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Tag: <span>winning strategies</span>

Tag: winning strategies

9 Tips for Winning Virginia Lottery Scratchers

We’ve been studying the secrets behind the Virginia Lottery Scratcher system to really understand the ways the Average Joe can maximize his chances. Here’s some tips you should remember before you buy any lottery scratcher:

the 9 tips for maximizing chances at winning money with Virginia Lottery scratcher tickets.
The 9 tips in short

1. Check the scratcher prize odds first.

Many don’t realize it but the Virginia Lottery commission posts all the odds for each game on it’s website: https://www.valottery.com/scratcher-search. The website shows the overall odds for winning any prize along with the odds of winning the top prize. For this $30 scratcher game, that comes to 1 in 2.95 for any prize and 1 in 2,448,000 for the top prize of $5 million.

That means you can do the math and see whether it’s worth a higher cost for better odds of prizes that return more money. In comparison to that $30 per ticket scratcher game which has odds of 1 in 2.95 for winning $30 or more, this $1 scratcher game has odds of 1 in 5.05 of winning a prize of $1 or more. Additionally, the odds of winning the top prize for that game may be much better – 1 in 367,200 – but the top prize is only $1,777.

2. Check the number of remaining lottery scratcher prizes

While you’re looking at the scratcher game pages, you may have noticed the table showing the number of prizes remaining in circulation for that game along with the number of prizes distributed at the start of the game. Every seller of scratchers scans winning prizes into the Virginia Lottery system, so they know exactly how many prizes remain available to win. The VALottery.com website updates these counts daily.

While you may be just as likely to win a prize at any time, due to random disbursement of prizes among the rolls issued to sellers, logically it makes sense that fewer prizes in circulation = prizes are harder to find. The remaining prize counts will tell you if this scratcher game is more depleted than others.

3. Check the current odds, not just the starting odds, from the number of remaining scratchers

Under number 1, I should have said you can check what the odds were at the start of game. You can calculate the current odds of winning any prize from the count of remaining prizes, if you do a little reverse math: total up the number of prizes remaining and multiply the sum by the overall odds to get the total number of scratcher tickets issued. Then divide the sum of prizes from that total of tickets issued.

Note that the overall odds never change – you used that number to calculate the total tickets issued, after all, and in theory all prizes are claimed equally over time. However, you can calculate the probability of landing any particular prize from the count of remaining tickets with that prize. AND you don’t have to rely on the outdated initial count of prizes issued; it can be accurate within the last 24 hours.

If that sounds like a lot of work, we’re here to help! Check out our list of current odds for all scratchers on our home page: scratcherstats,com. In fact we take it one step further – that list ranks the scratchers by the best current odds. See our Methods page for more details on the rankings by probability.

4. Don’t just check the probability of any prize, but the probability of winning prizes that return a profit

Winning a prize is always fun, but more often that prize will be for the amount of time you spent buying that ticket. Don’t get me wrong, I like getting money back, but I prefer getting a little something extra. That’s why you should calculate the probability of winning a profit, not just the probability of winning any prizes, from the number of prizes remaining. On our ranking list, we’ve factored that into the rankings. Find out more about how we compiled that ranking here.

The odds of a “profit prize” are lower than winning any prize, of course. For example, looking at the statistics we list for each Virginia scratcher, the average of winning any prize is 25%, while the average of winning a profit is 14%. But those odds of a profit range depending on the game, anywhere from 3% to 35%. If you plunk down cash for a scratcher, you’re going to want to get the one most likely to return some extra cash. That’s why you should use our list before buying.

5. Play the games with more prizes, not bigger prizes

If you’re following the tips above then you’re ready to play for more frequent small wins rather than rare big wins. Think of trying to find lots of coins buried in the mud with a few rare gold dubloons. If you aim to scoop up as many quarters, dimes, and nickels with the attitude that a big win would be nice but not expected, you may find yourself winning a pretty nice pot of change in the end.

6. Buy more than one scratcher at a time

The heart of the best strategy when buying scratchers is this: buy a string of scratchers, ideally from the same roll. As explained in more detail here, the reason is that you maximize your chances by buying a number of scratchers most likely to contain a winning ticket. Along with calculating the probability of winning tickets from the number of remaining prizes presented on the website, you can can also calculate the standard deviation. Given the statistical laws of a normal distribution, you are 99.7% likely to turn up at least one winning ticket when purchasing a string of tickets equal to the odds of winning plus three standard deviations from a single roll of scratchers.

