*The term "magic number" was apparently coined by Eugene Wigner. There are some isotopes that are doubly magic, having a magic number of protons and a magic number of neutrons, as shown in this figure. Double magic allows the existence of unlikely stable isotopes, such as calcium-40, the most abundant isotope of calcium. Calcium-40 has far fewer neutrons than expected. Lead-208 is the heaviest stable nuclide. (Created using Inkscape)*

As I wrote in an earlier article (Allen Telescope Array, April 26, 2011), there's a joke about lotteries. It might be known to everyone, but I'll retell it, anyways.

A religious man prays to God each night that he will win the state lottery. He does this for many years, but he never wins. Finally, the exasperated man asks God in a prayer, "Why won't you let me win the lottery?" God replies, "I want you to win, but you never buy a ticket!"My father enjoyed playing the New York Lottery in which three numbers from 0-9 were drawn. That's despite the state's small payout for the 1 in 1000 odds. As many who were not statistically-minded, he thought there was a way for him to "beat the system." He recorded each day's winning numbers looking for a pattern of repeating digits, and he asked me to do an analysis to determine what numbers he should play. I couldn't just dismiss the idea as absurd, so I did a careful mathematical analysis to prove the point. He was disappointed, but I think he continued to play. One sure way to beat the odds is to rig the game to make certain that your numbers come up. That's what happened in the 1980 Pennsylvania Lottery scandal. This lottery was also a three digit game with the numbers dramatically selected using numbered ping pong balls blowing around in a container. The conspirators purposely weighted all balls, except those for

*Lottery simulation results.This is a scatterplot derived from the deviation from an ideal result in 1,000 successive simulations using each strategy in 100,000,000 trials.An ideal result would have all points placed at (1.0,1.0). All the points fall within a percent of this ideal.(Graphed using Gnumeric*)

*Histogram of the Lottery simulation.This shows the distribution of the deviation of one lottery strategy over the other, and the results indicate much less than a 1% deviation for most trials.The calculated standard deviation is 0.45%.(Graphed using Gnumeric*)

- Robert Bailey, $343.8 Million Lottery Winner, New York City, New York Lottery Website, November 14, 2018.
- Faith Karimi, "New York man wins $344 million Powerball jackpot by playing same numbers for 25 years," WKTV Website, November 15, 2018.
- Georgett Roberts, "Meet the winner of the biggest lottery jackpot in New York history," New York Post, November 14, 2018.
- George Marsaglia, "64-bit KISS RNGs, The Coding Forums, February 28, 2009.