Say I want to buy ten scratch-off tickets. The local store sells a variety of scratch-off $1 tickets. Are my odds any better if I buy all ten in a row (from the same roll of tickets), or should I mix things up buying different tickets (from various rolls of tickets)? What do the statisticians say? I assume there is a factual answer to this.
In theory, the odds of any particular ticket being a winner don’t change. However, that assumes a completely random distribution of winning tickets.
Reasoning by analogy to baseball cards, at least as recently as the mid-90s, there was a certain manufacturer that always put a pack with a particularly valuable “rare” card in a particular location within a case of packages. If you knew that location, and happened to get to a freshly opened case in a store, you could reliably pick the package containing the most valuable card in the entire case.
I suspect a similar system is at least possible in rolls of scratch-off tickets. If so, and if you could learn the system, buying consecutive tickets might be to your advantage.
Possible, yes. But the potential for abuse would be high (store employees - or their friends - make a habit of scooping up the favored tickets) which gives a strong reason to believe steps would have been taken to avoid this.
There is, and it is that (assuming all those games are the same odds) it makes no difference whatsoever. Why would it make any difference, are you thinking?
Similarly with pick-a-number games (eg lotto); the odds don’t change no matter what numbers you pick. In that case what can change though is how many co-winners you get, so you should pick numbers that others are unlikely to pick (eg numbers over 31, which cannot be birthdays) so that in the extremely unlikely chance you win you share the prize with fewer people.
Better still of course is to put that money in the bank instead. You can’t lose it and you get interest for free.
Your best odds are to find the lottery that has the best odds of finding anything and buying multiple of those. Buying tickets from different games just means that you’re buying tickets from games with worse odds.
Overall, if you want to gamble though, you’re better to play the stock market. Buy a nice index fund, wait 15 years, and presto free money.
Your best odds are to look online at the lottery website to see what prizes have been won, and how long the game has been going on. Many tickets are sold after the largest prizes have already been found (see here). By knowing that the top prizes are still available, and when the game is scheduled to end, you can improve your odds slightly.
To expand on what brickbacon said- The online site and the cards themselves also indicate the exact odds to win any prize (usually ranging from like 1 in 3 to 1 in 8) and the odds in winning the grand prize on the card.
If you take the time to check to see what prizes have already been won and the remaining number of cards outstanding (also provided on the websites) you can recalculate your odds of winning any prize or the grand prize.
For example, If i wanted to buy some cards I would look for a card that for example had 8 out of 10 grand prizes remaining but half of the cards had already been sold.
I used to work at a store that sold scratch-offs. The best thing I could come up with to increase my odds was to play the games that no one has won in a while. So if one person loses 10 straight games on a ticket I would buy the next one.
All in all, I lost a lot of money doing this.
Technically, it did improve your odds, but not per-roll of lottery tickets (assuming they were random) but rather because it removed the number of duds from the total supply of all tickets. But of course that supply was so large that the 10 tickets didn’t make any appreciable difference.
In the UK you can, I believe, check with Camelot about the remaining prizes for any particular flavour of scratch card. If there are only 3 top prizes for grabs, and they have all been claimed, then this obviously means that only lower denomination wins are left, so maybe avoid that game. Is there a similar facility in the US?
As far as winning anything at all, I don’t think one strategy is better than the other unless one knew how many prizes each roll contained AND how many each had already paid out.
BUT…I think the odds of winning more than one big prize are better when getting each ticket from a different roll.
Here’s my thinking: There are X big prizes per roll. It’s extremely unlikely that more than, say two of them are within a batch of ten consecutive tickets on any given roll. (I’m thinking the lottery designers purposely space them out to avoid one person getting eight prizes out of ten tickets.) So with those ten tickets, there’s a maximum of two big prizes to be had. With one ticket from each of ten different rolls, however, ten big prizes are possible.
Your odds of getting any one of them is 10X less since you have bought 1/10th the tickets from each roll. This doesn’t help you.
No, this is not true. Random means random, and lotteries are about as random as is humanly possible. They don’t “space them out” in any way besides using a random number generator. That will sometimes put big winning tickets close together.
My point was that IF they were spaced out as I (wrongly?) speculated, then it would be impossible to win more than two from one strategy, while it would be possible to win ten from the other strategy. Possible, even at 10,000,000:1 odds, is better than impossible.
ETA: I agree that the overall chances of winning at all are not improved.
Regardless, remember that state sanctioned lotteries (at least in my state) payout less than “illegal” lotteries, since a percentage of the state sanctioned games benefit a charity. State sanctioned lottery winnings must also be reported to the IRS.
Vinnie the nose told me this. 
That’s true, but it might decrease the chance of you buying tickets after the big prizes have already been found. It could also increase the chance, depending on the distribution of the… It doesn’t really matter, checking online is a far better strategy.
Yes, that information is available from the lottery offices and usually posted on their websites.
Because I **just know **someone will want a cite, here:
Prizes yet unclaimed for Oregon scratch off games.
Cool, so we should buy consecutive cards from the same roll, then and win twice!
What if I can only afford one card, and after narrowing my choice to three the clerk scratches off one of them to demonstrate that it wasn’t a winner (since from following the pattern he knows it’s not a winner), would it be to my advantage to pick a different card or keep the one I have? Would it matter if the clerk was a steward on a treadmill-bound airplane?