No. You probably won’t.
But if I’ve learned anything from every network news outlet it’s that you can print any ridiculous story heading with a qualifying question mark and not be penalized any journalistic integrity.
In actuality, this article is the first in a series of attempts at the “1 to 10 Challenge”, an exercise in outside-the-box thinking. The idea is simple: turn $1 into $10.
And for my first shot at the challenge, I’ll be selling used lottery scratchers on eBay.
Turn a $1 investment into $10 via any unconventional or nontraditional means.
Sell partially scratched lottery tickets on eBay.
I’m going to warn you right now, the following section contains quite a bit of icky math. If this sort of thing turns you off (why are you here then?) and you want to skip it, unconditionally accept the following:
“A partially-scratched lottery ticket may be worth more than a new lottery ticket.”
Got that? See you after class.
Early one morning, while brooding over my poor Google AdSense performance (I’m up to 1 cent!), my mind wandered toward my college Systems Engineering classes. I remembered the many “would you rather have” games that we were taught, and the powerful draw they had on people’s wallets — my own included. A thought struck me.
I did some Googling that afternoon, and the apparent lack of any other documentation suggested I might have an original idea. After discussing the concept with some smarter contacts, I realized this was certainly a chin-scratching issue. And while the underlying concepts involved are centuries old, I’m very interested in seeing how it all plays out.
Before we started, we need to first talk about Expected Value (EV).
Let’s play a game. You pay me $1 and I’ll flip a coin. If it comes up heads, I’ll hand you $2. If it comes up tails, you get nothing. Under probability theory, this is considered a fair game.
Simplified, the EV of the game can be calculated like this: (the chance of winning) * (the prize) – (the cost to play). If the EV is greater than $0, the player has an advantage. Less than $0, and the house has an advantage.
In our game, the EV is $0 (50% * $2 – $1). Therefore, both the house and the player have the same chance of coming out ahead; if you were to play this game forever, you should come out even. Pretty much every form of modern gambling gives the player a negative EV. The tired Vegas adage “the house always wins” is true. Lottery scratchers are no different.
Example Game 1
Consider a theoretical $1 scratcher game, “Sprocket Cash”. There are 6 boxes. Scratching a box reveals a prize amount. If the player scratches 3 matching prizes, they win that prize.
Now, “Sprocket Cash” is not a very fun game. There is a 85% chance that a scratched box will contain a $0 prize, and a 15% chance that it will contain a $15 prize. Unfortunately, with these odds, your chance of hitting 3 or more $15 prizes is only around 6.5%. Regardless, the total EV of this game is actually (-$0.02), meaning it is only slightly unfair — for comparison, real scratchers are around (-$0.40).
Let’s pretend you scratch all the boxes and have no matches. What is the EV of this game now? There is no chance for you to win any money and you’ve already paid $1.00. So your EV is (-$1.00). Shucks.
But did you notice what happened? The EV changed! Somewhere between buying the ticket and defiantly hurling the losing ticket to the parking lot ground, the EV went from (-$0.02) to (-$1.00). But why did the EV change? And how?
EVs are not static. As the game changes, so does the EV. Since your chance of ultimately winning could increase or decrease throughout the progression of the game, the EV will always reflect that advantage. (See the classic Monty Hall Problem.)
In “Sprocket Cash”, does the EV simply fall from (-$0.02) to (-$1.00)? Not necessarily.
Okay, you buy a fresh $1 game. Your first scratch is a $15 prize. Nice!
What is the game’s EV now? Your chance of winning the $15 prize has increased — you only need 2 more scratches out of 5, while before you needed 3 out of 6. In fact, the chance of winning the $15 prize has gone from 6.5% to 20.4%. Crunching the numbers, we find that the EV of the game has suddenly become +$3.05! You are beating the house!
If this is difficult to wrap your head around, let’s take the example to the extreme. Would you rather have a fresh lottery scratcher, or a game with two $15 prizes already scratched? The EV of the second game dwarfs the first.
Example Game 2
Still not convinced? Let’s try a different approach. I’ll flip a coin twice. If it comes up heads both times, I’ll give you $10. How much would you pay me to play this game? The chance of getting heads twice is 25% (50% * 50%). So if you pay me $2.50 (25% * $10), this is a fair game.
So you pay me $2.50 and I flip the coin.
