1000
nil
Line 891:
switching: wins 638 times out of 1000
nil
</syntaxhighlight>
=={{header|COBOL}}==
{{works with|OpenCOBOL}}
<
PROGRAM-ID. monty-hall.
Line 983:
END PROGRAM get-rand-int.
END PROGRAM monty-hall.</
{{out}}
Line 992:
=={{header|ColdFusion}}==
<
function runmontyhall(num_tests) {
// number of wins when player switches after original selection
Line 1,033:
}
runmontyhall(10000);
</cfscript></
Output:
<pre>
Line 1,040:
=={{header|Common Lisp}}==
<
(let ((array (make-array 3
:element-type 'bit
Line 1,054:
(defun won? (array i)
(= 1 (bit array i)))</
<
for round = (make-round)
for initial = (random 3)
Line 1,072:
#1# 1/100))))))
Stay: 33.2716%
Switch: 66.6593%</
<
;Find out how often we win if we always switch
(defun rand-elt (s)
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(defun monty-trials (n)
(count t (loop for x from 1 to n collect (monty))))
</syntaxhighlight>
=={{header|D}}==
<
void main() {
Line 1,122:
writefln("Switching/Staying wins: %d %d", switchWins, stayWins);
}</
{{out}}
<pre>Switching/Staying wins: 66609 33391</pre>
Line 1,128:
=={{header|Dart}}==
The class Game attempts to hide the implementation as much as possible, the play() function does not use any specifics of the implementation.
<
class Game {
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play(10000,false);
play(10000,true);
}</
<pre>playing without switching won 33.32%
playing with switching won 67.63%</pre>
Line 1,218:
{{works with|Delphi|XE10}}
{{libheader| System.SysUtils}}
<
{$APPTYPE CONSOLE}
Line 1,267:
WriteLn('Switching wins ' + IntToStr(switchWins) + ' times.');
end.
</syntaxhighlight>
{{out}}
<pre>Staying wins 333253 times.
Line 1,276:
{{trans|C#}}
<
var stayWins = 0
Line 1,295:
print("Staying wins \(stayWins) times.")
print("Switching wins \(switchWins) times.")</
{{out}}
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=={{header|Eiffel}}==
<
note
description: "[
Line 1,617:
end
</syntaxhighlight>
{{out}}
<pre>
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=={{header|Elixir}}==
<
def simulate(n) do
{stay, switch} = simulate(n, 0, 0)
Line 1,659:
end
MontyHall.simulate(10000)</
{{out}}
Line 1,669:
=={{header|Emacs Lisp}}==
{{trans|Picolisp}}
<
(let ((prize (random 3))
(choice (random 3)))
Line 1,683:
(dotimes (i 10000)
(and (montyhall nil) (setq cnt (1+ cnt))))
(message "Strategy switch: %.3f%%" (/ cnt 100.0)))</
{{out}}
Line 1,691:
=={{header|Erlang}}==
<
-export([main/0]).
Line 1,718:
false -> OpenDoor
end.
</syntaxhighlight>
Sample Output:
<pre>Switching wins 66595 times.
Line 1,724:
=={{header|Euphoria}}==
<
switchWins = 0
stayWins = 0
Line 1,744:
printf(1, "Switching wins %d times\n", switchWins)
printf(1, "Staying wins %d times\n", stayWins)
</syntaxhighlight>
Sample Output:<br />
:Switching wins 6697 times<br />
Line 1,751:
=={{header|F_Sharp|F#}}==
I don't bother with having Monty "pick" a door, since you only win if you initially pick a loser in the switch strategy and you only win if you initially pick a winner in the stay strategy so there doesn't seem to be much sense in playing around the background having Monty "pick" doors. Makes it pretty simple to see why it's always good to switch.
<
let monty nSims =
let rnd = new Random()
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let Wins (f:unit -> int) = seq {for i in [1..nSims] -> f()} |> Seq.sum
printfn "Stay: %d wins out of %d - Switch: %d wins out of %d" (Wins StayGame) nSims (Wins SwitchGame) nSims</
Sample Output:
<pre>Stay: 332874 wins out of 1000000 - Switch: 667369 wins out of 1000000</pre>
I had a very polite suggestion that I simulate Monty's "pick" so I'm putting in a version that does that. I compare the outcome with my original outcome and, unsurprisingly, show that this is essentially a noop that has no bearing on the output, but I (kind of) get where the request is coming from so here's that version...