7. Buy only the number of scratchers you need to win a prize

Some people think buying a whole roll of scratchers will guarantee a big winner, or at least enough prizes to make some money over the amount spent on the roll. But according to the law of diminishing returns, that’s a waste of money. You’ll get a minuscule increase in odds by buying all those tickets. On the other hand, you can maximize your potential returns by buying a number of tickets equal to one standard deviation from the mean odds of a prize worth more than the cost of the ticket (i.e., mean “profit” prize odds + one standard deviation). Depending on the scratcher game, that means buying anywhere from 28 to just 4 tickets. The logic is explained in this blog post.

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. Of a total 85 scratchers, there are 19 of which you need to only buy 10 tickets for the best odds of winning.

8. Take advantage of second chances

Many of the Virginia Lottery scratcher games have an “eXra Chances” logo on them. Scratch off that logo to find the scratcher serial number and you can enter to win a drawing every week for a prize worth anywhere from $500 to $1,000. The prize changes, of course: one week it’s a $600 home improvement gift card, and the next month they rotate to $1,000 gift card or $2,000 for appliances. Add to those opportunities another five scratchers with similar “Second Chances” games that you can enter for a prize drawing. In fact, if you keep an eye out, you might find these eXtra Chances in the trash.

9. Keep your losers for tax season

The IRS lets you deduct gambling losses from your winnings. If you do win, you’re going to want to keep all your winnings, of course. The way to do that is to take advantage of tax deductions. Doing so means you keep the government from claiming 24% of those winnings. Read this blog post for more details.

More Tips:

aside Statistical Analysis | Tax tips

9 Tips for Winning California Lottery Scratchers

We’ve been studying the secrets behind the California Lottery Scratcher system to really understand the ways the Average Joe can maximize his chances. Here’s some tips you should remember before you buy any lottery scratcher:

the 9 tips for maximizing chances at winning money with Virginia Lottery scratcher tickets.
The 9 tips in short

1. Check the scratcher prize odds first.

Many don’t realize it but the California Lottery commission posts all the odds for each game on its website: https://www.calottery.com/scratchers. The website shows the overall odds for winning any prize along with the odds of winning the top prize. For this $30 scratcher game, that comes to 1 in 2.98 for any prize and 1 in 3,025,367 for the top prize of $10 million.

That means you can do the math and see whether it’s worth a higher cost for better odds of prizes that return more money. In comparison to that $30 per ticket scratcher game which has odds of 1 in 2.98 for winning $30 or more, this $1 scratcher game has odds of 1 in 4.56 of winning a prize. Additionally, the odds of winning the top prize for that $30 game may be much better – 1 in 480,631 – but the top prize is only $5,000

2. Check the number of remaining lottery scratcher prizes

While you’re looking at the scratcher game pages, you may have noticed the table showing the number of prizes remaining in circulation for that game along with the number of prizes distributed at the start of the game. Every seller of scratchers scans winning prizes into the California Lottery system, so they know exactly how many prizes remain available to win. The CALottery.com website updates these counts daily.

While you may be just as likely to win a prize at any time, due to random disbursement of prizes among the rolls issued to sellers, logically it makes sense that fewer prizes in circulation = prizes are harder to find. The remaining prize counts will tell you if this scratcher game is more depleted than others.

3. Check the current odds, not just the starting odds, from the number of remaining scratchers

Under number 1, I should have said you can check what the odds were at the start of game. You can calculate the current odds of winning any prize from the count of remaining prizes, if you do a little reverse math: total up the number of prizes remaining and multiply the sum by the overall odds to get the total number of scratcher tickets issued. Then divide the sum of prizes from that total of tickets issued.

Note that the overall odds never change – you used that number to calculate the total tickets issued, after all, and in theory all prizes are claimed equally over time. However, you can calculate the probability of landing any particular prize from the count of remaining tickets with that prize. AND you don’t have to rely on the outdated initial count of prizes issued; it can be accurate within the last 24 hours.

If that sounds like a lot of work, we’re here to help! Check out our list of current odds for all scratchers on our home page: scratcherstats,com. In fact we take it one step further – that list ranks the scratchers by the best current odds. See our Methods page for more details on the rankings by probability.

