Despite earning an MA in mathematics from the University of Illinois in 1968, I don’t consider myself a mathematician. College math classes in the late 60’s focused on “modern math” with very little practical application and almost no computer or even calculator technology. Those were the days of punch cards, and Fortran, and Max Beberman and abstract algebra. There were no statistics courses in our curriculum either, even though most of my classmates were preparing to enter or return to teaching after finishing our NSF academic year institute. So when I talk about the Powerball lottery’s changing odds, I’ll give you some very basic information, and then I’ll direct you to a site where the real mathematicians among you can satisfy your desire to know more.
Readers who do not care for mathematics should skip the next five paragraphs, everything between the $$$’s. Those casually curious about how odds are figured can read on. Expert and serious mathematicians should link to the web address for fivethirtyeight.com instead.
$$$ $$$ $$$
Everybody knows how Powerball is played. Currently the winning Powerball ticket consists of matching five white balls chosen without replacement from a group of 59, and one red ball, the Powerball, chosen from a group of 35. Everyone knows how to play, but not ot everyone knows how the odds of winning are calculated.
The calculation of the number of possible draw combinations is simple: ((59*58*57*56*55)*35 / (5*4*3*2*1). where * indicates multiplication and / indicates division. This simplifies to 175,223,510 combinations, so the odds of winning the Powerball today is 1:175,223,510. (Sticklers for accuracy might say 1:175,223,509 since there is 1 winning combination and 175,223,509 losing ones out of the 175,223,510 possibilities. Either number will do.)
The general formula for drawing m correct items from a set of n items without replacement and regardless of order is: C = n*(n-1)*(n-2)*… (n-m+1)/(m!), where C is the number of combinations, n is the number of items in the set, and m is the number of items to be selected. In the calculation above, the five white balls count down from 59 through 55. The 5! figure is the product of 5*4*3*2*1 because we have to choose 5 numbers for white balls and the number 35 accounts for the solitary red ball.
My husband prefers to calculate the probability of winning by multiplying 1/(59*C5)*1/35. That’s the number of combinations of 59 things taken five at a time. Either way there are 175,223,510 possible choices for you to pick for your Powerball ticket. I find it easier to just look at the back of the ticket where we bubble in our choices to see what the odds are myself. Or to just ignore the odds entirely since they're so astronomical they don't really matter. If you would like to calculate the new odds for yourself, however, the following information will allow you to use the formula above to do it. Or you can just accept the odds figure I’ll give you from an internet source.
The new rules going into effect for the October 7 drawing this year will change the field of 59 to one of 69 for white balls. The second red ball field will decrease from 35 to 26. If you want to calculate the odds yourself, in the above formula n becomes 69, m is still 5, and the number 35 for the red ball will be replaced by 26. If I’ve made no errors typing, and you’ve made no errors calculating, the odds to win the new Powerball jackpot will be 1 in 292,201,338.
$$$ $$$ $$$
So, now that we’ve finished with the arithmetic for calculating the odds of winning, we find our chances will actually be WORSE after the new rules go into effect. (Surprise, surprise!) Our odds of winning the Powerball will drop from 1 in 175,233,510 with the current 59 white balls and 35 red ones to 1 in 292,201,338 with the new 69 white and 26 red ones. The Powerball will be harder to win (and its already practically impossible), but the jackpot will be bigger if we do. The chance that it could make the winner a billionaire is about 7.5 times as high.
Walt Hickey has a wonderful article on the fivethirtyeight.com site that you will enjoy. He has devised a basic model simulating Powerball jackpots over the next five years of play. Under the old rules, there was a billion-dollar lottery in only 8.5% of the simulated 5-year periods. Under the new rules, there could be a billion-dollar simulated lottery in 63.4% of the periods. The Powerball jackpot starts at $40,000 and rises at least $10 million between drawings, no matter how many tickets are sold. More tickets are sold as the jackpot gets bigger so the increase is not always $10 million. Mr. Hickey has graphs and calculations based on various assumptions that lead him to believe the 17th drawing might be the elusive billion-dollar lottery. That’s the one December 2 if you have faith in his figures.
Even though it will be harder to win the jackpot under the new rules, the odds of winning secondary Powerball prizes will improve. You currently have a 1 in 32 chance to win anything at all. After October 7, you will have a 1 in 25 chance to win a prize. More small prizes. Less big ones. Just like our slot pays! The third prize category is better. It is currently $10,000, but with the new rules winners in that category will make $50,000.
I may buy a ticket for the first drawing on October 7 since that is also my birthday, but it will probably be the only one I ever buy. My odds of being struck by lightning are much better than winning the Powerball jackpot. Nationalgeographic.com says my chances of being hit are 1 in about 700,000. Discovertheodds.com says the US Weather Service calculated that there were 280 deaths between 2001 and 2010 from lightening strikes with a US population of about 310,000,000 so the odds are 1:1,107,143. The same source says the odds change depending on where you Iive. In Montana the odds were 1:249,500, but in California, where I live, the odds are 1:7,538,382.
Bottom line, there’s not much chance of winning the Powerball under old or new rules. You are much more likely to be struck by lightening than win either one. Besides, playing the slots is a lot more fun than gambling on the lottery any day. I’d rather take my chances with the machines at my Native American casinos than with the lottery kiosks. Wouldn’t you?
Bottom line, there’s not much chance of winning the Powerball under old or new rules. You are much more likely to be struck by lightening than win either one. Besides, playing the slots is a lot more fun than gambling on the lottery any day. I’d rather take my chances with the machines at my Native American casinos than with the lottery kiosks. Wouldn’t you?
No comments:
Post a Comment