<
let rnd = new Random()
let MontyPick winner pick =
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let Wins (f:unit -> int) = seq {for i in [1..nSims] -> f()} |> Seq.sum
printfn "Stay: %d wins out of %d - Switch: %d wins out of %d" (Wins StayGame) nSims (Wins SwitchGame) nSims</
=={{header|Forth}}==
===version 1===
<
variable stay-wins
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cr switch-wins @ . [char] / emit . ." switching wins" ;
1000 trials</
or in iForth:
<
0 value switch-wins
Line 1,837:
dup 0 ?DO trial LOOP
CR stay-wins DEC. ." / " dup DEC. ." staying wins,"
CR switch-wins DEC. ." / " DEC. ." switching wins." ;</
With output:
Line 1,848:
{{works with|GNU Forth}}
While Forthers are known (and regarded) for always simplifying the problem, I think version 1 is missing the point here. The optimization can only be done if one already understands the game. For what it's worth, here is a simulation that takes all the turns of the game.
<
here seed !
Line 1,876:
' keep IS applyStrategy run ." Keep door => " .result cr
' switch IS applyStrategy run ." Switch door => " .result cr
bye</
{{out}}
Line 1,886:
=={{header|Fortran}}==
{{works with|Fortran|90 and later}}
<
IMPLICIT NONE
Line 1,931:
WRITE(*, "(A,F6.2,A)") "Chance of winning by switching is", real(switchcount)/trials*100, "%"
END PROGRAM MONTYHALL</
Sample Output
Chance of winning by not switching is 32.82%
Line 1,937:
=={{header|FreeBASIC}}==
<
' compile with: fbc -s console
Line 1,971:
Print : Print "hit any key to end program"
Sleep
End</
{{out}}
<pre>If you stick to your choice, you have a 33.32 percent chance to win
Line 1,985:
=={{header|Go}}==
<
import (
Line 2,011:
fmt.Printf("Keeper Wins: %d (%3.2f%%)",
keeperWins, (float32(keeperWins) / floatGames * 100))
}</
Output:
<pre>
Line 2,019:
=={{header|Haskell}}==
<
trials :: Int
Line 2,052:
percent n ++ "% of the time."
percent n = show $ round $
100 * (fromIntegral n) / (fromIntegral trials)</
{{libheader|mtl}}
With a <tt>State</tt> monad, we can avoid having to explicitly pass around the <tt>StdGen</tt> so often. <tt>play</tt> and <tt>cars</tt> can be rewritten as follows:
<
play :: Bool -> State StdGen Door
Line 2,077:
cars n switch g = (numcars, new_g)
where numcars = length $ filter (== Car) prize_list
(prize_list, new_g) = runState (replicateM n (play switch)) g</
Sample output (for either implementation):
<
The stay strategy succeeds 34% of the time.</
=={{header|HicEst}}==
<
DLG(NameEdit = plays, DNum=1, Button='Go')
Line 2,115:
WRITE(ClipBoard, Name) plays, switchWins, stayWins
END</
<
! plays=1E4; switchWins=6673; stayWins=3327;
! plays=1E5; switchWins=66811; stayWins=33189;
! plays=1E6; switchWins=667167; stayWins=332833;</
=={{header|Icon}} and {{header|Unicon}}==
<
rounds := integer(arglist[1]) | 10000
Line 2,140:
write("Strategy 2 'Switching' won ", real(strategy2) / rounds )
end</
Sample Output:<pre>Monty Hall simulation for 10000 rounds.
Line 2,147:
=={{header|Io}}==
<
switchWins := 0
doors := 3
Line 2,169:
.. "Keeping the same door won #{keepWins} times.\n"\
.. "Game played #{times} times with #{doors} doors.") interpolate println
</syntaxhighlight>
Sample output:<pre>Switching to the other door won 66935 times.
Keeping the same door won 33065 times.
Line 2,178:
The core of this simulation is picking a random item from a set
<
And, of course, we will be picking one door from three doors
<
But note that the simulation code should work just as well with more doors.
Line 2,188:
Anyways the scenario where the contestant's switch or stay strategy makes a difference is where Monty has picked from the doors which are neither the user's door nor the car's door.