4. Don’t just check the probability of any prize, but the probability of winning prizes that return a profit

Winning a prize is always fun, but more often that prize will be for the amount of time you spent buying that ticket. Don’t get me wrong, I like getting money back, but I prefer getting a little something extra. That’s why you should calculate the probability of winning a profit, not just the probability of winning any prizes, from the number of prizes remaining. On our ranking list, we’ve factored that into the rankings. Find out more about how we compiled that ranking here.

The odds of a “profit prize” are lower than winning any prize, of course. For example, looking at the statistics we list for each California scratcher, the average of winning any prize is 19%, while the average of winning a profit is 12%. But those odds of a profit range depending on the game, anywhere from 3% to 21%. If you plunk down cash for a scratcher, you’re going to want to get the one most likely to return some extra cash. That’s why you should use our list before buying.

5. Play the games with more prizes, not bigger prizes

If you’re following the tips above then you’re ready to play for more frequent small wins rather than rare big wins. Think of trying to find lots of coins buried in the mud with a few rare gold dubloons. If you aim to scoop up as many quarters, dimes, and nickels with the attitude that a big win would be nice but not expected, you may find yourself winning a pretty nice pot of change in the end.

6. Buy more than one scratcher at a time

The heart of the best strategy when buying scratchers is this: buy a string of scratchers, ideally from the same roll. As explained in more detail here, the reason is that you maximize your chances by buying a number of scratchers most likely to contain a winning ticket. Along with calculating the probability of winning tickets from the number of remaining prizes presented on the website, you can can also calculate the standard deviation. Given the statistical laws of a normal distribution, you are 99.7% likely to turn up at least one winning ticket when purchasing a string of tickets equal to the odds of winning plus three standard deviations from a single roll of scratchers.

7. Buy only the number of scratchers you need to win a prize

Some people think buying a whole roll of scratchers will guarantee a big winner, or at least enough prizes to make some money over the amount spent on the roll. But according to the law of diminishing returns, that’s a waste of money. You’ll get a minuscule increase in odds by buying all those tickets. On the other hand, you can maximize your potential returns by buying a number of tickets equal to one standard deviation from the mean odds of a prize worth more than the cost of the ticket (i.e., mean “profit” prize odds + one standard deviation). Depending on the scratcher game, that means buying anywhere from 28 to just 4 tickets. The logic is explained in this blog post.

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. Of a total 85 scratchers, there are 19 of which you need to only buy 10 tickets for the best odds of winning.

8. Take advantage of second chances

California Lottery offers second chances to a win with your losing tickets. Scratch off that logo to find the scratcher serial number and you can enter to win a drawing every week for a prize worth up to $25,000. In fact, if you keep an eye out, you might find these second chance tickets in the trash.

9. Keep your losers for tax season

The IRS lets you deduct gambling losses from your winnings. If you do win, you’re going to want to keep all your winnings, of course. The way to do that is to take advantage of tax deductions. Doing so means you keep the government from claiming 24% of those winnings. Read this blog post for more details.

More Tips:

aside background | Statistical Analysis | Tax tips

Avoid Scratcher Games with No Top Prizes?

Would it be a good strategy to buy lottery scratchers when there are no top prizes remaining? Once the top prize is gone, the odds of winning it will be zero. Many state lotteries allow games to continue even if no one has a chance to win the top prize. But maybe the game offers still more prizes that you can win?

Some games may still offer many other prizes, and your odds of winning money haven’t changed with the handful of top prizes no longer in the pool. But realistically, if the $1 million prize is already taken, would you turn your nose up at a $50,000 prize?

Strategies for Winning Lottery Scratchers

There is no sure way to win money with lottery scratchers, as the outcome is determined by chance and the odds of winning vary for each game. However, some strategies that people use to increase their chances of winning include:

  1. Choose games with the best odds of winning, as different games have different odds of winning based on how many prizes have been claimed already.
  2. Look for scratchers with a higher payout ratio, the percentage of total sales that is returned to players as prizes.
  3. Buy multiple scratchers at once, as this increases your chances of winning.

How to Choose the Best Scratchers

This website helps you do numbers 1 and 2 – our scratcher game rankings help you choose the game to buy for the best odds, before you put your money down. The data we provide tells you which games no longer offer top prizes.

