Tag Archives: probability

What’s the expected value of your Powerball ticket?

As the Powerball jackpot grows to over $300 million, we start to wonder if maybe buying a ticket is “worth it.” While the lottery is “worth it” in that ticket sales goes to things like state education, buying tickets is typically not worth it for yo because the projected payoff is far less than the ticket price.

The concept of Expected Value is a central idea in probability and statistics and refers to a weighted average outcome. For our Powerball example, the expected value equals the probability of getting each combination of winning numbers, multiplied by the payoff of the combinations.

Spreadsheet Inputs

The Powerball website has a table with the odds and the payouts of each winning combination of numbers, making our job relatively easy.

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We can transcribe these into a spreadsheet:

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Spreadsheet output

There isn’t much logic to this one. First we convert the odds column into probability, by taking one over the odds plus one.

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Then we multiply the probabilities with the respective payouts by using the Sumproduct() Function:

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Since Powerball tickets cost $2, it seems we’re still losing about 65 cents on each ticket even with the jackpot above $300 million.

It looks even worse given the $302 million is the simple sum of annuity payments, while the cash value is much less at $187.3 million.

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That takes us down to 96 cents.

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Taking into account a 35% tax rate would then take us down to 62 cents. And then there’s the chance that there are multiple jackpot winners, resulting in a split (we won’t get into that one here, but check out this fivethirtyeight post for more). Finally, let’s use the Goalseek function in excel to see when it becomes worth it to buy a lottery ticket taking into account a 35% tax bracket.

Pull up Goalseek from the Data Tab –> What-If Analysis –> Goal Seek

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Then we set the after tax expected value cell (D16) to $2, by changing the jackpot cell (B5). Basically Goalseek is Excel’s functionality for “guessing and checking”, for those who are not as algebraically inclined…

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The answer? $806 million! And that isn’t accounting for potential splits which is pretty likely once the jackpot gets that high.

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How to decide (fairly) where to grab lunch with friends

Taking a walk and grabbing lunch is one of the simple pleasures of the workday. Unless of course, you bring your lunch to work. Sometimes with a group of people it is hard to decide on where everyone should go to lunch together. Maybe only one person enjoys the guilty pleasure of Taco Bell, while the others want to stick with Whole Foods. Or maybe half of the group wants burgers and the other half pizza.

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Here’s a relatively simple Google Mobile spreadsheet. It’s part 2 of our mobile phone spreadsheet series (See Part 1 on Tracking New Year’s Resolutions) that uses a weighted lottery to fairly determine where to go for lunch, taking into account each person’s individual preferences. Basically, each person gets 10 “points” to allocate to three restaurant choices. Each point is effectively a lottery ticket, and the spreadsheet randomly chooses the restaurant, with the probability weighted by how many points each restaurant has received. Continue reading

Monte Carlo Simulation – Fantasy Football playoff predictor

How likely will you make the fantasy football playoffs? It’s week 11 of the Fantasy Football season, which means there’s only three more weeks until the Fantasy Football playoffs. All your hard work up to this point – drafting your team, closely following daily fantasy football podcasts and injury reports, and agonizing over who to play in your Flex spot – rests upon what happens in these next few weeks. Continue reading

What are the chances a Little League baseball player gets to the Major Leagues someday?

baseballIt’s that time of the year when Little League World Series coverage heats up on ESPN, and viewers get to see a miniaturized version of baseball played at the highest level. This year has been especially impressive with a super-team from Las Vegas that rarely makes errors, the Chicago team that beat them, and of course the sensational female pitcher Mo’ne Davis, who throws as hard as some high school pitchers. Every Little Leaguer dreams of making it to the big leagues, someday making a career of playing the game they love.  But how hard is it to get there? This is a question that we will try to solve this week with the help of a spreadsheet.

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Probabilities & Dice Roll Simulations in Spreadsheets

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Photo: Amie Chuang

What is the probability of rolling any pair of numbers with two dice? Let’s first solve this and then confirm our calculated probability by simulating 500 dice rolls with a spreadsheet! In this post, we will focus on understanding basic probability concepts and then discover how with spreadsheets, we can actually see whether our calculated probability holds true!

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