<
(Here, I have decided that the result will be a list of three door numbers. The first number in that list is the number Monty picks, the second number represents the door the user picked, and the third number represents the door where the car is hidden.)
Line 2,194:
Once we have our simulation test results for the scenario, we need to test if staying would win. In other words we need to test if the user's first choice matches where the car was hidden:
<
In other words: drop the first element from the list representing our test results -- this leaves us with the user's choice and the door where the car was hidden -- and then insert the verb <code>=</code> between those two values.
Line 2,200:
We also need to test if switching would win. In other words, we need to test if the user would pick the car from the doors other than the one Monty picked and the one the user originally picked:
<
In other words, start with our list of all doors and then remove the door the monty picked and the door the user picked, and then pick one of the remaining doors at random (the pick at random part is only significant if there were originally more than 3 doors) and see if that matches the door where the car is.
Line 2,206:
Finally, we need to run the simulation a thousand times and count how many times each strategy wins:
<
320 680</
Or, we could bundle this all up as a defined word. Here, the (optional) left argument "names" the doors and the right argument says how many simulations to run:
<
1 2 3 simulate y
:
Line 2,221:
labels=. ];.2 'limit stay switch '
smoutput labels,.":"0 y,+/r
)</
Example use:
<
limit 1000
stay 304
switch 696 </
Or, with more doors (and assuming this does not require new rules about how Monty behaves or how the player behaves):
<
limit 1000
stay 233
switch 388 </
=={{header|Java}}==
<
public class Monty{
public static void main(String[] args){
Line 2,262:
System.out.println("Staying wins " + stayWins + " times.");
}
}</
Output:
<pre>Switching wins 21924 times.
Line 2,273:
This solution can test with n doors, the difference in probability for switching is shown to diminish as the number of doors increases.
<
function montyhall(tests, doors) {
'use strict';
Line 2,312:
};
}
</syntaxhighlight>
{{out}}
<
montyhall(1000, 3)
Object {stayWins: "349 34.9%", switchWins: "651 65.1%"}
Line 2,322:
montyhall(1000, 5)
Object {stayWins: "202 20.2%", switchWins: "265 26.5%"}
</syntaxhighlight>
Slight modification of the script above for modularity inside of HTML.
<
<body>
Line 2,373:
}
</script></
'''Output:'''
<
First Door Wins: 346 | 34.6%
Switching Door Wins: 654 | 65.4%</
===Basic Solution===
<!-- http://blog.dreasgrech.com/2011/09/simulating-monty-hall-problem.html -->
<
var totalGames = 10000,
selectDoor = function () {
Line 2,427:
console.log("Wins when not switching door", play(false));
console.log("Wins when switching door", play(true));
</syntaxhighlight>
{{out}}
<
Playing 10000 games
Wins when not switching door 3326
Wins when switching door 6630
</syntaxhighlight>
=={{header|jq}}==
Line 2,453:
This solution is based on the observation: {{quote|If I initially guessed the winning door and didn't switch, or if I initially guessed a losing door but then switched, I've won.}}
<
input as $r
| if $r < . then $r else rand end;
Line 2,470:
"Switching wins \(.switchWins) times\n" ;
1e3, 1e6 | logical_montyHall</
====Simulation====
{{trans|Kotlin}}
<
input as $r
| if $r < . then $r else rand end;
Line 2,499:
"Switching wins \(.switchWins) times\n" ;
1e3, 1e6 | montyHall</
{{out}}
<pre>
Line 2,517:
'''The Literal Simulation Function'''
<
function play_mh_literal{T<:Integer}(ncur::T=3, ncar::T=1)
Line 2,539:
return (isstickwin, isswitchwin)
end
</syntaxhighlight>
'''The Clean Simulation Function'''
<syntaxhighlight lang="julia">
function play_mh_clean{T<:Integer}(ncur::T=3, ncar::T=1)
ncar < ncur || throw(DomainError())
Line 2,554:
return (isstickwin, isswitchwin)
end
</syntaxhighlight>
'''Supporting Functions'''
<syntaxhighlight lang="julia">
function mh_results{T<:Integer}(ncur::T, ncar::T,
nruns::T, play_mh::Function)
Line 2,602:
return nothing
end
</syntaxhighlight>
'''Main'''
<syntaxhighlight lang="julia">
for i in 3:5, j in 1:(i-2)
show_simulation(i, j, 10^5)
end
</syntaxhighlight>
This code shows, for a variety of configurations, the results for 3 solutions: literal simulation, clean simulation, analytic. Stick is the percentage of times that the player wins a car by sticking to an initial choice. Switch is the winning percentage the comes with switching one's selection following the goat reveal. Improvement is the ratio of switch to stick.