The normal distribution bell chart overlayed on scratcher tickets

For number 3, it’s up to you to buy the number you can afford. But we recommend you buy a string of tickets, as your strategy can take advantage of the statistical probability in a normal bell curve. You only need to buy enough tickets equivalent to two standard deviations from the mean probability of winning a profit prize. And you’ll have given yourself a 98% chance of landing at least one prize. Our rankings tell you exactly how many tickets that would be.

Should You Buy a Lottery Scratcher with No Top Prizes?

Back to the strategy of buying scratcher games with no top prizes remaining:

When top prizes are gone, the payout ratio, which is the percentage of total sales that is returned to players as prizes, can be lower. Lower payout ratios mean that less of the money spent on the scratchers goes back to players as prizes.

But again, don’t we only care whether we ourselves win a prize? I’ll take any prize as a win! Maybe these games can have better odds of winning something, over games where the top prize waits to be claimed.

As of this writing 1/28/2023, we post data for eight states and the District of Columbia. Here’s a breakdown of the average probability of winning a profit prize – more than the cost of the ticket – by state depending on whether the top prizes remain:

State No Top Prize Remaining Top Prizes Remaining
Arizona N/A 15.1%
California 11.3% 15.8%
DC 13.6% 15.8%
Maryland 12.9% 15.8%
Missouri 15.6% 12.8%
New Mexico 14.0% 15.9%
New York 12.6% 13.3%
Oklahoma 11.8% 14.2%
Virginia 15.1% 15.8%
Average Total 13.4% 14.9%

So in fact, your odds of winning a profit prize are better if the top prizes are still unclaimed. It may be that these are games still new to the public, and there are just more tickets remaining with any prize! For almost every state, the probability of winning more than you paid for the scratcher is higher than if the top prizes are gone.

The notable exception Missouri, where the odds of winning a profit prize are 2.8 percentage points higher for games with no top prizes than for games where the top prizes remain. If you live in Missouri, you may want to rank by those scratchers without top prizes.

It is a better strategy to check the odds of winning and the payout ratio before buying lottery scratchers. You can find this data on our scratcher rankings pages, one for each state. Also, set a budget and stick to it, gamble responsibly and within your means. Don’t spend more that you can pay within your paycheck.

aside Uncategorized

9 Tips for Winning Arizona Lottery Scratchers

We’ve been studying the secrets behind the Arizona Lottery Scratcher system to really understand the ways the Average Joe can maximize his chances. Here’s some tips you should remember before you buy any lottery scratcher:

the 9 tips for maximizing chances at winning money with Virginia Lottery scratcher tickets.
The 9 tips in short

1. Check the scratcher prize odds first.

Many don’t realize it but the Arizona Lottery commission posts all the odds for each game on it’s website: https://www.arizonalottery.com/scratchers/all-games/. The website shows the overall odds for winning any prize along with the odds of winning the top prize. For this $5 scratcher game, that comes to 1 in 3.34 for any prize and 1 in 261,225 for the top prize of $100,000.

That means you can do the math and see whether it’s worth a higher cost for better odds of prizes that return more money. In comparison to that $5 per ticket scratcher game, this $1 scratcher game has odds of 1 in 4.38 of winning a prize of $1 or more. Additionally, the odds of winning the top prize for that game may be worse – 1 in 495,937.5 – but the top prize is only $5,000.

2. Check the number of remaining lottery scratcher prizes

While you’re looking at the scratcher game pages, you may have noticed the table showing the number of prizes remaining in circulation for that game along with the number of prizes distributed at the start of the game. Every seller of scratchers scans winning prizes into the Arizona Lottery system, so they know exactly how many prizes remain available to win. The ArizonaLottery.com website updates these counts daily.

While you may be just as likely to win a prize at any time, due to random disbursement of prizes among the rolls issued to sellers, logically it makes sense that fewer prizes in circulation = prizes are harder to find. The remaining prize counts will tell you if this scratcher game is more depleted than others.

3. Check the current odds, not just the starting odds, from the number of remaining scratchers

Under number 1, I should have said you can check what the odds were at the start of game. You can calculate the current odds of winning any prize from the count of remaining prizes, if you do a little reverse math: total up the number of prizes remaining and multiply the sum by the overall odds to get the total number of scratcher tickets issued. Then divide the sum of prizes from that total of tickets issued.

