math in real life

powerball

Powerball is all the rage right now. Despite knowing that I could have spent my $6 on something useful, I still gave in to the hype.

powerball

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“An Annuity Option means winners can choose to be paid in 30 graduated annuity payments made over a twenty-nine (29) year period. A Cash Option means winners can choose a one-time cash payment which will be (approximately) the cost of the annuity divided by the number of winning tickets. Note: If a winner fails to claim the jackpot and select a jackpot payment option within 60 days, the prize will be automatically paid as an annuity. All prizes must be claimed within one year of the drawing.”

My Facebook newsfeed has been hopping with erroneous applications of dividing the jackpot by the U.S. population as a “solution for poverty,” people making fun of the incorrect math, fun math discussion, and fun speculation of “what would you do if you won?” My friend Heather pointed out “So I tried to figure out a scam to win: if you need 292M permutations to win, at $2 a ticket you need a bankroll of $584M – the lump sum pay out is 62%, and that definitely puts you in the 39.6% income tax bracket… The take home is $487M (not counting the cost of the team of lawyers you now need to employ). Back to the drawing board.” Likewise, my friend Jonathan said “Also, isn’t the $1.3 billion mythical? In the sense that, if one elects a one-time payment, the payout is substantially less, and the $1.3 B number is only achieved by adding together 30 years of nominal payments of 1/30th of $1.3B. Of course, in 30 years, the last payment will be worth less than half its value in today’s dollars. In a real-life conversation, my friend Ashley said that she’d rather take the lump sum and invest it because she could get a better interest rate than with the annuity. I would love to examine the concepts of probability, expected value, inflation, annuity, and taxes with students (not to mention the social aspects of lottery winning). It would make good fodder for a math debate…

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I would also be interested in having students analyze the changes in the Powerball game structure:
“Powerball® Enriched: Starting Jackpots Double to $40 Million
In January 2012, Powerball® was redesigned to bring even more excitement and value to its players. Jackpots in the multi-state game now start at $40 million and grow faster overall. There are more chances to win a prize of at least $1 million cash and the overall odds of winning any prize in the game are also better. Beginning with the January 15, 2012 drawing, game tickets increased from $1 to $2 per wager.
The Power Play® add-on feature is also available for an extra $1 per play. For that extra $1, players have the chance to multiply their prize by as much as ten times. Just before each Powerball drawing, a multiplier number (2X, 3X, 4X, 5X and 10X) is randomly drawn. If a player purchased the Power Play option for an extra $1 per play, that randomly selected number is used to multiply any prizes won, with the exception the JACKPOT and the Match 5 prize (which increases from $1 million to a set $2 million with Power Play).

Powerball with Powerplay gets bigger!
October 4, 2015 – The multi-state Powerball lottery game changed the matrix which is designed to produce larger jackpots and add more winning experiences. In the new matrix, players will select 5 out of 69 white-ball numbers and 1 of 26 Powerball numbers. The overall odds of winning a prize in the game improves from 1 in 31.8 to 1 in 24.9.”

Questions
1) How would you approach this with your students?
2) What would you do first if you won the jackpot?

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