Line 2,677:
=={{header|Kotlin}}==
{{trans|Java}}
<
import java.util.Random
Line 2,704:
fun main(args: Array<String>) {
montyHall(1_000_000)
}</
Sample output:
{{out}}
Line 2,714:
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">
'adapted from BASIC solution
DIM doors(3) '0 is a goat, 1 is a car
Line 2,740:
PRINT "Switching wins "; switchWins; " times."
PRINT "Staying wins "; stayWins; " times."
</syntaxhighlight>
Output:
<pre>
Line 2,748:
=={{header|Lua}}==
<
local car = math.random(3)
local pchoice = player.choice()
Line 2,764:
for i = 1, 20000 do playgame(player) end
print(player.wins)
end</
=={{header|Lua/Torch}}==
<
local car = torch.LongTensor(n):random(3) -- door with car
local choice = torch.LongTensor(n):random(3) -- player's choice
Line 2,793:
end
montyStats(1e7)</
Output for 10 million samples:
Line 2,802:
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
Module CheckIt {
Enum Strat {Stay, Random, Switch}
Line 2,847:
}
CheckIt
</syntaxhighlight>
{{out}}
<pre>
Line 2,856:
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
Module[{r, winningDoors, firstChoices, nStayWins, nSwitchWins, s},
r := RandomInteger[{1, 3}, nGames];
Line 2,865:
Grid[{{"Strategy", "Wins", "Win %"}, {"Stay", Row[{nStayWins, "/", nGames}], s=N[100 nStayWins/nGames]},
{"Switch", Row[{nSwitchWins, "/", nGames}], 100 - s}}, Frame -> All]]</
;Usage:
<syntaxhighlight lang
[[File:MontyHall.jpg]]
=={{header|MATLAB}}==
<
assert(numDoors > 2);
Line 2,928:
disp(sprintf('Switch win percentage: %f%%\nStay win percentage: %f%%\n', [switchedDoors(1)/sum(switchedDoors),stayed(1)/sum(stayed)] * 100));
end</
Output:
<
Switch win percentage: 66.705972%
Stay win percentage: 33.420062%</
=={{header|MAXScript}}==
<
(
doors = #(false, false, false)
Line 2,960:
iterations = 10000
format ("Stay strategy:%\%\n") (iterate iterations false)
format ("Switch strategy:%\%\n") (iterate iterations true)</
Output:
<
Switch strategy:66.84%</
=={{header|NetRexx}}==
Line 2,969:
{{trans|REXX}}
{{trans|PL/I}}
<
* 30.08.2013 Walter Pachl translated from Java/REXX/PL/I
**********************************************************************/
Line 3,003:
method r3 static
rand=random()
return rand.nextInt(3) + 1</
Output
<pre>
Line 3,012:
=={{header|Nim}}==
{{trans|Python}}
<
randomize()
Line 3,049:
echo "Stay = ",stay
echo "Switch = ",switch</
Output:
<pre>Stay = 337
Line 3,055:
=={{header|OCaml}}==
<
type door = Car | Goat
Line 3,083:
strat (100. *. (float n /. float trials)) in
msg "switch" switch;
msg "stay" stay</
=={{header|PARI/GP}}==
<
my(stay=0,change=0);
for(i=1,trials,
Line 3,098:
};
test(1e4)</
Output:
Line 3,106:
=={{header|Pascal}}==
<
uses
Line 3,156:
end.
</syntaxhighlight>
Output:
Line 3,165:
=={{header|Perl}}==
<
use strict;
my $trials = 10000;
Line 3,191:
print "Stay win ratio " . (100.0 * $stay/$trials) . "\n";
print "Switch win ratio " . (100.0 * $switch/$trials) . "\n";</
=={{header|Phix}}==
Modified copy of [[Monty_Hall_problem#Euphoria|Euphoria]]
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">swapWins</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stayWins</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">winner</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">choice</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">reveal</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">other</span>
Line 3,212:
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Stay: %,d\nSwap: %,d\nTime: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">stayWins</span><span style="color: #0000FF;">,</span><span style="color: #000000;">swapWins</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">elapsed</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span><span style="color: #0000FF;">)})</span>
<!--</
{{out}}
<pre>
Line 3,221:
=={{header|PHP}}==
<
function montyhall($iterations){
$switch_win = 0;
Line 3,247:
montyhall(10000);
?></
Output:
<pre>Iterations: 10000 - Stayed wins: 3331 (33.31%) - Switched wins: 6669 (66.69%)</pre>
=={{header|Picat}}==
<
_ = random2(), % different seed
member(Rounds,[1000,10_000,100_000,1_000_000,10_000_000]),
Line 3,280:
choice(N) = random(1,N).