Heads. Alright, you’re half way there. Before I can get to the second coin flip, you stop me. How much money is your position in the current game worth? That is, if you were to sell your spot in the game to someone else, how much should you charge?
Well, you only need one more heads to win the $10, so the fair cost is $5.00 (50% * $10). If you can find a buyer and sell it for the fair price of $5.00, you’ve made a profit of $2.50! You see where I’m getting at here?
Once again, the key point here is this: a partially used lottery ticket may be worth more than a fresh ticket.
Don’t Try This At Home
Before we go further, it’s important to understand that this door swings both ways. If you had scratched a $0 the first time, “Sprocket Cash” would decrease to an EV of (-$0.50). So there is certainly some risk here.
In fact, if you were to calculate the EV of a strategy selling a “Sprocket Cash” scratcher with a single box revealed, you’d be losing about $0.12 every ticket — it’s better to actually play the game than to try this strategy. So before you fire up your own eBay auction, know that from a purely statistical standpoint used lottery tickets are a bad investment strategy.
Also, note that I’ve made the assumption that lottery tickets are produced randomly — that each single box is chosen at random from set odds. Real lottery tickets are not manufactured this way. In a clever/evil marketing scheme, tickets are produced to create “close-calls” to engage the player. So scratching two $2,000,000 prizes may not necessarily increase the value of the ticket. Kinda sucks, but makes sense from a marketing standpoint.
Regardless of all this statistical jazz, real lotteries themselves make the state of California over $3 billion a year. So there is definitely a public stupidity variable involved that’s not included in our classic statistics models.
So, to simplify my justification:
- Lottery scratchers are not worth $1
- People are willing to pay $1 for a lottery scratcher
- A partially scratched lottery ticket may be worth more than a fresh ticket
And the question?
- Are people willing to pay more for a partially scratched lottery ticket?
Let’s give this idea a go.
At this point I’d like to state that I have absolutely no expectations or delusions about the possible success of my plan. In fact, I entirely expect to lose money in my attempt. But silencing my curiosity, coupled with the opportunity to loudly declare “for science!”, make it worth the price of admission.
I purchased a few “Make Me a Millionaire” tickets from my local Vons. Some of you may know of my previous gambling escapades; I could definitely sense some undeniable power of these things. Like a bad case of the chicken pox, I struggled to restrain myself from the urge to scratch them. So stashing the tickets away from sight and pleased with my previous analogy, I returned home to do some quick research before I started the auction.
Surprisingly, I was easily able to find some deeper statistics on the game through the official lottery site. Using my Excel-Fu, I was able to confirm that theses tickets were not produced randomly. Given the odds of winnings each prize, one can calculate the probability of “getting 3″ prizes, and then “getting 1″ prize. In a perfectly randomly generated ticket, the sum of all “getting 1″ probabilities for each prize amount should add up to 100%.
“Make Me a Millionaire” does not. Therefore, this ticket has some sneaky marketing hidden inside. Fortunately, this marketing may be to my advantage.
I scratched one box off each of the tickets. Of the five tickets I had purchased, two had $3, two had $25, and one had $500. I decided that attempting to sell the $3 tickets probably wouldn’t generate that much money, so I gave in to my gambling urges and scratched the two $3 tickets — and won $2! Well, I’ve at least made part of my money back.
I created auctions for the three remaining tickets, which can be found below. The auctions will start at $0.35 and continue through next Wednesday.
Updates and results as they come.
UPDATE [08/05] 11:55AM:
It was pointed out to me that it may be a misdemeanor in California to resell lottery tickets. I am temporarily pulling the auctions until I verify this myself.
UPDATE [08/05] 12:01PM:
Any lawyers out there care to chime in?
UPDATE [08/05] 12:41PM:
Well, that pretty much says it all.
Blast! I think this whole plan should be filed under “interesting, but illegal”.
California law and eBay’s policy forbids the resale of lottery tickets — something you’d think I would have considered at the onset of my plan. But alas, my head was in the statistics clouds.
Scratching the remaining tickets unsuprisingly yielded no winners.
The final numbers:
- 5 lottery tickets: (-$5.00)
- 1 winning ticket: +$2.00
- Net: (-$3.00)
- Target: +$50.00
- Challenge Status: FAIL
Off to a rocky start with the “1 to 10 Challenge”.
Guest contributor Blaine is up next. We’ll see if he can do better.