The Odds of Winning The Lottery

When the recent Mega Millions Lottery jackpot of $355 million hit the news and I kept hearing how horrible of a gamble the lottery was. With odds of winning the jackpot at 1 in 175,711,536 the lottery is a bad bet to be sure. But odds like that are hard to conceptualize. On the other hand, with such a huge amount of money on the line who could resist the chance at winning big for only $1?

So, just for fun, I created a Lottery Excel Spreadsheet to calculate the expected return on a lottery ticket for a given jackpot amount. The key variables determining the return are:

  • The Probabilities of Each Lotto Prize
  • The Amount of the Jackpot
  • The Number of Tickets Sold (predicted from historical data)
  • The Number of Winning Tickets
  • The Income Tax Rate

As it turns out for a Lotto jackpot like the most recent of $380 million the expected return on a $1 ticket is -23¢. Not great, but everyone knows that the house always wins anyway, so how does this compare to casino gambling bets?

Expected Returns on a $1 bet at the casino:

  • Roulette – Red/Black: -5.26¢
  • Craps – Pass-Line: -1.41¢
  • Craps – Seven: -16.67¢
  • Slot Machines: -3¢ to -14¢

So the Lottery is a much worse bet than anything in Vegas. And it just gets worse as the size of the jackpot decreases to more common levels. A $100 million jackpot has a return of -63¢.

However, when it comes to big multi-million dollar win (the low-likelihood scenarios in either case), the Lotto actually offers better odds because other games have decreasing probabilities with each repeated play. Although, if you are ok with turning your $1 into a mere $20 million after tax or less ( a $54 million Lotto jackpot), then you are much better off doubling down on a $1 bet in craps (odds of 1 in 97,079,014). Although you’ll still have to win 26 times in a row.

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One Response to The Odds of Winning The Lottery

  1. Bill Berg says:

    Remember, the lottery is a volunteer tax for those with poor math skills.

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