pick(L) = L[random(1,L.len)].</
{{out}}
Line 3,304:
=={{header|PicoLisp}}==
<
(let (Prize (rand 1 3) Choice (rand 1 3))
(if Keep # Keeping the first choice?
Line 3,322:
(do 10000 (and (montyHall NIL) (inc 'Cnt)))
(format Cnt 2) )
" %" )</
Output:
<pre>Strategy KEEP -> 33.01 %
Line 3,329:
=={{header|PL/I}}==
{{trans|Java}}
<
ziegen: Proc Options(main);
/* REXX ***************************************************************
Line 3,366:
Return(res);
End;
End;</
Output:
<pre>
Line 3,376:
Use ghostscript or print this to a postscript printer
<syntaxhighlight lang="postscript">%!PS
/Courier % name the desired font
20 selectfont % choose the size in points and establish
Line 3,411:
showpage % print all on the page</
Sample output:
Line 3,420:
=={{header|PowerShell}}==
<
$intIterations = 10000
$intKept = 0
Line 3,473:
Write-Host "Keep : $intKept ($($intKept/$intIterations*100)%)"
Write-Host "Switch: $intSwitched ($($intSwitched/$intIterations*100)%)"
Write-Host ""</
Output:
<pre>Results through 10000 iterations:
Line 3,481:
=={{header|Prolog}}==
{{works with|GNU Prolog}}
<syntaxhighlight lang="prolog">
:- initialization(main).
Line 3,525:
win_count(1000, false, 0, StayTotal),
format('Staying wins ~d out of 1000.\n', [StayTotal]).
</syntaxhighlight>
{{out}}
<pre>
Line 3,533:
=={{header|PureBasic}}==
<
stay.i
redecide.i
Line 3,567:
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()</
Output:<pre>Trial runs for each option: 1000000
Line 3,574:
=={{header|Python}}==
<
I could understand the explanation of the Monty Hall problem
but needed some more evidence
Line 3,618:
print sum(monty_hall(randrange(3), switch=True)
for x in range(iterations)),
print "out of", iterations, "times.\n"</
Sample output:
<pre>Monty Hall problem simulation:
Line 3,630:
===Python 3 version: ===
Another (simpler in my opinion), way to do this is below, also in python 3:
<
#1 represents a car
#0 represent a goat
Line 3,662:
print("Stay =",stay)
print("Switch = ",switch)
#Done by Sam Witton 09/04/2014</
=={{header|Quackery}}==
<
[ 0 ( number of cars when not changing choice )
Line 3,683:
say "Approximate ratio of car wins with strategy A over strategy B: "
swap 100 round
vulgar$ echo$ cr ] is trials ( n --> )</
{{out}}
Line 3,708:
=={{header|R}}==
<
N <- 10000 # trials
true_answers <- sample(1:3, N, replace=TRUE)
Line 3,765:
change <- runif(N) >= .5
random_switch[change] <- other_door[change]
summary(random_switch == true_answers)</
Line 3,831:
=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
Line 3,868:
(for-each test-strategy (list keep-choice change-choice))
</syntaxhighlight>
Sample Output:
Line 3,881:
This implementation is parametric over the number of doors. [[wp:Monty_Hall_problem#Increasing_the_number_of_doors|Increasing the number of doors in play makes the superiority of the switch strategy even more obvious]].
<syntaxhighlight lang="raku"
enum Strategy <Stay Switch>;
Line 3,919:
'% of the time.'
