The Methods Behind the Stats
The what and how on the statistics provided for the Virginia Lottery scratchers on this site.
What’s the best scratchers strategy?
Buying a string of VA lottery scratcher tickets based on the best odds from the number of prizes remaining. This site provides you a ranking calculated from the remaining prizes listed on the Virginia Lottery website, so you can find the best scratch offs at a glance.
Retailers buy scratchers in packs of 20, 40, 100, or 200 tickets, depending on the ticket cost (see details in Virginia Lottery’s retailer manual). We assume that Virginia Lottery distributes the prizes randomly throughout the packs. Therefore, the frequency of each prize corresponds to the percentage remaining in circulation. Given the statistical laws of a normal distribution, you are 68% likely to turn up at least one winning ticket when purchasing a string of tickets from a single pack equal to the odds of winning a prize worth more than the cost of the ticket plus one standard deviation .
We used to recommend buying as many scratchers as equalled three standard deviations from the average prize odds. Buying that many scratchers at once would up the odds of winning at least one prize to 99.7%. However, after conducting this 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.
For example, if the odds of winning are 4 to 1, and we add to that one standard deviation of .75, that means that buying 5 tickets is 68% likely to result in a prize. (See more details below.) All 5 could still be losers, but statistically the likelihood of losing on every single one is much more slim. Buying a single ticket here and there is a poor strategy. Either the ticket before or after that purchase could be a winner. So buying several at once–and buying a number in accordance with the current odds–will maximize your chances of winning.
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 by the “Max Tickets to Buy” field – based on the calculation of the profit prize odds plus one standard deviation – to see which require the least number of tickets in order to potentially win at least one prize.
Isn’t playing the lottery scratcher games a fool’s errand?
Yes, most of the ways that people play it. First, they throw money at games like Powerball or Mega Millions with miniscule odds of 1 in 300 million, when even the longest odds in lottery scratchers top prizes is around 1 in 3 million.
The second mistake is people play with no knowledge of the odds or the true number of winning tickets remaining. So they have no concept of the statistical likelihood of winning before buying lottery tickets. They turn to myths, superstitions, false assumptions, and idealistic beliefs about the “best” ways to play the games.
There are no 100% guarantees. However, armed with more accurate data and a list of games with the best statistical probabilities, you can improve your odds of winning.
Where did the scratchers data come from?
The original data comes from the state lottery commission websites. These lottery commissions post updated data daily. Each retailer scans the ticket barcode into a machine to determine if it is a winning ticket. The lottery commission’s system tracks the scratcher tickets in real time and updates their websites each day. We’ve taken that data and analyzed it to produce something you can use to maximize your odds of winning . . . or at least not lose as much.
How were the scratcher statistics calculated?
We started by calculating the total number of tickets in circulation, multiplying the initial odds of winning any prize given on the Virginia Lottery by the total number of initial prizes. For example, if the odds of winning a prize were 4.25 to 1, and the total number of prizes remaining were 1,125,000, then the total number of scratcher tickets is 4.25 x 1,125,000 = 4,781,250. Using the data on the website also allowed us to calculate other statistics. We provide the average probability of winning, the standard deviation, the percent of prizes remaining, and the expected value of each scratcher ticket. (See the glossary below for a more detailed explanation of each of the statistics provided on this site.) We then used these statistics to rank them.
How was this ranking was compiled?
We ranked the scratchers according to certain groups of statistics:
1) Rank by Best Probability of Winning Any Prize
2) Rank by Best Probability of Winning a Profit Prize
3) Rank by Least Expected Losses
4) Rank by Most Available Prizes
5) Rank by Best Change in Probabilities
These ranking groups are the average rankings by each statistic included in that group (see details below). We then ranked the scratchers by their average of these rankings. The home page ranks a scratcher by its ranking in its cost group (e.g., among $1 scratchers)m and then by overall ranking among all scratchers.
So this scratcher strategy will help me win a lot of money, then?
This strategy is likely to help you lose less, but may not help you win money. You are more likely to get a winning ticket if you buy a number of tickets three standard deviations from the mean. However, that does not mean that you will win enough to cover the total cost of buying all those tickets. Remember that scratchers are still a gamble, and gambling involves a risk of losing money. Please don’t spend more money buying scratchers than you can afford to lose. And also remember that gambling can be addictive – as addictive as drugs, alcohol, or sex for some people. If it becomes a compulsion then please seek help.
Glossary of Statistics Provided:
Below is a glossary of explanations for the statistics on this site, listed under each ranking group:
Rank by Best Probability of Winning Any Scratcher Prize
- Odds of Any Prize: The odds of winning any of the prizes for that scratcher game. This number equals the total scratcher tickets remaining divided by the total prizes remaining, as shown on the Virginia Lottery website.
