You ever see these videos where some guy buys a whole roll of lottery scratchers and films himself scratching them off one by one? The logic seems natural – buying a whole roll has to return some big winners, right? But take a look at the odds of any scratcher: even if you had $4,000 in cash to buy the roll of 200 of the 100X The Money scratcher game, your odds of making that cash back would be 1 in 28,662 – even if no one had claimed any of the prizes yet!
Sometimes these guys might catch a lucky break and get a big remaining prize, but mostly the few prizes they land don’t come close to covering the cost of the roll. That’s because they forgot about the law of diminishing returns.
Buying a whole means spending more money than you need to in order to win money, which means spending more money than you’ll win back in that roll of tickets. In that video, he spends $300 on the roll but takes in only $184, for a $106 loss.
Since the Virginia Lottery website provides updated numbers on the remaining scratcher prizes, you can buy a number of tickets within one standard deviation of the mean odds of winning a prize worth more than the ticket cost (i.e., the odds of a profit prize + one standard deviation). This would use the 68-95-99.7 rule, giving you a 68% chance to win a prize and avoid diminishing returns. Here we provide you with a ranking of the best Virginia Lottery scratchers with the best odds just for this reason. That ranking includes a “Max Tickets to Buy” feature, based on this calculation, so you don’t need to do that math yourself.
We used to recommend buying as many scratchers as equalled three standard deviations from the average prize odds, which would bump up your probability of winning a prize to 99.7%. However, after conducting a statistical simulation to test the potential earnings based on buying various numbers of tickets we’ve revised our recommendation. It turns out that it’s not necessary to buy so many scratchers tickets to maximize earnings – you can better limit your losses for the best potential earnings by buying the number of tickets equal to the odds of winning a prize greater than the cost of the ticket.
The ranking of scratchers provides a list of scratcher tickets with the best tradeoff between number of tickets to buy and probability of winning. Filter the list for the scratchers that require the least number of tickets in order to win a prize. As of this writing, of a total 87 scratchers there are 20 of which you need only buy 10 or fewer tickets for the best odds of winning.
These may only include 5 scratchers that cost less than $10 each – so that might require spending $100 or more at a time to take in a profit. If you’ve got the cash, then it’s best to spend it on the more expensive scratchers since they have the best odds of any scratcher.
Still even if $1 scratchers generally have the worst odds buying then again buying 23 of those costs less than 7 of a $20 scratcher with the best odds.
So if you catch yourself thinking “surely there’s gonna be some big winners in this roll” remember this: odds are it will only be a bunch of small winners that won’t help overcome the cost of the roll. You want to maximize your chance of winning some cash? Heed the law of diminishing returns – stick to the numbers for the best odds based on the number of remaining scratchers.