}
}</
{{out}}
<pre>With 3 doors:
Line 3,931:
===version 1===
{{trans|Java}}
<
* 30.08.2013 Walter Pachl derived from Java
**********************************************************************/
Line 3,961:
Say 'NetRexx:' time('E') 'seconds'
Exit
r3: Return random(2)+1</
Output for 1000000 samples:
<pre>
Line 3,985:
===version 2===
<
parse arg # seed . /*obtain the optional args from the CL.*/
if #=='' | #=="," then #= 1000000 /*Not specified? Then 1 million trials*/
Line 3,998:
say 'switching wins ' format(wins.0 / # * 100, , 1)"% of the time."
say ' staying wins ' format(wins.1 / # * 100, , 1)"% of the time." ; say
say 'performed ' # " times with 3 doors." /*stick a fork in it, we're all done. */</
{{out|output|text= when using the default inputs:}}
<pre>
Line 4,008:
=={{header|Ring}}==
<
total = 10000
swapper = 0
Line 4,031:
see "the 'sticker' won " + sticker + " times (" + floor(sticker/total*100) + "%)" + nl
see "the 'swapper' won " + swapper + " times (" + floor(swapper/total*100) + "%)" + nl
</syntaxhighlight>
Output:
<pre>
Line 4,041:
=={{header|Ruby}}==
<
stay = switch = 0 #sum of each strategy's wins
Line 4,067:
puts "Staying wins %.2f%% of the time." % (100.0 * stay / n)
puts "Switching wins %.2f%% of the time." % (100.0 * switch / n)</
Sample Output:
<pre>Staying wins 33.84% of the time.
Line 4,073:
=={{header|Run BASIC}}==
<
input "Number of tries;";tries ' gimme the number of iterations
Line 4,094:
PRINT " Result for ";tries;" games."
PRINT "Switching wins ";switchWins; " times."
PRINT " Staying wins ";stayWins; " times."</
=={{header|Rust}}==
{{libheader|rand}}
<
use rand::Rng;
use rand::seq::SliceRandom;
Line 4,124:
percent = switch_wins as f64 / GAMES as f64 * 100.0
);
}</
=={{header|Scala}}==
<
object MontyHallSimulation {
Line 4,159:
switchStrategyWins, percent(switchStrategyWins)))
}
}</
Sample:
Line 4,170:
=={{header|Scheme}}==
<
(define (random-permutation list)
(if (null? list)
Line 4,239:
;; > (compare-strategies 1000000)
;; (stay-strategy won with probability 33.3638 %
;; and switch-strategy won with probability 66.716 %)</
=={{header|Scilab}}==
{{incorrect|scilab|Several syntax and logical errors: switch is a keyword, the variable a is never used, and in the result the sum does not yield 100000 (which is logical since both result are taken from different random samples, but they should not). Also some useless complexity: the nested if can be simplified with logical operators.}}
<syntaxhighlight lang="text">// How it works:
// MontyHall() is a function with argument switch:
// it will be called 100000 times with switch=%T,
Line 4,281:
end
disp("Switching, one wins"+ascii(10)+string(wins_switch)+" games out of "+string(games))
disp("Staying, one wins"+ascii(10)+string(wins_stay)+" games out of "+string(games))</
Output:
Line 4,294:
=={{header|Seed7}}==
<
const proc: main is func
Line 4,316:
writeln("Switching wins " <& switchWins <& " times");
writeln("Staying wins " <& stayWins <& " times");
end func;</
Output:
Line 4,325:
=={{header|Sidef}}==
<
var switchWins = (var stayWins = 0) # sum of each strategy's wins
Line 4,345:
say ("Staying wins %.2f%% of the time." % (100.0 * stayWins / n))
say ("Switching wins %.2f%% of the time." % (100.0 * switchWins / n))</
{{out}}
<pre>
Line 4,354:
=={{header|SPAD}}==
{{works with|FriCAS, OpenAxiom, Axiom}}
<syntaxhighlight lang="spad">
montyHall(n) ==
wd:=[1+random(3) for j in 1..n]
Line 4,361:
p:=(st/n)::DoubleFloat
FORMAT(nil,"stay: ~A, switch: ~A",p,1-p)$Lisp
</syntaxhighlight>
Domain:[http://fricas.github.io/api/Integer.html?highlight=random Integer]
Line 4,384:
=={{header|Stata}}==
<
set obs 1000000
gen car=runiformint(1,3)
Line 4,393:
gen choice2=6-shown-choice1
gen succ2=car==choice2
tabstat succ1 succ2, s(mean)</
'''Output'''
Line 4,404:
=={{header|Swift}}==
<
func montyHall(doors: Int = 3, guess: Int, switch: Bool) -> Bool {
Line 4,426:
print("Switching would've won \((Double(switchWins) / Double(switchResults.count)) * 100)% of games")
print("Not switching would've won \(((Double(switchResults.count - switchWins)) / Double(switchResults.count)) * 100)% of games")</
{{out}}
Line 4,434:
=={{header|Tcl}}==
A simple way of dealing with this one, based on knowledge of the underlying probabilistic system, is to use code like this:
<
for {set i 0} {$i<$total} {incr i} {
if {int(rand()*3) == int(rand()*3)} {
Line 4,443:
}
puts "Estimate: $stay/$total wins for staying strategy"
puts "Estimate: $change/$total wins for changing strategy"</
But that's not really the point of this challenge; it should add the concealing factors too so that we're simulating not just the solution to the game, but also the game itself. (Note that we are using Tcl's lists here to simulate sets.)
