Powerball Jackpot up to $85 million

There was no winner in last night's Powerball drawing.  Saturday's jackpot is now estimated to be up to $85 million.  While that is quite a large number (yikes!), it is by now means unusual in the history of Powerball jackpots.  According to Powerball.com, this year's winners have had the following jackpots:

Unknown Ohio	June 2, 2010	Unknown	$261,600,000 annuity $134,917,238.27 cash
Chris Shaw Missouri	April 21, 2010	Cash	$258,500,000.00 annuity $124,875,122.48 cash
Sandra Mcneil New Jersey	March 13, 2010	Cash	$211,700,000.00 annuity $101,600,000.00 cash
Frank Griffin North Carolina	February 6, 2010	Cash	$141,400,000.00 annuity $69,682,459.88 cash
Name Withheld Arkansas	January 2, 2010	Cash	$25,000,000.00 annuity $12,153,621.78 cash

The average jackpot won was $179,640,000!  So the $85 million estimated jackpot for this Saturday is not that large by historical standards.  Given that the odds of winning are over 1 in 195,000,000, that really shouldn't be a surprise.

Texas Woman Wins the Lottery for the Fourth Time! What are the odds?

(Austin) – Joan R. Ginther of Bishop in South Texas has won $10 million, the top prize in $140,000,000 Extreme Payout, a Texas Lottery® scratch-off ticket...

"Ms. Ginther today made her fourth appearance at Lottery Headquarters in Austin, collecting the top prize of $10 million in $140,000,000 Extreme Payout, a $50 ticket," said Texas Lottery Commission Executive Director Gary Grief. "Ms. Ginther won a $5.4 million share of an $11 million Lotto Texas jackpot in July of 1993, as well as a top prize of $2 million in the Holiday Millionaire scratch-off game in 2006. In August of 2008, she collected a $3 million prize in Millions and Millions, another scratch-off, which she purchased at the same retail location as the ticket she collected on today. Today’s prize is the second of the three top prizes offered in $140,000,000 Extreme Payout..."

Full news release at the Texas Lottery Commission.

Wow!!!  What are the chances of that happening?  The answer depends on a lot of variables: 1) the odds of winning each game; 2) the amount spent on tickets; and 3) the point in time of the odds calculation. 

1) The Odds of Winning Each Game
The odds of winning her latest prize, the $140,000,000 Extreme Payout game, are 1:1,200,000.  If we were to calculate the odds of winning all four prizes and we assume that Ms. Ginther only bought one of each ticket (more on that later) we would multiple the odds of each game.  So, if the odds of the other game are 1:500,000, 1:2,000,000, and 1:250,000, then her odds of winning all four prizes would be 1:300,000,000,000,000,000,000,000!!!

2) Amount Spent on Tickets
The last calculation we made assumed that Ms. Ginther only bought one of each ticket.  But what if she bought more than one?  Let's see how that variable will affect the odds of winning her latest prize, the $140,000,000 Extreme Payout game.  The odds of winning $10 million are 1:1,200,000.  Let's assume that over the past year, Ms. Ginther (presumably still a wealthy woman from her past winnings) has purchased 100 of these $50 tickets for a total cost of $5,000.  Her odds of winning would now be much, much better: 1:12,000 (1,200,000 / 100 = 12,000).  So, let's now assume the lucky winner bought 100 tickets of each game in which she won.  Her odds of winning would now be 1:3,000,000,000,000,000, which is still a very small chance!

3) The Point in Time of the Odds Calculation
This is another way of saying, what are the odds of Ms. Ginther winning one game?  Let's go back in time to a few weeks ago before her latest win, and ask the following question: given that Ms. Ginther has already won 3 games, what are the odds of her winning $10 million playing the $140,000,000 Extreme Payout game if she buys 100 tickets?  Because all 4 events are independent of each other (one does not affect any other), her odds of winning would be just the odds of winning $10 million: 1:12,000.

So, the probability of Ms. Ginther winning all 4 games is indeed very, very small, but if we assume that she bought a large number of $50 tickets, her odds of winning just the $10 million are much, much better.

NC Lottery Millionaire Raffle and MI Lottery Red Hot Raffle Calculation

A few state lotteries run raffles once or twice a year.  It's pretty simple: you buy a numbered ticket; if your number matches the number the lottery picks from all the numbered tickets that were sold, you win.  Typically the price of a ticket is either $10 or $20 and the top prize is between $100,000 to $1,000,000.

Right now, only two state lotteries are running raffles: Michigan (Red Hot Raffle) and North Carolina (Millionaire Raffle).  Are these two raffles a good deal for the player?  In other words, are there other games within each state lottery that have better odds of winning the same prize?

Let's start with Michigan.  A Red Hot Raffle ticket costs $10, the top prize is $100,000 and the odds of winning are 1:50,000.  A comparable game in Michigan is Fantasy 5 which costs $1, has a starting jackpot of $100,000 and 1:575,757 winning odds.

	Ticket Cost	Odds of Winning	$10 Play Odds of Winning
Red Hot Raffle	$10	1:50,000	1:50,000
Fantasy 5	$1	1:575,757	1:57,576

If you were to buy ten $1 Fantasy 5 tickets, your odds would be 1:57,576.  Normally, Fantasy 5 has the best odds to win $100,000.  In this case Red Hot Raffle technically has better odds.  However, most of the time, the Fantasy 5 jackpot is quite a bit higher, in which case you're better off getting a Fantasy 5 ticket.  The downside is that if someone else has the same winning numbers, you're going to be sharing the jackpot, unlike in a Raffle, where you're guaranteed to keep the whole prize.

North Carolina's Millionaire Raffle costs $20, has a top prize of $1 million (with taxes paid, so the actual value is $1,470,579) and 1:166,667 winning odds.  There are 3 other games in the NC Lottery that have a $1 million prize: Mega Millions w/ Megaplier, Powerball with Power Play, and the $200 Million Extravaganza Instant Scratch Off game.

	Ticket Cost	Odds of Winning	$20 Play Odds of Winning
Millionaire Raffle	$20	1:166,667	1:166,667
Mega Millions with Megaplier	$2	1:6,833,227	1:683,323
Powerball with Power Play	$2	1:5,138,133	1:513,813
$200 Million Extravaganza	$20	1:1,344,000	1:1,344,000

Applying the same type of calculation as we did for Michigan, in this case we have a clear winner: the Millionaire Raffle. Not only does it have much better odds of winning (about 3 times better than Powerball), it also has a better prize: $1 million with taxes paid.  The only downside is you have to spend $20 to get a chance to win.