Note that the overall odds never change – you used that number to calculate the total tickets issued, after all, and in theory all prizes are claimed equally over time. However, you can calculate the probability of landing any particular prize from the count of remaining tickets with that prize. AND you don’t have to rely on the outdated initial count of prizes issued; it can be accurate within the last 24 hours.

If that sounds like a lot of work, we’re here to help! Check out our list of current odds for all scratchers on our home page: scratcherstats,com. In fact we take it one step further – that list ranks the scratchers by the best current odds. See our Methods page for more details on the rankings by probability.

4. Don’t just check the probability of any prize, but the probability of winning prizes that return a profit

Winning a prize is always fun, but more often that prize will be for the amount of time you spent buying that ticket. Don’t get me wrong, I like getting money back, but I prefer getting a little something extra. That’s why you should calculate the probability of winning a profit, not just the probability of winning any prizes, from the number of prizes remaining. On our ranking list, we’ve factored that into the rankings. Find out more about how we compiled that ranking here.

The odds of a “profit prize” are lower than winning any prize, of course. For example, looking at the statistics we list for each Arizona scratcher, the average of winning any prize is 25%, while the average of winning a profit is 14%. But those odds of a profit range depending on the game, anywhere from 3% to 35%. If you plunk down cash for a scratcher, you’re going to want to get the one most likely to return some extra cash. That’s why you should use our list before buying.

5. Play the games with more prizes, not bigger prizes

If you’re following the tips above then you’re ready to play for more frequent small wins rather than rare big wins. Think of trying to find lots of coins buried in the mud with a few rare gold dubloons. If you aim to scoop up as many quarters, dimes, and nickels with the attitude that a big win would be nice but not expected, you may find yourself winning a pretty nice pot of change in the end.

6. Buy more than one scratcher at a time

The heart of the best strategy when buying scratchers is this: buy a string of scratchers, ideally from the same roll. As explained in more detail here, the reason is that you maximize your chances by buying a number of scratchers most likely to contain a winning ticket. Along with calculating the probability of winning tickets from the number of remaining prizes presented on the website, you can can also calculate the standard deviation. Given the statistical laws of a normal distribution, you are 99.7% likely to turn up at least one winning ticket when purchasing a string of tickets equal to the odds of winning plus three standard deviations from a single roll of scratchers.

7. Buy only the number of scratchers you need to win a prize

Some people think buying a whole roll of scratchers will guarantee a big winner, or at least enough prizes to make some money over the amount spent on the roll. But according to the law of diminishing returns, that’s a waste of money. You’ll get a minuscule increase in odds by buying all those tickets. On the other hand, you can maximize your potential returns by buying a number of tickets equal to one standard deviation from the mean odds of a prize worth more than the cost of the ticket (i.e., mean “profit” prize odds + one standard deviation). Depending on the scratcher game, that means buying anywhere from 28 to just 4 tickets. The logic is explained in this blog post.

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. Of a total 85 scratchers, there are 19 of which you need to only buy 10 tickets for the best odds of winning.

8. Take advantage of second chances

Many of the Arizona Lottery scratcher games may have an option to submit for the chance to win a “second chance” prize. Scratch off that logo to find the scratcher serial number and you can enter to win a drawing every week for a prize worth anywhere from $500 to $1,000. In fact, if you keep an eye out, you might find these eXtra Chances in the trash.

9. Keep your losers for tax season

The IRS lets you deduct gambling losses from your winnings. If you do win, you’re going to want to keep all your winnings, of course. The way to do that is to take advantage of tax deductions. Doing so means you keep the government from claiming 24% of those winnings. Read this blog post for more details.

More Tips:

aside Uncategorized

Earn money with lottery scratchers by not making this mistake

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. 

The law of diminishing returns applied to lottery scratchers - buying more tickets doesn't mean bigger prizes
The law of diminishing returns – buying more lottery scratchers doesn’t mean bigger prizes

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. 

The filter options on the scratcher rankings list - filter by "Max Tickets to Buy" to know how many to purchase for the best odds

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. 

More Tips:

quote Statistical Analysis

The Ideal Number of Scratcher Tickets

A Test for Maximal Winnings

What’s the ideal number of tickets to buy? This question has vexed me for years.

There must be a number that maximizes potential returns from scratcher prizes that also limits losses. That number could even allow you to propel your occasional prize winnings forward to more scratchers. 

