Calculating the value of a single lottery ticket

Here’s a neat question – how much is a lottery ticket worth before the numbers are drawn?

The problem is a fun one for someone with a love of statistics, or someone who just wants to prove a point about why they never buy a lottery ticket. To answer it, I first make a few assumptions.

  1. The value of a future dollar is uncertain, so I will only base the value of winning a jackpot on the cash payment option, and not the annuity payments.
  2. Any prize over $5000 will automatically be taxed at a rate of 25% to federal and possibly some additional amount to state and local depending on the winner’s location. Hence, a jackpot-winning ticket is only worth at most 75% of the cash payment option after taxes.
  3. The more tickets that are purchased, the more likely it is that the jackpot will be shared if won, and so the number of tickets purchased must be a factor in any value equation.
  4. The non-jackpot prizes, since they cannot be shared and do not increase from drawing to drawing, will reduce to a simple constant in terms of the theoretical value of a ticket. (not actually true in California for some reason, so CA residents shouldn’t rely on this calculator too much)

To calculate the constant value of the non-jackpot prizes, I can use the odds and prizes printed right on the website of the lottery commission and add the resultant values of each together. For instance, a 1 in 50 chance of winning two dollars confers a pre-drawing value of 4 cents onto a random ticket.

The math is complicated, so I won’t post it all here, but if you’re interested you can read about it over at my personal blog.

Since the calculator involves knowing the number of tickets in play, I’ve worked out a formula for guesstimating the number of tickets sold for a Mega Millions or a Powerball drawing based on the going jackpot. To see it in action, fill in the cash prize amount and then click the appropriate setup link (or leave it blank and the current numbers will fill in for you automatically). I derived the formula using Excel’s trendline function. I’m actually pretty happy with my result. The R-squared value on what turned out to be a classic-looking quadratic was .9955 for Mega Millions and .9875 for Powerball, which is more than suitable for our purposes.

To quickly populate the settings for one of the two big US multi-state drawings, click one of the options below:
Set form for Mega Millions
Set form for Powerball

Jackpot Cash (not annuity) Value: $ million
State and Local Taxes:
(federal taxes automatically fixed at 25%)		 %
Number of Tickets in Play: million
Jackpot Odds of Winning: 1: million
Other Prizes, Odds

Hypothetical value of 1 random lottery ticket:

April 02 2008 05:55 pm | ajax

3 Responses to “Calculating the value of a single lottery ticket”

  1. Renee on 06 May 2008 at 3:33 pm #

    Found you on HBblogs. This is neato – nice job.

  2. Jay on 13 Sep 2008 at 11:37 am #

    Great idea too bad nothing happens when you press calculate

  3. Wolfman on 29 Oct 2009 at 9:19 am #

    I finally went back and fixed this. It works again (for now).