We include a third strategy that is proposed by some people (who haven't thought much about it) for this game: just picking at random between all the doors offered by Monty the second time round.
<
# Utility: pick a random item from a list
Line 4,512:
puts "Estimate: $stay/$total wins for 'staying' strategy"
puts "Estimate: $change/$total wins for 'changing' strategy"
puts "Estimate: $anew/$total wins for 'picking anew' strategy"</
This might then produce output like
Estimate: 3340/10000 wins for 'staying' strategy
Line 4,521:
=={{header|Transact SQL}}==
T-SQL for general case:
<syntaxhighlight lang="transact sql">
---- BEGIN ------------
create table MONTY_HALL(
Line 4,563:
from MONTY_HALL
---- END ------------
</syntaxhighlight>
<pre>
% OF WINS FOR KEEP % OF WINS FOR CHANGE % OF WINS FOR RANDOM
Line 4,572:
=={{header|UNIX Shell}}==
{{works with|bash|2.x| and most bash-compatible unix shells}}
<
# Simulates the "monty hall" probability paradox and shows results.
# http://en.wikipedia.org/wiki/Monty_Hall_problem
Line 4,643:
echo "Wins (switch to remaining door): $num_win"
echo "Losses (first guess was correct): $num_lose"
exit 0</
Output of a few runs:
<pre>
Line 4,697:
for the switching strategy.
<
#import nat
#import flo
Line 4,713:
#show+
main = ~&plrTS/<'stay: ','switch: '> format* <staying_wins,switching_wins></
Output will vary slightly for each run due to randomness.
<pre>
Line 4,724:
Vedit macro language does not have random number generator, so one is implemented in subroutine RANDOM (the algorithm was taken from ANSI C library).
<
#91 = 3 // random numbers in range 0 to 2
#1 = 0 // wins for "always stay" strategy
Line 4,757:
#93 = 0x7fffffff % 48271
#90 = (48271 * (#90 % #92) - #93 * (#90 / #92)) & 0x7fffffff
return ((#90 & 0xffff) * #91 / 0x10000)</
Sample output:
Line 4,767:
=={{header|Wren}}==
{{trans|Kotlin}}
<
var montyHall = Fn.new { |games|
Line 4,790:
}
montyHall.call(1e6)</
{{out}}
Line 4,801:
=={{header|X++}}==
<
int changeWins = 0;
Line 4,834:
print strFmt("Staying wins %1 times.", noChangeWins);
pause;
</syntaxhighlight>
Output:
Line 4,841:
=={{header|XPL0}}==
<
int Game, Wins;
include c:\cxpl\codes;
Line 4,871:
RlOut(0, float(Wins)/float(Games)*100.0);
Text(0, "% of games.^M^J");
]</
Example output:
Line 4,881:
=={{header|Yabasic}}==
<
numTiradas = 1000000
Line 4,903:
print "Si cambia, tiene un ", cambia / numTiradas * 100, "% de probabilidades de ganar."
end
</syntaxhighlight>
=={{header|zkl}}==
{{trans|Go}}
<
reg switcherWins=0, keeperWins=0, shown=0;
Line 4,924:
switcherWins, switcherWins.toFloat() / games * 100).println();
"Keeper Wins: %,d (%3.2f%%)".fmt(
keeperWins, keeperWins.toFloat() / games * 100).println();</
{{out}}
<pre>
|