Buying too many tickets results in losing money to diminishing returns. Yet, buy too few and you may not win enough prizes. Either way, you never win enough cash to overcome the amount you spend buying scratchers.

I’ve recommended buying a cluster of scratchers equal to that of three standard deviations from the average odds of winning prizes. This would use the 68-95-99.7 rule and avoid diminishing returns. So if the average odds is 4 to 1 (one prize for every four scratcher tickets) then the number of scratchers might be 9 or as many as 12, depending on how large the standard deviation. In that cluster would be at least one winning scratch-off. But would you win enough prizes to make up for the cost?

Finally, I decided: let’s just test it. Get scratchers in clusters, and see how many return a profit in the end.

“Buy” Enough Scratchers to Find Out if the Strategy Works

Unfortunately, I don’t have the cash to do a true statistical test. 

To separate what’s statistically true from what’s just luck, you’ve got to buy enough scratchers for a large enough sample. For the millions of scratchers issued, that means over 1,000 tickets for each game for a sample that would have a small margin of error (+/- 3%) and a high level of confidence (95%). That would have required spending millions for each game only to lose millions for most games. 

But I could conduct a simulation. I could do that in a fraction of the time it would take to buy all the real tickets I would have needed. Create arrays of tickets, randomly select “tickets,” and see how many turn up winners. Then see if the amount of winnings overcome the amount that would have been spent. 

I wrote some code in Python to:

  1. Create an array to serve as a “pool” of all scratcher tickets – including all prizes – still unclaimed, as posted on VaLottery.com.
  2. Calculate the number of tickets needed for a statistically significant number of tickets, based the total tickets still available.
  3. Create an array that serves as a “roll” of scratchers, and fill that array by randomly selecting a “ticket” from the large pool of scratchers. Whether this was a winner depended on the actual prize probabilities.
  4. Select a cluster of tickets, starting at a randomly selected number in a “roll” of tickets (based on the actual roll sizes by game cost, based on the retailer manual). This way, the tickets would be “bought” just like if you walked into 7-Eleven and started buying them with zero idea of how many tickets from that roll had been bought before you.
  5. Add each cluster to a running list of clusters, summing up the total wins and loses. 
  6. Calculate the number of “observed winners” and statistically compare that with the current probabilities. 
Flow chart showing the process of creating a simulation to statistically test the outcomes of buying tickets repeatedly in clusters.
Chart demonstrating the process of the scratchers simulation

With this code, I could run this simulation to test the impact by various amounts of cluster sizes.

I ran this simulation for a statistically significant sample size of scratchers for each game. Furthermore, I ran this simulation for each game using different cluster sizes. The cluster sizes varied depending on the number of standard deviations, ranging from three below the average probability of winning a prize to three above the probability of winning. I ran these simulations based on data posted by the Virginia Lottery on March 8, 2022.

I ultimately ran seven trials for each scratcher game – one for each standard deviation from three below the mean to three above the mean, including once for the mean itself. This means that each trial involved simulating the ticket outcomes of an average 1,100 tickets per game, in 200+ clusters that ranged in size from one to 181.

Further-furthermore, I did it all over again based on the number of standard deviations from the probability of winning a prize that returns a profit over the cost of scratcher – a “profit prize.” So I ran a total of 1,177 trials.

As it turned out from my experiment, conducting this test in reality would have required spending as much as $11.2 million only to lose as much as $10.9 million. Of course, most games resulted in a loss. 

The Monopoly Fortunes scratcher image, one of the only games to return a large profit in a statistically-based simulation.
A winner in the end

Yet, some games actually returned not only a profit, even as much as hundreds of thousands of dollars. For one game, the $5 Monopoly Fortunes game actually resulted in over $1 million – though for me it was just Monopoly money.

The Results – Some Scratcher Games Returned More Prizes than Expected

Once I had the final results in hand, I tested whether the “observed” prize frequency (i.e., The number of “prizes won” divided by the number of “tickets bought”) was consistent with the actual probability, based on the data provided on the official Virginia Lottery website.

For 27% of trials (315 trials), the number of prizes was exactly within the expected range of prizes based on the data posted on VALottery.com. A two-way Z-test, by calculating a Z-score from the proportions, confirmed as much. For these trials, the observed percent of prizes “won” was within a statistically expected range of the known probability, and as the p-value was below 0.05 I had to accept the null hypothesis, i.e., that the observed win rate was statistically the same as the expected win rate.

