Sleeping Beauty problem: Difference between revisions

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=={{header|Go}}==
=={{header|Go}}==
{{trans|Wren}}
{{trans|Wren}}
{{libheader|Go-rcu}}
<lang go>package main
<lang go>package main


Revision as of 08:45, 12 June 2021

Task
Sleeping Beauty problem
You are encouraged to solve this task according to the task description, using any language you may know.
Background on the task

In decision theory, The Sleeping Beauty Problem is a problem invented by Arnold Zoboff and first publicized on Usenet. The experimental subject, named Sleeping Beauty, agrees to an experiment as follows: Sleeping Beauty volunteers to be put into a deep sleep on a Sunday. There is then a fair coin toss. If this coin toss comes up heads, Sleeping Beauty wakes once (on Monday) and is asked to estimate the probability that the coin toss was heads. Her estimate is recorded and she is then put back to sleep for 2 days until Wednesday, at which time the experiment's results are tallied.

If instead the coin toss is tails, Sleeping Beauty wakes as before on Monday and asked to estimate the probability the coin toss was heads, but is then given a drug which makes her forget that she had been woken on Monday before being put back to sleep again. She then wakes only 1 day later, on Tuesday. She is then asked (on Tuesday) again to guess the probability that the coin toss was heads or tails. She is then put back to sleep and awakes as before 1 day later, on Wednesday.

Some decision makers have argued that since the coin toss was fair Sleeping Beauty should always estimate the probability of heads as 1/2, since she does not have any additional information. Others have disagreed, saying that if Sleeping Beauty knows the study design she also knows that she is twice as likely to wake up and be asked to estimate the coin flip on tails than on heads, so the estimate should be 1/3 heads.

Task

Given the above problem, create a Monte Carlo estimate of the actual results. The program should find the proportion of heads on waking and asking Sleeping Beauty for an estimate, as a credence or as a percentage of the times Sleeping Beauty is asked the question.


Arturo

Translation of: Wren

<lang rebol>sleepingBeauty: function [reps][ 

   wakings: 0
   heads: 0
   do.times: reps [
       coin: random 0 1
       wakings: wakings + 1
       if? coin = 0 -> heads: heads + 1
       else -> wakings: wakings + 1
   ]
   print ["Wakings over" reps "repetitions =" wakings]
   return 100.0 * heads//wakings

]

pc: sleepingBeauty 100000 print ["Percentage probability of heads on waking =" pc "%"]</lang>

Output:
Wakings over 100000 repetitions = 150096 
Percentage probability of heads on waking = 33.24805457840316 %

C++

<lang cpp>#include <iostream>

  1. include <random>

int main() { 

   std::cout.imbue(std::locale(""));
   const int experiments = 1000000;
   std::random_device dev;
   std::default_random_engine engine(dev());
   std::uniform_int_distribution<int> distribution(0, 1);
   int heads = 0, wakenings = 0;
   for (int i = 0; i < experiments; ++i) {
       ++wakenings;
       switch (distribution(engine)) {
       case 0: // heads
           ++heads;
           break;
       case 1: // tails
           ++wakenings;
           break;
       }
   }
   std::cout << "Wakenings over " << experiments
             << " experiments: " << wakenings << '\n';
   std::cout << "Sleeping Beauty should estimate a credence of: "
             << double(heads) / wakenings << '\n';

}</lang>

Output:
Wakenings over 1,000,000 experiments: 1,500,090
Sleeping Beauty should estimate a credence of: 0.333253

BASIC

BASIC256

Translation of: FreeBASIC

<lang BASIC256> iteraciones = 1000000 cara = 0 dormir = 0

for i = 1 to iteraciones lanza_moneda = int(rand * 2) dormir = dormir + 1 if lanza_moneda = 1 then cara = cara + 1 else dormir = dormir + 1 end if next i

print "Wakings over "; iteraciones; " repetitions = "; dormir print "Percentage probability of heads on waking = "; (cara/dormir*100); "%" end </lang>

Output:
Igual que la entrada de FreeBASIC.

