[alicebot-archcomm] more random <random>

[Noel Bush]

Thanks, John and Rich, for the informative replies.

I guess my concern has to do with an unanswered requirement that seems
to be lurking, not the nature of randomness itself.  The point about
never finding an even distribution in a small sample is definitely
important.  And it helps me to understand better the need for a
variation on the <random> theme, as was recently discussed on the
mailing list.

As in,

<shuffle>
  <li>One thing.</li>
  <li>Another thing.</li>
  <li>And so on.</li>
</shuffle>

In which one item is chosen each time, "randomly" (without further
discussing what that is), and then the same element will not be chosen
again in the same bot-user context until all elements from the <shuffle>
have been "used up".

I think this meets a need for what people would tend to mislabel
"random" (myself included).  It could be that this function is even more
needed than an actual <random>, since people are actually seeking a way
to create "varied, not-so-repetitive" responses, not really something
that corresponds to a mathematical definition of random.

On Sun, 2002-04-28 at 20:30, John Foderaro wrote:
> 
> 
> >> The problem is that if two different <random> elements are
> >> imagined to each have an independent random "space", tying all of their
> >> choices to the same sequence of pseudo-random numbers really throws a
> >> wrench into the works. 
> 
>  I know what you're saying but I don't think there is anything to worry
> about.  Random number generators will produce a nice even distribution
> but only over a very large number of samples.  If you're asking
> for a random number between 0 and 4 (inclusive) and call random 5
> times you almost certainly won't get each number chosen once. 
> And that's the correct result since the odds of that happening
> if the random number generator were truly random is very small.
> 
> I wrote little test program to show this:
> 
> If I chose 5 random numbers I get one 2, two 3's and 2 4's.
>  
> cl-user(31): (testit :count 5)
> 0: 0  0.0d0
> 1: 0  0.0d0
> 2: 1  0.2d0
> 3: 2  0.4d0
> 4: 2  0.4d0
> 
> 
> If I chose one million random numbers I get this distribution.
> Now the distribution is very nice over the 5 possible numbers:
> 
> cl-user(32): (testit :count 1000000)
> 0: 199398  0.199398d0
> 1: 199834  0.199834d0
> 2: 200394  0.200394d0
> 3: 200158  0.200158d0
> 4: 200216  0.200216d0
> 
> 
> 
> Suppose that after every 7th random number I obtain I call
> the random number generator and throw away the value.  This is
> simulating the case of running another <random> tag with a
> different number of elements.
> 
> We still end up with a nice distribution:
> 
> cl-user(34): (testit :count 1000000 :toss-out 7)
> 0: 200119  0.200119d0
> 1: 200194  0.200194d0
> 2: 199914  0.199914d0
> 3: 199833  0.199833d0
> 4: 199940  0.19994d0
> 
> 
> So I don't think there is any need to create multiple independent
> random number sequences, one for each <random> tag.
> 
> 
> --john foderaro
> 
> ps. here's my test code
> 
> (in-package :user)
> 
> (defvar results (make-array 5))
> 
> (defun testit (&key (count 10000) (toss-out 0))
>   (dotimes (i (length results)) (setf (svref results i) 0))
>   
>   (dotimes (i count)
>     
>     ; throw out a random result periodically
>     (if* (and (> toss-out 0)
> 	      (zerop (mod i toss-out)))
>        then (random (+ (length results) 4)))
>     
>     ; now collect some random info
>     (incf (svref results (random (length results)))))
>   
>   (dotimes (i (length results))
>     (format t "~d: ~d  ~s~%" 
> 	    i 
> 	    (svref results i)
> 	    (/ (float (svref results i) 1.0d0) count)))
>   )
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