- Probability of Any Prize: The total prizes remaining divided by the total scratcher tickets remaining. This is shown as a percentage for the odds of winning any prize.
- Odds of Any Prize Plus Three Standard Deviations: Three standard deviations from the mean, added to the mean (i.e., the odds of winning any prize). Given a normal distribution, this number means that per the 65-95-99.7 rule there is a 99.7% likelihood that buying this number of tickets will include at least one prize-winning ticket. For example, if the odds are 4 to 1, and the standard deviation is 1.25, then 4 + 1.25 = 7.75, or rounded up to 8 to 1 odds (because you can’t buy a partial ticket). In order words, buying 8 tickets means there is a 99.7% probability that one of those 8 is a winner. Although, this is probably true only for a prize equal to the cost of the ticket.
Rank by Best Probability of Winning a Profit Prize
- Odds of a Profit Prize: This is the same as the odds of any prize. Except it is calculated by dividing all tickets by only the sum of prizes that exceed the cost of the ticket; winning means making a profit on the expense of the ticket. For example, if the odds of winning any prize on a $20 ticket is 4.25 to 1, then the odds of winning a prize worth $25 or more might be 5.75 to 1.
- Probability of a Profit Prize: This is also the same as the probability of winning any prize, except only the sum of prizes greater than the ticket cost by all tickets remaining. For example, if the probability of winning any prize with a $20 ticket is 25%, the odds of winning a prize worth $25 or more might be 15%.
- Odds of Profit Prize Plus Three Standard Deviations: Three standard deviations for only profit prizes, added to the odds for a profit prize. In this case, buying a corresponding number of tickets means a 99.7% probability of winning a prize worth more than the cost of the ticket. However, this number may be substantially higher; for example, if the odds of any prize plus three standard deviations is 8, then this number may be as high as 12 or 15.
Rank by Least Expected Losses
- Expected Value of Any Prize: The “expected value” (or EV) is often used to determine if Powerball is worth playing. The EV basically determines whether you would come out with any money after purchasing all the tickets to win every prize. We calculated the EV by using the formula “(Prize – Cost) x (Probability of Any Prize)” for each prize amount, and summed the result. If the sum is positive, the scratcher actually makes the most mathematical sense as a good bet. However, know this: the EV is usually negative. Still, purchasing every ticket is an unrealistic strategy – the real strategy is playing the probabilities. We converted the EV into percentages of the ticket cost. For example, if the EV is $15 for a $20 ticket, we converted the EV to 75%. Converting to a percentage allows for cross-scratcher comparisons. The higher the EV, the least likely the probability of losing money.
- Expected Value of a Profit Prize: The same as above, except this EV includes only those prizes worth more than the cost of the ticket. Of course, the EV of profit prizes (like stated above, converted to a percentage of the ticket cost) is typically lower than the EV for any prize.
Rank by Most Available Scratcher Prizes
- Percent of Prizes Remaining: The average of the number of winning tickets in circulation for each prize.
- Percent of Profit Prizes Remaining: The average of the number of winning tickets in circulation for those prizes worth more than the cost of the ticket.
- Ratio of Decline in Prizes to Decline in Losing Tickets: Sometimes the prizes are claimed faster than the losing tickets. This can leave an imbalance with a disproportionate number of losing tickets in circulation. Sometimes, it’s the other way around: the losing tickets are bought at a faster rate than the winning ones, leaving a disproportionate number of prizes in circulation. This imbalance, however, is only very slight. For example, the ratio could be 1.0000002, meaning for every ten million tickets there are two more winning tickets than losing ones.
Rank by Best Change in Scratcher Probabilities
- Change in Odds of Any Prize: The percentage change from the initial odds when the scratcher game first started to the most recent odds (as calculated from the number of prizes remaining reported on the Virginia Lottery website). The odds decrease as people land the prizes, or the odds improve as customers take losing tickets out of circulation. The amount of change in the odds is very slight. For example, the improvement could be 0.000038% or the decline could be -0.000501%.
- Change in Odds of a Profit Prize: The same as above, except calculated using only prizes worth more than the cost of the ticket. Note that the two numbers still correspond exactly.
- Change in Probability of Any Prize: The percent change in probability of winning any prize from the initial probability published on the Virginia Lottery website, based on the current number of prizes available.
- Change in Probability of a Profit Prize: The percent change in probability of winning a prize worth more than the cost of the scratcher from the initial probability published on the Virginia Lottery website, based on the current number of prizes available.
- Change in Expected Value of Any Prize: The change in the EV (as described above) from the initial EV of a scratcher containing any prize.
- Change in Expected Value of a Profit Prize: The change in the EV (as described above) from the initial EV of a scratcher containing a prize worth more than the cost of the ticket.