FreeBASIC

<lang freebasic> Const iteraciones = 1000000 Randomize Timer Dim As Uinteger cara = 0, dormir = 0

For i As Uinteger = 1 To iteraciones 

   Dim As integer lanza_moneda = Int(Rnd * 2) + 1
   dormir += 1 
   if lanza_moneda = 1 then cara += 1 else dormir += 1

Next i

Print Using "Wakings over #####,### repetitions = #####,###"; iteraciones ; dormir Print using "Percentage probability of heads on waking = ###.######%"; (cara/dormir*100)'; "%" Sleep </lang>

Output:
Wakings over 1,000,000 repetitions = 1,499,718
Percentage probability of heads on waking =  33.358405%

Yabasic

Translation of: FreeBASIC

<lang Yabasic> iteraciones = 1000000 cara = 0 dormir = 0

for i = 1 to iteraciones 

   lanza_moneda = int(ran(2))
   dormir = dormir + 1 
   if lanza_moneda = 1 then cara = cara + 1 else dormir = dormir + 1 endif

next i

print "Wakings over ", iteraciones, " repetitions = ", dormir print "Percentage probability of heads on waking = ", (cara/dormir*100), "%" end </lang>

Output:
Igual que la entrada de FreeBASIC.


Dyalect

Translation of: Swift

<lang dyalect>let experiments = 10000 var heads = 0 var wakenings = 0 for _ in 1..experiments { 

   wakenings += 1
   match rnd(min: 0, max: 10) {
       <5 => heads += 1,
       _ => wakenings += 1
   }

} print("Wakenings over \(experiments) experiments: \(wakenings)") print("Sleeping Beauty should estimate a credence of: \(Float(heads) / Float(wakenings))")</lang>

Excel

LAMBDA

Binding the name SLEEPINGB to the lambda expression below in the Excel Workbook Name Manager:

(See LAMBDA: The ultimate Excel worksheet function)

Works with: Office 365 betas 2021

<lang lisp>SLEEPINGB =LAMBDA(n, 

   LET(
       headsWakes, LAMBDA(x,
           IF(1 = x,
              {1,1},
              {0,2}
           )
       )(
           RANDARRAY(n, 1, 0, 1, TRUE)
       ),
       CHOOSE(
           {1,2},
           SUM(INDEX(headsWakes, 0, 1)),
           SUM(INDEX(headsWakes, 0, 2))
       )
   )

)</lang>

Output:

The pair of values in cells B2 and C2 both result from the application of SLEEPINGB in B2.

The credence value is returned as a ratio by the expression B2/C2 in cell D2,

with the format setting Number > Fraction > Up to three digits.

fx =SLEEPINGB(1000000)
A B C D
1 Heads Wakenings Credence
2 Results 500111 1499889 1/3

F#

<lang fsharp> // Sleeping Beauty: Nigel Galloway. May 16th., 2021 let heads,woken=let n=System.Random() in {1..1000}|>Seq.fold(fun(h,w) g->match n.Next(2) with 0->(h+1,w+1) |_->(h,w+2))(0,0) printfn "During 1000 tosses Sleeping Beauty woke %d times, %d times the toss was heads. %.0f%% of times heads had been tossed when she awoke" woken heads (100.0*float(heads)/float(woken)) </lang>

Output:
During 1000 tosses Sleeping Beauty woke 1519 times, 481 times the toss was heads. 32% of times heads had been tossed when she awoke

Factor

Works with: Factor version 0.99 2021-02-05

<lang factor>USING: combinators.random io kernel math prettyprint ;

sleeping ( n -- heads wakenings )
   0 0 rot [ 1 + .5 [ [ 1 + ] dip ] [ 1 + ] ifp ] times ;

"Wakenings over 1,000,000 experiments: " write 1e6 sleeping dup . /f "Sleeping Beauty should estimate a credence of: " write .</lang>

