From: Chris Pine <nemo@...>
Date: 2003-04-20T13:42:13+09:00
Subject: Re: Biased weighted random?

----- Original Message -----
From: "Daniel Carrera" <dcarrera@math.umd.edu>

If you keep the ratios constant, the probabilities *must* change.  Take
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Yes, that's what we've been saying.  That's why your algorithm doesn't work.
The idea was to have the *long-term* probabilities be according to the
weights.


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If on the first trial I select event 1, and I don't want repetitions, then
the new probability of event 1 is 0.  If we keep the ratio between the
probabilities of events 2 and 3 constant, then necessarily the new
probabilities are:

event 1 has prob 0
event 2 has prob .5
event 3 has prob .5
----------------------------

*Long-term* probabilities... this is just the probabilities at one step.


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As for Hal's experiment, the sample was too small to be statistically
significant (it was small enough to fit in a couple of lines).  You will
almost never see that kind of "perfect" distribution.  That kind of
distribution is not representative of what a typical random distribution.
----------------------------

Not statistically significant?!  He ran it 200,000 times!  The probabilities
were clearly converging:

   200: {"a"=>73,    "b"=>61,    "c"=>41,    "d"=>25}
  2000: {"a"=>700,   "b"=>608,   "c"=>449,   "d"=>243}
 20000: {"a"=>6842,  "b"=>6064,  "c"=>4492,  "d"=>2602}
200000: {"a"=>68441, "b"=>60009, "c"=>45798, "d"=>25752}

You said yourself that the long-term probabilities were different from those
suggested by the *desired* weightings (in this case 8, 6, 4, and 2); so we
are all agreed that that algorithm doesn't work.

I'm not sure what you are trying to say.

Chris