Scratch-off lottery games WILL eat your lunch

A few weeks ago I met “J” of BudgetsAreSexy.com, and Nicole of Breaking Even Communications, up in DC.  It was a great way to spend a Sunday afternoon, and in the process I really got a feel for what generous hearts they both have.

Subsequently J gave me a sneak peek at another charity project he had in the works.  At the moment it appears he has it on the back burner, but from what I saw it was really polished and had a nice message to it.

So I wasn't surprised when I saw that he had more giving activity going on this weekend.  He bought $100 worth of scratch-off lottery tickets and pledged any winnings to Project Hopeful.  After all was said and done, he raised more than $200 through his winnings and other matching donations.  Not bad at all!

In the weekend leading up to The Big Scratch, he entertained guesses for what his winnings would be.  He was hoping for $125, but my guess was closer to the right answer than anyone else's.

I guessed he'd win $39, and he actually won $38.

Now, I understand completely that this was all in fun and I know without a shadow of a doubt that J's heart was in the right place in doing this, and I'm not trying to take that away from him at all.  But I knew that it was almost a sure thing that he wouldn't win more than the cost of the tickets.

Why?  Mathematics.  The more tickets you buy, the more likely you are to come close to the mathematical odds that were set forth in the game. There are two extremes.  If you buy one ticket, you either win 100% of the time, or you lose 100% of the time.  That's one extreme.  If you buy all of the tickets, and if the odds of winning are 1:4.21, or 23.75%, then you'll win 23.75% of the time.  That's the other extreme.

J bought 100 tickets, and he had 20 winning tickets out of 100, or 20%.  That's not that far off from 23.75%.  Had he gone all out and spent his yearly entertainment budget of $1200 (assuming $100/month), his win percentage would likely have been within a percent of the actual odds.

“Well, one of those tickets could have been a big winner, MBH.”  Absolutely right.  But not likely!

Let's take ‘Tis The Season, one of the games J played. I'll assume that the 1:4.21 odds apply to this game (they may not). The Maryland Lottery page shows the number of unclaimed prizes. Here are the numbers as of right now:

$1,000 – 16
$500 – 316
$100 – 567
$50 – 741
$12 – 7,592
$6 – 33,176
$3 – 57,130
$2 – 191,098
$1 – 270,869

Just as you'd expect: There are a lot more smaller prizes than big ones remaining. But let's add another row to these numbers:

$1,000 – 16
$500 – 316
$100 – 567
$50 – 741
$12 – 7,592
$6 – 33,176
$3 – 57,130
$2 – 191,098
$1 – 270,869
$0 – 1,802,431 (est.)

I took the number of unclaimed prizes (561,505) and multiplied that sum by 3.21 (4.21 – 1) to estimate the number of non-winning tickets.  The majority of tickets are in that last (unwritten) line.

Playing the lottery long-term is a money-loser. It will eat your lunch without question.  J just took the opportunity to compress a year's worth of lottery playing (two tickets per week) into a single weekend.

So anyway, I'm glad that J raised as much as he did.  He even offered to buy me a beer for being the best guesser.  But after this post, I'm probably the one who will need to be buying. 😉