|Posted: April 27, 2012, 9:37 pm - IP Logged|
"Opinion: Lottery Ball Drop Machines may be at their physical limits when producing five number lottery combinations such as 1-2-3-4-5 or 52-53-54-55-56."
Have a look at the statistics for the 714 MM drawings since the last matrix change. Drawing 5 balls from 56 means that 8.93% of the balls are drawn, so each ball has an 8.93% chance of being drawn. Any ball that was actually drawn 8.93% of the time would have been drawn 63.75 times.
Balls numbered 1 through 5 have been drawn 56, 72, 61, 69 and 68 times, respectively. That's an average of 65.2 times. Overall, the ball machines seem to do an above average job of selecting balls 1 through 5.
Balls numbered 52 through 56 have been drawn 72, 74, 59, 52 and 63 times, respectively. That's an average of 64.0 times. Overall, the ball machines seem to do an above average job of selecting balls 52 through 56.
If the machines were biased towards balls with a particular position at the start we would expect them to be picked more frequently. Intuitively I would expect the bias to be towards balls with mixing times that were either more or less than the average for all balls. The actual results show that the 5 balls with both the most and least mixing time were picked more than average, but both sets are within 2.25% of the average, which is a pretty narrow range. Within each set of 5 individual balls were drawn both more and less than the average. I see absolutely nothing to indicate that the starting position ofthose balls has a meaningful effect on its chances of being drawn.
" if the machine has a bias, the bias may produce more combinations with a sum of"
If the machines have difficulty producing combinations at opposite ends the only remining possibility I see is that selecting some balls from either end somehow reduces the chances of selecting more balls from the same range. I'll consider that it's possible, but I see absolutely no reasonable evidence for it. Feel free to try and convince me.
FWIW, I recently read an article about studies on mixing of items. IIRC, the conclusion was that the results were applicable to a wide variety of things. Again, IIRC, an effective mixing action consistently produced random results after 11 repetitions. Once randomness was achieved additional mixing didn't chnage the degree of randomness.