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Re: Testing random

Newsgroups comp.lang.python
Date 2015-06-16 13:48 -0700
References (5 earlier) <1656356.OjxBvjpJ5d@PointedEars.de> <mailman.259.1433695485.13271.python-list@python.org> <5515034.V7dcXEWAvK@PointedEars.de> <88ba163e-74f4-40fa-ab3e-1feeb051b961@googlegroups.com> <17701105.fuEQZlnPee@PointedEars.de>
Message-ID <ff4a8ffd-50fe-4705-b33a-fcf63bcccc11@googlegroups.com> (permalink)
Subject Re: Testing random
From Ned Batchelder <ned@nedbatchelder.com>

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On Tuesday, June 16, 2015 at 3:21:46 PM UTC-4, Thomas 'PointedEars' Lahn wrote:
> Ned Batchelder wrote:
> 
> > You aren't agreeing because you are arguing about different things.
> > Thomas is talking about the relative probability of sequences of digits.
> 
> There is no such thing as “relative probability”, except perhaps in popular-
> scientific material and bad translations.  You might mean relative 
> _frequency_, but I was not talking about that specifically.
> 
> > Chris is talking about the probability of a single digit never appearing
> > in the output.
> 
> I do not think that what I am talking about and what you think Chris is 
> talking about are different things.
> 
> > Thomas: let's say I generate streams of N digits drawn randomly from 0-9.
> > I then consider the probability of a zero *never appearing once* in my
> > stream.  Let's call that P(N)
>  
> In probability theory, it is called the probability P(E) of the event E that 
> in n trials the probability variable X never assumes the value 0, which can 
> be defined as
> 
>   P(E), E = {e_i | n ∈ ℕ \ {0}, i = 1, …, n} \ {X ≠ 0}, Ω = {1, 2, …, 9} 
> 
> where the e_i are the singular events, or outcomes, of the probabilistic 
> experiment, and Ω is the sample space of the e_i.
> 
> > Do you agree that as N increases, P(N) decreases?
> 
> I do not agree that P(E), as defined above, decreases as n increases.
> 
> See also: <http://rationalwiki.org/wiki/Gambler%27s_fallacy>

I apologize, I'm sure I've been using the mathematical terms imprecisely.
We are all intelligent people, so I still believe we disagree because we
are talking about different things.

To put us all on a footing where (I hope) we have a shared understanding,
this Python program demonstrates what I was talking about:



import random

def die_roll():
    """Roll the die once, produce a number 0-9."""
    return random.randint(0, 9)

def die_rolls(n):
    """Roll the die n times, produce a list of numbers from 0-9."""
    return [die_roll() for _ in xrange(n)]

def any_zeros(seq):
    """Is there any zero in `seq`?"""
    return any(x == 0 for x in seq)

def probability_of_no_zero(nrolls, nseq):
    """Determine the chance of no zero in a sequence of rolls.

    This is done empirically, by producing `nseq` sequences of
    `nrolls` rolls of the die.  Each sequence is examined to
    see if it has a zero.  The total number of no-zero
    sequences divided `nseq` is the probability.
    """
    no_zeros = 0
    for _ in xrange(nseq):
        seq = die_rolls(nrolls)
        if not any_zeros(seq):
            no_zeros += 1
    return float(no_zeros)/nseq

for n in range(10, 101, 10):
    # Calculate the probability of getting no zeros by trying
    # it a million times.
    prob = probability_of_no_zero(n, 1000000)
    print "n = {:3d}, P(no zero) = {:.8f}".format(n, prob)



Running this gives:

$ pypy testrandom.py
n =  10, P(no zero) = 0.34867300
n =  20, P(no zero) = 0.12121900
n =  30, P(no zero) = 0.04267000
n =  40, P(no zero) = 0.01476600
n =  50, P(no zero) = 0.00519900
n =  60, P(no zero) = 0.00174100
n =  70, P(no zero) = 0.00061600
n =  80, P(no zero) = 0.00020600
n =  90, P(no zero) = 0.00006300
n = 100, P(no zero) = 0.00002400


As n increases, the probability of having no zeros goes down.

--Ned.

