Odds of a Christmas Lottery

Yesterday I was given the gift of potential money at work. No, I wasn’t awarded a Christmas bonus, but one of my coworkers left a holiday card on my desk, while I had stepped away momentarily, before she made a quick exit. Inside the envelop  was a holiday card containing a friendly greeting to wish me a wonderful holiday season and a photocopy of two lottery tickets–the Mega Millions and California’s Super Lotto Plus–and their corresponding numbers. Should either ticket contain all the required numbers for the large jackpot, the winnings would be split evenly between my coworkers and me.

While I appreciate the sentiment of the friendly gesture from my coworker, I began to wonder if she should have spent $24 on the two lottery tickets. The reason is due to a formula my friend Ray had mentioned to me once. He had learned of the formula in one of his required business classes while working towards his MBA. Simply stated, if the jackpot times the odds of winning is great than 1 (one), then one is justified in purchasing a one dollar ticket; otherwise, one would be advised against purchasing the ticket.

For the first lottery, which is the Mega Millions, the total jackpot is $173 million. According to the MM’s website, the odds of winning the jackpot are 1 in 176,000,000 or (1/176,000,000). My calculations show $173,000,000 x (1/176,000,000) yields 0.983, which is less than 1, so one should not purchase the ticket.

For the second lottery, which is California’s Super Lotto Plus, the total jackpot is $7,000,000 with odds of wining the jackpot being 1 in 41,000,000 or (1/41,000,000). My calculation shows $7,000,000 x (1/41,000,000), which is 0.171. Since that value is less than 1, one should not purchase any lottery tickets for the Super Lotto Plus either.

My coworker bought $12 worth of tickets for each lottery. I understand her kind gesture aligns with the spirit of the season, which I really appreciate and will be sure to give her much thanks the next time I see her. My intent was not to criticize her purchase–it was a friendly gesture, after all, and done as an act of good will–but simply to apply a formula someone had told me about regarding the lottery.

I guess I was wondering too loudly because one my coworkers chided me for “jinxing” the numbers; thus, lowering our chances of winning the prizes, although I think I stand a better chance of being struck by lightning or being involved in a shark attack.

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