Optimal strategy for purchasing scratch off lottery tickets

It is generally assumed that winning scratch off lottery tickets are double-blind randomly distributed. However, I suspect some "scattering" (probably systematically, but possibly manually) of the occassional "clumps" of winners is conducted to ensure that they are more evenly distributed throughout an entire print run. I have no facts to back this up, just my observation, and a guess based on how it would work if I ran the world.

In any case, If I was going to purchase 100 $1 scratchers, what would be the optimal strategy to maximize the chance of a big winner?

Without additional information it doesn't matter. The pool you're drawing from may be partitioned into subsets with varying properties, but you have no information about how that's done or where each subset may be. From your perspective it's as if it wasn't done at all. Given that, save gas money and buy everything from one store.

Edit to add: I just noticed your poll replies and one involves multiple games. From that standpoint, buy tickets from the game with the highest probability of an award which qualifies for your "big award" threshold.

Interesting question, but I believe the answer is "It doesn't matter".

Assuming the games have an equal number of big winning tickets left (check the claimed prizes statement before buying any), and have the same random "scattering", it shouldn't matter which games you buy from.

Now, there are two cases to consider: every store has, say, 1 big winner, OR, the big winners are randomly scattered so that some stores have 0 and some stores have many. Problem is, in the 2nd case you don't know which store you are at! I believe the odds work out to be the same in the end.

The only way to take advantage of known scattering (e.g. 1 big winner per store), is to buy & scratch one at a time from the same store until you hit, then move on to the next store. If you buy them all up front without scratching, I say it's all a wash.

Yes, I would expect some sort of "adjustments" to be made to the winners prior to their being shipped out. I don't know how long a game goes for but you don't want any "winners" too early. Also you don't want winners concentrated at particular vendors. So the Lottery scratchoff computer program would look like this:
Create Placeholders for Dummy Numbers that won't win.
Salt-in the winning numbers in some sort of fashion that all vendors and all mailing dates are included.
Create a Print Run that prints everything on one set of printers to be cut into rolls and sent to vendors.

Result: High volume vendors are more likely to have winners and print runs just prior to mailing dates would be richer also.

IDK if that would be necessary. You certainly want some winners early. You just don't want the main prize won too quickly, all the rest are expendable. So it makes sense to place the main prize somewhere among the last issue of the tickets.

Random distribution should take care of the rest. It's not particularly important for each individual store to have a winner, as media and social media can take care of getting the word around.

Let's assume that I buy tickets for the same game in a single store one at a time, revealing each one as I go. Assume that I hit a big prize, but not the top prize, on the 10th one. Should I stop purchasing tickets at that store, reasoning that only minor prizes and losers remain, or keep buying, reasoning it doesn't matter if I change stores or games since they are randomly distributed?

There is no ideal time or place to purchase them. You could check the state's website to see how many tickets & top prizes remain, but keep in mind that the info is dated.

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As far as clumping and scattering and "salting" goes, you're all way off.

The lottery purchases ALL the tickets for a particular game from the printing company at one time. It is the most economical way to print. Whether each order amounts to a couple boxes, a couple pallet sized forklift loads, or even truckloads, is unknown. But it's also irrelevant.

If the game is popular, the lottery makes a minor change to the design, such as the background color, on each successive replacement order. Keep that in mind if you have any old, uncashed tickets. Although the game remains the same, each printing run is considered a separate game, and the one year to cash winners starts shortly after they run out or stop distributing a particular printing run.


So the printer delivers all the tickets. Each box contains dozens of shrink wrapped packeges of tickets. Probably 12 dozen packages per box, and 100 to 500 tickets per package, depending upon the physical size.

The printer "probably" scatters the winners only to a very small degree if at all. I.E. Perhaps limiting each package to a maximum of one top prize. Beyond that, everything is irrelevant because when they are delivered to the lottery's warehouse, things get moved around. And the individual stores order the tickets by the package not by the box.

Am I painting a picture yet? There is no master plan that directs a particular ticket to a particular store.

What I'm trying to say is, the normal warehousing and distribution will scatter the winners without any deliberate attempt to scatter them. It will also, completely by chance, occasionally allow one store to get more than one of the top prizes of a particular game.


FYI: Theft of the lottery tickets is not an issue. Each shrink wrapped package has a unique barcode on the back of all the tickets. When the lottery retailer opens a package of tickets, he has to activate that bar code. Until then, you can't cash any of the winners from that package. The only tickets worthwhile to a thief, are the ones in the dispenser case at the retailer. The unopenened ones in the stockroom are worthless if stolen.

Quote: Ayecarumba

However, I suspect some "scattering" (probably systematically, but possibly manually) of the occassional "clumps" of winners is conducted to ensure that they are more evenly distributed throughout an entire print run. I have no facts to back this up, just my observation, and a guess based on how it would work if I ran the world.

It is a very common mistake to observe "clumping" and conclude that a process is not random. In reality, the lack of any "clumping" is the unnatural pheonomena. If someone manually tries to create what they think is a random process, they will generally put in fewer "clumps" than would be predicted hypothetically.

Quote: pacomartin

It is a very common mistake to observe "clumping" and conclude that a process is not random. In reality, the lack of any "clumping" is the unnatural pheonomena. If someone manually tries to create what they think is a random process, they will generally put in fewer "clumps" than would be predicted hypothetically.

Thanks DJ for the thorough response. However, even you seem to concede that there is some "scattering" to keep major prizes from clumping.

Paco, it is the lack of clumping in my, or anyone else that I have spoken to's experience, that leads me to believe "scattering" is occuring. If random assignments were always upheld, I would expect to hear news of two or three major prizes hitting within a few tickets, if not back to back to back.

Quote: DJTeddyBear

FYI: Theft of the lottery tickets is not an issue. Each shrink wrapped package has a unique barcode on the back of all the tickets. When the lottery retailer opens a package of tickets, he has to activate that bar code. Until then, you can't cash any of the winners from that package. The only tickets worthwhile to a thief, are the ones in the dispenser case at the retailer. The unopenened ones in the stockroom are worthless if stolen.

Interesting. But I'd say there has to be another method to activate them, because we used to get a few packs (150 $2 tickets per pack, for example) mailed directly to us at the radio station from the NJ Lottery to give away at live broadcasts and whatnot. These tickets were exactly the same as the ones in the stores, and that's where listeners had to go to redeem them. I can say 100% that our shrink-wrap never had the extra bar code. I guess they activated them at the Brunswick Circle in Lawrenceville right before they mailed them to us.

We had a few $100 winners over the course of the years, but never more than that, and (because of that), I don't believe we ever had a "pack" that generated more than $300 in winnings. This was hundreds of packs...we got 4 or 5 every month for almost a decade and we were very careful about recording bigger winners. So basically, I'd say it doesn't matter how you buy them, because unless you hit a "big winner" (more than $500?), you are not going to win in the long run with a big purchase ($100 or more) in tickets.