Output:
Wakenings over 1,000,000 experiments: 1500127
Sleeping Beauty should estimate a credence of: 0.3332204540015612

Go

Translation of: Wren
Library: Go-rcu

<lang go>package main

import ( 

   "fmt"
   "math/rand"
   "rcu"
   "time"

)

func sleepingBeauty(reps int) float64 { 

   wakings := 0
   heads := 0
   for i := 0; i < reps; i++ {
       coin := rand.Intn(2) // heads = 0, tails = 1 say
       wakings++
       if coin == 0 {
           heads++
       } else {
           wakings++
       }
   }
   fmt.Printf("Wakings over %s repetitions = %s\n", rcu.Commatize(reps), rcu.Commatize(wakings))
   return float64(heads) / float64(wakings) * 100

}

func main() { 

   rand.Seed(time.Now().UnixNano())
   pc := sleepingBeauty(1e6)
   fmt.Printf("Percentage probability of heads on waking = %f%%\n", pc)

}</lang>

Output:

Sample run: 

Wakings over 1,000,000 repetitions = 1,500,256
Percentage probability of heads on waking = 33.310582%

Julia

<lang julia>""" 

   Run the Sleeping Beauty Problem experiment `repetitions` times, checking to see
   how often we had heads on waking Sleeping Beauty.

""" function sleeping_beauty_experiment(repetitions) 

   gotheadsonwaking = 0
   wakenings = 0
   for _ in 1:repetitions
       coin_result = rand(["heads", "tails"])

       # On Monday, we check if we got heads.
       wakenings += 1
       if coin_result == "heads"
           gotheadsonwaking += 1
       end

       # If tails, we do this again, but of course we will not add as if it was heads.
       if coin_result == "tails"
           wakenings += 1
           if coin_result == "heads"
               gotheadsonwaking += 1   # never done
           end
       end
   end

   # Show the number of times she was wakened.
   println("Wakenings over ", repetitions, " experiments: ", wakenings)

   # Return the number of correct bets SB made out of the total number
   # of times she is awoken over all the experiments with that bet.
   return gotheadsonwaking / wakenings

end

CREDENCE = sleeping_beauty_experiment(1_000_000) println("Results of experiment: Sleeping Beauty should estimate a credence of: ", CREDENCE)

</lang>

Output:


Wakenings over 1000000 experiments: 1499534
Results of experiment:  Sleeping Beauty should estimate a credence of: 0.33374768428058316

Nim

<lang Nim>import random

const N = 1_000_000

type Side {.pure.} = enum Heads, Tails

const Sides = [Heads, Tails]

randomize() var onHeads, wakenings = 0 for _ in 1..N: 

 let side = sample(Sides)
 inc wakenings
 if side == Heads:
   inc onHeads
 else:
   inc wakenings

echo "Wakenings over ", N, " experiments: ", wakenings echo "Sleeping Beauty should estimate a credence of: ", onHeads / wakenings</lang>

Output:
Wakenings over 1000000 experiments: 1499971
Sleeping Beauty should estimate a credence of: 0.3333591116094911

Pascal

Translation of: Phix

<lang pascal> program sleepBeau; uses 

 sysutils; //Format

const 

 iterations = 1000*1000;

fmt = 'Wakings over %d repetitions = %d'+#13#10+ 

     'Percentage probability of heads on waking = %8.5f%%';

var 

 i,
 heads,
 wakings,
 flip: Uint32;

begin 

 randomize;
 for i :=1 to iterations do
 Begin
   flip := random(2)+1;//-- 1==heads, 2==tails
   inc(wakings,1 + Ord(flip=2));
   inc(heads,Ord(flip=1));
 end;
 writeln(Format(fmt,[iterations,wakings,heads/wakings*100]));

end.</lang>

Output:
Wakings over 1000000 repetitions = 1499741
Percentage probability of heads on waking = 33.35636%