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Thread

Testing random Cecil Westerhof <Cecil@decebal.nl> - 2015-06-07 08:27 +0200
  Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 12:40 +0200
    Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-07 21:51 +1000
      Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 17:51 +0200
        Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 02:25 +1000
          Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 18:36 +0200
            Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 02:44 +1000
              Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 20:23 +0200
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 04:52 +1000
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 21:41 +0200
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-07 22:08 +0300
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 21:29 +0200
                Re: Testing random random832@fastmail.us - 2015-06-07 15:44 -0400
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:09 +0200
                Re: Testing random random832@fastmail.us - 2015-06-07 16:41 -0400
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:59 +0200
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:26 +1000
                Re: Testing random random832@fastmail.us - 2015-06-07 21:34 -0400
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 11:42 +1000
                Re: Testing random MRAB <python@mrabarnett.plus.com> - 2015-06-08 02:49 +0100
                Re: Testing random random832@fastmail.us - 2015-06-07 21:57 -0400
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-08 10:40 +0300
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-10 19:03 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-10 10:52 -0700
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-10 23:00 +0300
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-10 12:02 -0600
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-12 23:32 +0200
                Re: Testing random alister <alister.nospam.ware@ntlworld.com> - 2015-06-12 21:46 +0000
                Re: Testing random random832@fastmail.us - 2015-06-12 17:52 -0400
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-12 16:00 -0600
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-13 00:09 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-12 15:55 -0700
                Re: Testing random random832@fastmail.us - 2015-06-12 18:57 -0400
                Re: Testing random Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-06-13 08:53 +0100
                Re: Testing random random832@fastmail.us - 2015-06-10 14:26 -0400
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-07 14:21 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-16 21:18 +0200
                Re: Testing random random832@fastmail.us - 2015-06-16 16:23 -0400
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-16 13:48 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-16 23:57 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-16 15:30 -0700
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-16 16:58 -0600
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 11:28 +0200
                Re: Testing random Ned Batchelder <ned@nedbatchelder.com> - 2015-06-16 16:26 -0700
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-17 01:45 +0200
                Re: Testing random sohcahtoa82@gmail.com - 2015-06-16 17:36 -0700
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-17 11:01 +1000
                Re: Testing random Ethan Furman <ethan@stoneleaf.us> - 2015-06-16 18:32 -0700
                Re: Testing random Mark Lawrence <breamoreboy@yahoo.co.uk> - 2015-06-17 09:41 +0100
                Re: Testing random Grant Edwards <invalid@invalid.invalid> - 2015-06-17 14:04 +0000
                Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-17 09:01 -0600
                Re: Testing random MRAB <python@mrabarnett.plus.com> - 2015-06-17 01:42 +0100
                Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-17 08:53 +0200
                Re: Testing random Christian Gollwitzer <auriocus@gmx.de> - 2015-06-17 09:22 +0200
                Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-17 17:28 +1000
                Re: Testing random Tim Golden <mail@timgolden.me.uk> - 2015-06-17 08:30 +0100
                Re: Testing random Cecil Westerhof <Cecil@decebal.nl> - 2015-06-17 11:57 +0200
                Re: Testing random Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-06-17 01:36 +0000
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 12:33 +0200
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-17 22:47 +1000
                Re: Testing random Laura Creighton <lac@openend.se> - 2015-06-17 15:50 +0200
                Re: Testing random Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2015-06-17 01:35 +0000
                Re: Testing random Jussi Piitulainen <jpiitula@ling.helsinki.fi> - 2015-06-17 07:41 +0300
                Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:11 +1000
            Re: Testing random Ian Kelly <ian.g.kelly@gmail.com> - 2015-06-07 11:07 -0600
            Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 03:20 +1000
            Re: Testing random "C.D. Reimer" <chris@cdreimer.com> - 2015-06-07 10:36 -0700
            Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 04:28 +1000
              Re: Testing random Chris Angelico <rosuav@gmail.com> - 2015-06-08 04:40 +1000
        Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 04:24 +1000
  Re: Testing random Jonas Wielicki <jonas@wielicki.name> - 2015-06-07 12:41 +0200
  Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-07 22:52 +1000
    Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-07 23:06 +1000
    Re: Testing random Peter Otten <__peter__@web.de> - 2015-06-07 15:35 +0200
      Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 18:36 +0200
        Re: Testing random Peter Otten <__peter__@web.de> - 2015-06-07 18:48 +0200
          Re: Testing random Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-06-07 22:15 +0200
      Re: Testing random Steven D'Aprano <steve@pearwood.info> - 2015-06-08 11:35 +1000
  Re: Testing random Christian Gollwitzer <auriocus@gmx.de> - 2015-06-07 14:53 +0200
  Re: Testing random Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2015-06-07 11:04 -0400

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