Re: Testing P-3 for bias
- From: Stig Holmquist <stigfjorden@xxxxxxxxxxx>
- Date: Sat, 11 Oct 2008 10:21:51 -0400
On Fri, 10 Oct 2008 17:03:20 +0100, nigel <useweb@xxxxxxxxxx> wrote:
Stig Holmquist wrote:
Ten years ago, as some of you might remember, the Arizona P-3 game
used a flawed computer program to generate its numbers. After more
than one month, during the summer of 1998, it was discovered by the
public that digit 9 could not come up.Thus all bets using this digit
were wasted.
That's either a good reason to avoid computerised draws or a good reason
to target them with the help of some thorough analysis.
A simple probability calculation would have alerted the lottery
officials that something was amiss, but they did not test. The average
time for all digits to be drawn is 10 draws with a std.dev. of nearly
four draws. In stricct mathematical terms the average is 29.3 with a
std.dev. of 11.2.
Doesn't that assume that the three machines/random number generators are
identical? What if only one is flawed?
Unless I'm mistaken the Arizona game could not draw #9 in any
position. Thus it used only one generator. There is no reason for
using three, Go to any random generator site and you'll can get random
numbers of any length with just one machine.
Stig
A common statistical rule of thumb says that we can
be 99.7% sure something is out of order if a test value is outside of
the mean by more than three std.dev. Applied to digits it means
29.3+3x11.2=62.9, which divided by 3 comes to 21 draws. If you demand
99.99% certainty you need to use four std.dev., viz. 29.3+4x11.2= 74.1
equal to 25 draws.
What does 29.3-3x11.2 mean? The minimum number of balls to draw all ten
is ten and that requires a minimum of 4 draws. If the balls come out
more evenly than expected they can't reach three standard deviations
because that would require a negative number of draws. Are you sure
you're using the correct formula for the standard deviation?
If you go to a random numbers table in a textbook or get them from a
generator, you will discover there will be 3.5 digits missing on
average if you pick 10 numbers at random. Try it.
Stig
If you are concerned about the randomness of your state's P-3 game you
should at least test and examine the missing digit patterns. There are
other statistical test also that can be used. A good state lottery
does such testing all the time and will spot irregularities.
Needless to say, one should test the missing digits in each position
when the game is drawn with ping pong balls, but not by RNG.
Stig
.Stig Holmquist
Evil Nigel
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