Perl

<lang perl>use strict; use warnings;

sub sleeping_beauty { 

   my($trials) = @_;
   my($gotheadsonwaking,$wakenings);
   $wakenings++ and rand > .5 ? $gotheadsonwaking++ : $wakenings++ for 1..$trials;
   $wakenings, $gotheadsonwaking/$wakenings

}

my $trials = 1_000_000; printf "Wakenings over $trials experiments: %d\nSleeping Beauty should estimate a credence of: %.4f\n", sleeping_beauty($trials);</lang>

Output:
Wakenings over 1000000 experiments: 1499816
Sleeping Beauty should estimate a credence of: 0.333

Phix

constant iterations = 1_000_000,
fmt = """
Wakings over %,d repetitions = %,d
Percentage probability of heads on waking = %f%%
"""
integer heads = 0, wakings = 0
for i=1 to iterations do
    integer flip = rand(2) -- 1==heads, 2==tails
    wakings += 1 + (flip==2)
    heads += (flip==1)
end for
printf(1,fmt,{iterations,wakings,heads/wakings*100})
Output:

(You'll get the exact result less than 1% of the time!!) 

Wakings over 1,000,000 repetitions = 1,500,000
Percentage probability of heads on waking = 33.333333%

Python

Procedural

<lang python>from random import choice

def sleeping_beauty_experiment(repetitions): 

   """
   Run the Sleeping Beauty Problem experiment `repetitions` times, checking to see
   how often we had heads on waking Sleeping Beauty.
   """
   gotheadsonwaking = 0
   wakenings = 0
   for _ in range(repetitions):
       coin_result = choice(["heads", "tails"])

       # On Monday, we check if we got heads.
       wakenings += 1
       if coin_result == "heads":
           gotheadsonwaking += 1

       # If tails, we do this again, but of course we will not add as if it was heads..
       if coin_result == "tails":
           wakenings += 1
           if coin_result == "heads":
               gotheadsonwaking += 1   # never done



   # Show the number of times she was wakened.
   print("Wakenings over", repetitions, "experiments:", wakenings)

   # Return the number of correct bets SB made out of the total number
   # of times she is awoken over all the experiments with that bet.
   return gotheadsonwaking / wakenings


CREDENCE = sleeping_beauty_experiment(1_000_000) print("Results of experiment: Sleeping Beauty should estimate a credence of:", CREDENCE)

</lang>

Output:


Wakenings over 1000000 experiments: 1499765
Results of experiment:  Sleeping Beauty should estimate a credence of: 0.333542254953276


Functional

<lang python>Sleeping Beauty Problem

from random import choice from itertools import repeat from functools import reduce


  1. experiment :: (Int, Int) -> IO (Int, Int)

def experiment(headsWakings): 

   A pair of counts updated by a coin flip.
   
   heads, wakings = headsWakings

   return (
       1 + heads, 1 + wakings
   ) if "h" == choice(["h", "t"]) else (
       heads, 2 + wakings
   )


  1. ------------------------- TEST -------------------------
  2. main :: IO ()

def main(): 

   Observed results from one million runs.

   n = 1_000_000
   heads, wakes = applyN(n)(
       experiment
   )(
       (0, 0)
   )

   print(
       f'{wakes} wakenings over {n} experiments.\n'
   )
   print('Sleeping Beauty should estimate credence')
   print(f'at around {round(heads/wakes, 3)}')


  1. ----------------------- GENERIC ------------------------
  1. applyN :: Int -> (a -> a) -> a -> a

def applyN(n): 

   n applications of f.
      (Church numeral n).
   
   def go(f):
       def ga(a, g):
           return g(a)

       def fn(x):
           return reduce(ga, repeat(f, n), x)
       return fn
   return go


  1. MAIN ---

if __name__ == '__main__': 

   main()

</lang>

Output:
1500188 wakenings over 1000000 experiments.

Sleeping Beauty should estimate credence
at around 0.333

Quackery

<lang Quackery> [ $ "bigrat.qky" loadfile ] now! 