That’s a wonky statistician’s way of saying that I got as many prizes as I expected, regardless of how large or small the number of tickets in each cluster. On average, the proportion of tickets with a prize that I observed was 24% while the number of scratcher tickets that had a prize was also 24%. I did come out with more money in prizes after 20 of these trials, but my average total prize winnings was a loss of $8,545.

Another 37% of trials (438 trials) returned worse results than expected – there were fewer winning tickets than expected. The observed frequency of prize-winning tickets was 19%, while the average prize probability was 25%. In these trials, I came out ahead in just 12 trials and my final average tally was a negative $17,879.

Okay, so 1 out of 4 results were as expected, and another 2 out of 5 results were worse than expected. But that’s the boring part – the “expected” results aren’t all that exciting, are they? And there’s nothing exciting about winning the same or less than expected.

The exciting part is: when did I get a higher win rate than expected? Believe it or not, that happened. For 36% of trials (423 trials), I landed a statistically significant higher number of winning scratchers than the expected average. I observed an overage 32% of tickets had a prize, over the average expected 25% probability. My average tally was still negative, albeit a smaller average loss of $835.

However, I came out ahead in far more games in trials where the win rate was statistically higher than average. For 83 trials, I won more than I spent on scratchers; the final tally was on average $28,349 – boosted by high earnings that for some games totaled over hundreds of thousands.

The Best Number of Scratchers to Buy

“Okay, so how’d that happen?” you might be asking. Well, it all depends on the size of the clusters.

The question was always: how many tickets do I really need to buy? What’s the sweet spot between spending too much money on tickets and spending too little to win anything significant?

I narrowed down the cluster sizes that resulted in positive outcomes most often. But remember that the cluster size varied by the number of standard deviations from the mean prize probability. In my simulation, the cluster size corresponding to one standard deviation from the mean probability of a “profit prize” is the ideal number. This means that in general the number of scratcher tickets you’ll buy ranges from 5 to 12, an average of 8 tickets.

In past articles, I’d recommended a strategy that was three standard deviations from the profit prize mean, a range of 7 to 28, an average of 16. As it turned out, that was too many. You only need to buy half as many scratchers on average for the best odds.

Graph showing that the ideal number of tickets to buy for any game can be calculate as one standard deviation from the mean probability for "profit" prizes (those that amount to more than the cost of the ticket).

You can find the raw data here to see for yourself:

VAScratchersSimulationOutcomes_AllStDevs_AnyProfit_03082022-1Download

In that file you can find data on:

  • The number of games with a positive final tally
  • Number of games with a high z-score
  • Games with an observed frequency higher than the probability
  • Games with a higher average cluster outcome

Based on this data, I’ve gone back and revised my initial recommendation to buy based on three standard deviations from the mean. Turns out, you’re spending too much money doing that. This is good news – you can spend less to win more!

NOTE: Please remember that while I did this test based on real data, the results are only hypothetical. I could do the same test with same data and the results may differ.

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Is the Best Lottery Strategy to Buy New Scratchers?

Whenever the lottery releases new scratchers, people buy the new scratch-off games on the blind faith that the newer the game the better the chances to getting the remaining prizes before they’re claimed. But is buying new scratchers really the best strategy? 

We took a look at the data, and the answer is: Not really. In fact, you might have slight advantage buying older scratcher games. 

Scratchers can be worth buying, at least some that have better than average odds. They can have much better odds of actually winning some cash than the big name Virginia Lottery games like Megamillions, Keno, or Pick 3 and Pick 4.

But it might not matter when you buy them. The real question is: which scratchers are the best to buy right now? The only metric that matters is whether a scratcher game has the best odds for a high probability of winning prizes. 

Data Shows Tickets Go Fast at First . . .

Since we gather the data posted every day on the official Virginia Lottery website at VALottery.com, we can easily see whether the probabilities of winning a prize get any better or worse the longer the game goes on. Is it going to be Extreme Millions, or Hot 777s? Here at ScratcherStats.com, our first four of 9 tips for winning Virginia Lottery scratchers are to check the scratchers data. You can find a ranking list on our site and more in-depth stats here also.

Right now, among the 85 scratcher games available in Virginia, 44 have only been in circulation for less than 90 days, including four that started just this month. 

