When picking numbers for the Tennessee Powerball lottery game, there are 42 possible powerball numbers, 1 - 42. Scroll down to see a picture of a Powerbal lottery playslip. I recently purchase three quickpick Powerball lottery tickets. The Powerball numbers were 10, 38, and 42.
Out of the last 162 Powerball drawings (January 3, 2007 through July 16, 2008 ), numbers below 20 were picked 92 times (56.8%) and numbers 20 and above were picked 70 times (43.2%). There are 19 numbers below 20 (45.2%) and 23 numbers 20 and above (54.8%). Prior to 2007, powerball picks of numbers 20 and above were picked more often, as you would think they might be as there are more numbers. In 2007 and so far in 2008, powerball picks of numbers less than 20 have been picked more often (see counts after the Read more). Did something change in 2007 or is this just a phenomenon that happens with lotteries?
Also, how is that in the last 7 powerballs, three of them were 17? In 2008, the most picked powerball number was? 17, picked 5 times.
Do they still pick powerball numbers with the ping pong balls or do they now use a computer?
Does any of this really matter?
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58 drawings (January 2, 2008 through July 16, 2008)
37 picks of numbers below 20 (63.8%)
21 picks of numbers 20 and above (36.2%)
104 drawings (January 3, 2007 through December 29, 2007)
55 picks of numbers below 20 (52.9%)
49 picks of numbers 20 and above (47.1%)
104 drawings (January 4, 2006 through December 30, 2006)
50 picks of numbers below 20 (48.1%)
54 picks of numbers 20 and above (51.9%)
105 drawings (January 1, 2005 through December 31, 2005)
45 picks of numbers below 20 (42.9%)
60 picks of numbers 20 and above (57.1%)
72 drawings (April 21, 2004 through December 29, 2004)
35 picks of numbers below 20 (48.3%)
37 picks of numbers 20 and above (51.4%)
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Should be truly random
Oddly, I was just having a conversation about this. They do use ping pong balls for the draw, so the drawn number should be truly random, barring any hanky-panky.
Now the numbers that you get on the quick picks are only pseudo-random, as they are computer-generated. You have to wonder what they are using as a seed for the random number generator and how often they change it. Whether each ticketing device has it's own independent generator, or if they use a networked one. I had a friend who was a statistician who liked to run her own random number generator, and use those numbers. I think it's overkill.
Your sample size is still too small
The Law of Large Numbers suggests that eventually the real values will approach the expected value (in this case, the median of the actual values drawn and the median of the possible values, respectively). The sample sizes above are only in the hundreds, an insufficient value for the Law of Large Numbers. Absent a sufficiently large sample size, an evaluation of the actual values is not a determinant of either true randomness nor the validity of the expected value. Your left with methodology to determine validity.
There's also a Law of Truly Large Numbers that suggests that with a large enough sample size, any outcome possible, no matter how improbable, is also likely to happen. It's a misunderstanding of this Law that leads people to buy large numbers of lottery tickets in the belief it might somehow improve their chances of winning in a statistically meaningful way.
Does any of this really matter?
no.
~m.