 [ say "Number of trials:  "
   dup echo cr
   0 ( heads count )
   0 ( sleeps count )
   rot times
     [ 1+
       2 random if
         [ 1+ dip 1+ ] ]
   say "Data: heads count: " 
   over echo cr
   say "     sleeps count: "
   dup echo cr
   say "Credence of heads: "
   2dup 20 point$ echo$ cr
   say " or approximately: "
   10 round vulgar$ echo$ cr ] is trials ( n --> n/d ) 

   1000000 trials</lang>
Output:
Number of trials:  1000000
Data: heads count: 500212
     sleeps count: 1500212
Credence of heads: 0.33342754224069664821
 or approximately: 1/3

Raku

<lang perl6>sub sleeping-beauty ($trials) { 

   my $gotheadsonwaking = 0;
   my $wakenings = 0;
   ^$trials .map: {
       given <Heads Tails>.roll {
           ++$wakenings;
           when 'Heads' { ++$gotheadsonwaking }
           when 'Tails' { ++$wakenings }
       }
   }
   say "Wakenings over $trials experiments: ", $wakenings;
   $gotheadsonwaking / $wakenings

}

say "Results of experiment: Sleeping Beauty should estimate a credence of: ", sleeping-beauty(1_000_000);</lang>

Output:
Wakenings over 1000000 experiments: 1500040
Results of experiment:  Sleeping Beauty should estimate a credence of: 0.333298

REXX

When using Regina REXX,   the seed specified   (for random)   was   46. <lang rexx>/*REXX pgm uses a Monte Carlo estimate for the results for the Sleeping Beauty problem. */ parse arg n seed . /*obtain optional arguments from the CL*/ if n== | n=="," then n= 1000000 /*Not specified? Then use the default.*/ if datatype(seed, 'W') then call random ,,seed /* Specified? Then use as RAND seed*/ awake= 0 /* " " " " awakened. */ 

          do #=0  for n                         /*perform experiment:  1 million times?*/
          if random(,1)  then awake= awake + 1  /*Sleeping Beauty  is   awoken.        */
                         else #= # + 1          /*   "        "   keeps sleeping.      */
          end   /*#*/                           /* [↑]  RANDOM returns:    0  or  1    */

say 'Wakenings over ' commas(n) " repetitions: " commas(#) say 'The percentage probability of heads on awakening: ' (awake / # * 100)"%" exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>

output   when using the input of:     ,   46 
Wakenings over  1,000,000  repetitions:  1,500,000
The percentage probability of heads on awakening:  33.3333333%

Swift

<lang swift>let experiments = 1000000 var heads = 0 var wakenings = 0 for _ in (1...experiments) { 

   wakenings += 1
   switch (Int.random(in: 0...1)) {
   case 0:
       heads += 1
   default:
       wakenings += 1
   }

} print("Wakenings over \(experiments) experiments: \(wakenings)") print("Sleeping Beauty should estimate a credence of: \(Double(heads) / Double(wakenings))")</lang>

Output:
Wakenings over 1000000 experiments: 1500036
Sleeping Beauty should estimate a credence of: 0.3333013341013149

Wren

Library: Wren-fmt

<lang ecmascript>import "random" for Random import "/fmt" for Fmt

var rand = Random.new()

var sleepingBeauty = Fn.new { |reps| 

   var wakings = 0
   var heads = 0
   for (i in 0...reps) {
       var coin = rand.int(2) // heads = 0, tails = 1 say
       wakings = wakings + 1
       if (coin == 0) {
           heads = heads + 1
       } else {
           wakings = wakings + 1
       }
   }
   Fmt.print("Wakings over $,d repetitions = $,d", reps, wakings)
   return heads/wakings * 100

}

var pc = sleepingBeauty.call(1e6) Fmt.print("Percentage probability of heads on waking = $f\%", pc)</lang>

Output:

Sample run: 

Wakings over 1,000,000 repetitions = 1,500,321
Percentage probability of heads on waking = 33.304806%
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