I pulled this out of our mail the other day:

*Seriously?* Someone at the Pennsylvania Lottery must be playing a joke. Big Savings? Let me get this straight. You’re going to use a coupon to buy a lottery ticket, and that’s going to bring you big savings? Let’s think about this just a bit.

#### What Are Your Chances of Winning?

Let’s use the September coupon for our example. This coupon gives you one $2 Mega Millions with MegaPlier ticket for free if you buy one $2 Powerball with Power Play ticket. Basically, this is just one set of numbers because a regular ticket costs $1 for one play and the Power Play (or MegaPlier) doubles the cost of the ticket.

The Pennsylvania Lottery’s website says your overall chances of winning a prize with a Powerball ticket are 1 in 35.11.

We can figure out your chances for winning any of the specific prizes with some simple math. If your chances of winning a prize are 1 in 35.11, that means you have a 2.8482% chance ((1/35.11)*100) of winning every time you play Powerball. (Not very good, huh?) **Basically, you can only expect to win something once out of every 35 tickets you buy.** But that doesn’t tell us how much the ticket is really worth because your prize can range from $3 to $14,000,000 (or $6 to $14,000,000 if you buy the Power Play option) given the current jackpot. To figure out the

*value*of your ticket, we’ll need to do a little more math.

#### What’s Your Ticket Really Worth?

By using the odds given for each specific prize level, we can figure out the average prize for a winning ticket. Overall, you have a 2.8482% chance to win on any given ticket. You can use the same process to figure out your chances of winning a given prize. For example, the Pennsylvania Lottery website says you have a 1 in 61.73 chance of winning the lowest prize of $3. That’s a 1.61996% chance ((1/61.73)*100) of winning $3 on any given ticket. Since you have a 2.8482% chance of winning * any* prize,

**you’d expect a little more than half of your winning tickets to have a $3 prize**. (The math is simple: 1.61996/2.8482 = 0.568766 * 100 = 56.8766%.)

Continuing this process for each prize level, we can figure out your chances of winning a specific prize any time you have a winning ticket. This table shows those chances for a regular Powerball winning ticket.

Match |
Prize |
Chance of Winning This Prize on a Winning Ticket |

5 Numbers + Powerball | Jackpot (currently $14,000,000) | 0.000018% |

5 Numbers | $200,000 | 0.0006833% |

4 Numbers + Powerball | $10,000 | 0.0048552% |

4 Numbers | $100 | 0.1845% |

3 Numbers + Powerball | $100 | 0.2573% |

3 Numbers | $7 | 9.7787% |

2 Numbers + Powerball | $7 | 4.4604% |

1 Number + Powerball | $4 | 28.4363% |

Powerball Only | $3 | 56.8772% |

Now we can figure out the value of a winning ticket simply by multiplying the prize by your chance of getting that prize on any given winner. Doing that tells us that **the average winning ticket for regular Powerball is worth $7.65** ($8.65 – $1.00 for playing). Adding the Power Play to the mix changes the prize values, so the average winning ticket for Powerball plus Power Play is worth $24.04 ($26.04 – $2 for playing). (And technically, it would be worth a little less than that because there’s always the chance you might have to split the jackpot with someone else. But I don’t feel like finding the stats on that or doing the math.)

That leads us to the next question. If the average winning ticket is worth $7.65 (or $24.04 for Power Play), then what is the average ticket worth? You only have a 2.8482% chance of winning that $7.65 (or $24.04). We need to take into account the cost of your losing tickets, which you’ll have 97.1518% of the time. Remember, you have to buy 35.11 tickets before you can expect to have a winning ticket (based on the odds). That leaves you with 34.11 losing tickets. **If you’re playing regular Powerball, you’ll need to spend (that is, lose) $34.11 to win $7.65.** If you’re playing Powerball with Power Play, you’re looking at a cost of $68.22 to win $24.04.

Our last bit of math will tell us the average value of any given ticket. Let’s check regular Powerball first. On average, you’ll spend $34.11 to win $7.65 leaving you with an **overall loss of $26.46**. Divide that by the total number of tickets you had to buy (35.11) and you’ll find that the average regular Powerball ticket is worth * -$0.75*. To put it another way, instead of buying a $1 Powerball ticket you might as well throw three quarters in the trash. (Oh wait, I forgot…the Pennsylvania lottery benefits older residents – every day. So maybe you should just donate the three quarters instead.)

What about Powerball plus Power Play? It certainly looks like a more attractive value proposition at first glance since the average winning ticket is worth so much more. On average, you’ll spend $68.22 to win $24.04 leaving you with an **overall loss of $44.18**. So that means the average Powerball plus Power Play ticket is worth ** -$1.26**. This time, instead of donating three quarters rather than buy a Powerball plus Power Play ticket you should donate

*! In terms of absolute dollars, you lose more with Power Play but the % loss is better than regular Powerball. (In regular Powerball, you lose 75% of your money forever. With Power Play, it’s “only” 63%. Granted, it starts looking a little better when the jackpot is very large, but your chances of splitting the prize increase as more people buy tickets. This means the lottery is always going to be a losing bet.)*

**five quarters** Let’s put this all into a little perspective. **Buying a Powerball lottery ticket would be the equivalent of getting a $10,000 gift, going out into your back yard, and then proceeding to burn $7,500 of it for “fun”.** Big Fun – according to the Pennsylvania Lottery.

#### You Want Big Savings? I’ll Show You Big Savings.

I’m not going to take the time to prove that the lottery (in any form) is a waste of your money. You can simply look at the July 2009 – June 2010 annual income and expense report from the Pennsylvania Lottery to see that they **only end up paying out about 61% of their total sales to winners**. Talk about a great business! I’d take a 30% net profit margin any day. (The other 9% goes to other expenses.)

Looking at those numbers from the other end, we see that lottery players as a whole are buying something with a * guaranteed return of -39%*! You want big savings? Here’s a thought. Stop paying the poor people’s tax.