Surely, these games have more prizes remaining, including top prizes. From data collected February 22 through April 18, 2022, people throughout Virginia bought about 543,000 scratchers per day. This number excludes the tens of millions of new scratchers that the Virginia Lottery commission injects into stores every month. As you can see in this chart, Virginia store shelves received a boost of 19.2 million tickets on March 2 and 11.1 million on April 9.

Chart showing the number of winning scratcher tickets available, and the number of non-prize tickets calculated from the odds, using the data posted daily on VAlottery.com
Scratchers remaining daily based on VALottery.com data

Another chart, below, shows the average number of prizes claimed by the number of days since the game’s start date. Just a quick look at this one and you can see that people buy many more tickets at the start of the game. So, in a way, the top winning scratchers are the new games. In fact, by the end of the first 60 days, you can expect that people will have bought over 1.5 million tickets – and about 21% of those are for scratch-off games that started less than 60 days earlier. 

. . . but Most New Scratcher Tickets are Losers

Here’s the really interesting part: the ratio of people buying losing tickets is higher than winners for those first 60 days or so. While the average of winners bought to losers is usually 22% to 78%, during the first 60-90 days this ratio shifts to 14% winners and to as much as 86% losers.

Line chart showing the number of winning tickets and non-prize tickets claimed in the time after a scratcher game starts, summed in 30-day increments.
Total scratchers bought in the days after a new game starts

While people are buying more scratchers early in a game’s lifespan, more of these scratchers are losing tickets. People clear out more losers from the scratcher rolls when a game is new.

Why then make a fuss about a new scratcher game? The data indicates that you may even benefit from buying older games – there’s fewer losers to waste your time and money on. 

One question is whether the hullabaloo about a new game is for you, the humble gambler with hopes of winning a nice prize, or for the Lottery commission.  You’ll see the Virginia Lottery pump out new holiday-themed games. Even if some have the worst odds of any game, they go quickly. People buy them perhaps as easy office “appreciation” gifts or stocking stuffers. Some games are only open for short period, like Hot 777s – started in January this year and just closed on April 15.

But many games that have been out there for years, like Super Cash Frenzy has been around since March 2018 and still offers two tickets with the top prize of $4 million. Extreme Millions has been around since October 2017. Only recently did it sell out of its four chances to win $10 million but the Virginia Lottery officially closed the game on April 15, 2022. Yet another reason to look at the data is to check for top prizes, though the game may still be worth buying.

The Real Question: Do the Scratcher Odds Ever Get Better?

The fact is that all that really matters is how many scratcher prizes are out there right now. Does the probability of winning scratcher prizes increase the longer a game goes on? 

This scatter plot chart shows that, in fact, the probability does get better for older games. Even as the number of prizes still available decreases from nearly 100% to around 25%, the average probability of winning a prize actually increases, albeit slightly. The average probability changes from 25% for those games in their first 60 days to an average 28% for games older than three years. 

Scatter plot of the average percent of scratcher prizes remaining unclaimed and the probability of winning over time from the game start date, by number of days. Includes trendlines showing an R-square of 0.221 for percent remaining and 0.106 for probability of winning.
Scratcher prizes remaining and the average probability over time from game start

So buying older scratcher games can be a good lottery scratchers strategy because it offers an edge – at least a thin edge. Is it because many of the losing tickets have been bought already? Maybe that has an effect. The correlation between time and probability is nearly none – only an R-square of 0.106, meaning that the days since the game start date only explains about 10.6% of the variation in the prize probability.

Still, some edge is better than none. The trick to buying scratchers is to be choosey when picking the lottery scratcher game. Don’t just buy the game because it’s new.

Buy Scratchers by the Best Odds, Not the Age

When you examine games for how many remaining winners are in circulation, then all that matters is which give you the best odds right now. It doesn’t matter if the game started yesterday, or five years ago. It doesn’t even really matter if the top prize is already gone. What really matters is: which scratcher game offers the best odds for you?

If you want to know which is the best lottery scratcher to buy in Virginia, then use the data in this list. You can filter it by the best scratcher odds, based on a daily counts of data offered by the official Virginia Lottery website. Find even more stats for each Virginia Lottery scratcher game on this page.

Here’s a pro tip: look for the scratchers that require buying the fewest for the best chances of winning by using our “max tickets to buy” measure.

Use this data to your advantage – and you might just land some cash in your wallet!

More Tips:

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