->   Keep in mind that the study of statistics was created to try to
-> understand and find order where there supposedly isn't any order.
-> It isn't an exact science and should not be used or thought of as
-> such.
-> By imposing this definition that all possible outcomes should come
-> out an equal number of times, and since you said that is what you
-> found
-> with your routine, you should be concerned not overjoyed. Remember,
-> we want the most random routine, not the routine that produces a
-> pattern of outcomes more quickly over time.
->   What your argument seems to be is that if your routine, for the
-> most part, produces orderly "textbook" outcomes over time, it is
-> better.
->   I'm saying that if my routine does not or takes longer before any
-> pattern is seen it may just mean that my routine is better in that
-> no pattern is seen over time or my routine produces random outcomes
-> for a longer period of time before any pattern is seen. Not that I
-> believe that. I suspect that both routines over time are very likely
-> equal in their ability to produce random outcomes.
I said that non-degenerate outcomes should occur with equal frequencies
*in the long term*, i.e. a theoretically infinite number of trials. In
any finite experiment, frequencies can deviate from equality, but the
probabilities of deviations are calculable. Large deviations in long
experiments are so improbable as to be practically impossible.
I said (or meant to say) that your routine will give non-equal
frequencies of occurrence to, for example, the six possibilities of
permutating three characters *even if the experiment is extremely long*.
If you do 600, or 6000, or 6E20 trials, the frequencies with which the
six outcomes occur will *not* be even approximately 1/6 each. It will
*not* be true that the number of times the sequence "bac" occurs, for
example, divided by the total number of trials comes close to 16.667%
(i.e. 1 out of 6). (This is assuming that each trial starts with "abc".)
What will happen, with your routine, is that some sequences will occur
more often than 1 in 6 trials, and others less, *and this will be true
even over a very long experiment*. My routine, however, *will* give
frequencies that all tend toward 16.667% in a sufficiently long
experiment.
As I suggested, try it!
->   You should make certain that you run both routines more than
-> 600 times and see if that changes the results. Maybe one routine
-> produces more random outcomes before a pattern begins to develop.
-> Also keep in mind that BASIC's randomness is not the best possible.
->   As far as this thread goes you would have to post the complete code
-> that you are using to test the routines so that I can run them here
-> and you should also post your findings. I've learned that anyone can
-> claim anything and so I need to be able to duplicate your findings
-> before I ever agree with you that your routine is more random.
Well, I thought *you* had previously ruled out of bounds any suggestion
that RND is not adequately random! Actually, of course it fails the one
randomness test of non-repeatability. In just about every other respect,
however, it is remarkably close to random.
I did, previously, post the bit of code that I would use to randomize
the sequence of characters in a string. I haven't posted the entire test
program since I figured that you are obviously a good enough programmer
to be able to write a functional test routine yourself. However, if you
really want me to write and post the thing, I will.
-> No. Random means that any arrangement of outcomes is possible.
But some types of arrangement are often immensely more probable than
others. Fortunately, all the molecules of air in this room have not all
rushed out of the door, although that is theoretically possible. If I
found myself having difficulty breathing, random molecular motions would
not be among the explanations I would look at.
-> I doubt that happens in the real world. Police, like everyone else,
-> will use their experience when doing their job.
A couple of weeks ago, I flew to Mexico. On arrival at the airport,
after claiming my baggage, I had to pass through a gate where I was
asked to press a button. When you do this, either a red or a green light
comes on. If it is green, you are free to leave the airport. If it is
red, your bags get searched. (Mine was green.) The colour is chosen by
some sort of *random* gadget, so that a would-be smuggler can't hang
around waiting for someone to be searched, so he can then slip through
immediately after. The probablilty of being searched is constant for
everyone. Much the same logic applies to police checks.
->   This conference is very slow so I see no problem with this little
-> thread.
Okay. That's fine with me...
                                dow
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