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Sleeping Beauty problem

From Rosetta Code
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[edit]

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

C++[edit]

#include <iostream>
#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';
}
Output:
Wakenings over 1,000,000 experiments: 1,500,090
Sleeping Beauty should estimate a credence of: 0.333253

BASIC[edit]

BASIC256[edit]

Translation of: FreeBASIC
 
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
 
Output:
Igual que la entrada de FreeBASIC.

FreeBASIC[edit]

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

Yabasic[edit]

Translation of: FreeBASIC
 
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
 
Output:
Igual que la entrada de FreeBASIC.


Dyalect[edit]

Translation of: Swift
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))")

Excel[edit]

LAMBDA[edit]

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

(See LAMBDA: The ultimate Excel worksheet function)

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))
)
)
)
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#[edit]

 
// 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))
 
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[edit]

Works with: Factor version 0.99 2021-02-05
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 .
Output:
Wakenings over 1,000,000 experiments: 1500127
Sleeping Beauty should estimate a credence of: 0.3332204540015612

Go[edit]

Translation of: Wren
Library: Go-rcu
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)
}
Output:

Sample run:

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

Julia[edit]

"""
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)
 
Output:

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

Nim[edit]

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

Pascal[edit]

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

Perl[edit]

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

Phix[edit]

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[edit]

Procedural[edit]

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)
 
Output:

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


Functional[edit]

'''Sleeping Beauty Problem'''
 
from random import choice
from itertools import repeat
from functools import reduce
 
 
# 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
)
 
 
# ------------------------- TEST -------------------------
# 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)}')
 
 
# ----------------------- GENERIC ------------------------
 
# 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
 
 
# MAIN ---
if __name__ == '__main__':
main()
 
Output:
1500188 wakenings over 1000000 experiments.

Sleeping Beauty should estimate credence
at around 0.333

Quackery[edit]

  [ $ "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
Output:
Number of trials:  1000000
Data: heads count: 500212
     sleeps count: 1500212
Credence of heads: 0.33342754224069664821
 or approximately: 1/3

Raku[edit]

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

REXX[edit]

When using Regina REXX,   the seed specified   (for random)   was   46.

/*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 ?
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[edit]

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

Wren[edit]

Library: Wren-fmt
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)
Output:

Sample run:

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