Probability > Scratch Off Odds:
- Mathematicians have “cracked” the scratch off odds code, winning millions.
- The internet is full of tips to win—but which ones actually work?
- Only one tip guarantees a win.
There are a thousand different ways to use probability in real life, but in this article I’m going to show you how to use odds, probability, and expected value to increase your scratch off odds.
Watch the video so see what worked (and what didn’t):
Can’t see the video? Click here.
The Statisticians Who Cracked the Scratch Off Odds
Statistician Joan Gitner is famous for winning multi-million dollar payouts four times on scratch off tickets. That kind of luck happens once every quadrillion years. to give you an idea of how big a quadrillion is, one quadrillion seconds was 31,700,700 years ago. But Joan R. Gitner’s wins weren’t luck: She has a PhD in math from Stanford; That gave her a major advantage. Mohan Srivastava, a Canadian statistician, discovered in 2003 that winning tickets had a numerical pattern. Part of it wasn’t stats so much as it was sleuthing about, looking for patterns on scratch cards. The secret he uncovered was that winning scratch offs had certain number combinations on the cards. by using math, he figured out what cards were more likely to win. He estimated he could make $600 a day with his trick, but that was a lot less than what he made as a statistician.
Hypothesis Testing: Scratch Off Odds Tricks and Tips
There are a slew of other tips and tricks on the internet. They include:
- White lines on cards,
- Calculating odds and expected value,
- Buying in bulk,
- Playing the more expensive cards.
But which ones work, and which ones don’t? I enlisted the help of a group of friends to analyze thousands of tickets and figure out what tips and tricks work—and which ones don’t. To make this experiment scientifically sound, I used a few different hypothesis tests (including a t-test). It turns out there is only one technique that guarantees you’ll win something. And it might not be what you’re expecting.
How to Win Scratch Offs with Math: Some Tips
Let’s start with some basics. Scratch off tickets range from $1 to $30. They are deliberately made attractive and shiny to sell more. You can play crosswords, games like Monopoly, or just scratch off gold coins or dollar signs. But not all scratch cards are made equal. Don’t play shiny or fun, because more expensive cards have better odds. Some cards even have no prizes left. In fact, at any time, about 10% of games have zero big prizes left. It’s perfectly legal to keep on selling the tickets, after all the prizes have been won. So do a little research before you buy a ticket: go to any state lottery website and see which cards have zero big prizes remaining. You do not want to play those games.
Let’s answer the question, do winning cards look different? Mohan Srivastava’s trick was noting how many times single numbers appeared on Tic Tac Toe cards. Many single numbers were more likely to win than cards with repeated numbers.
Unfortunately, that particular numbering pattern is no more. Srivastava alerted the authorities and they pulled the game. There also used to be codes printed on the ticket telling you what you won, like ONE for one dollar or FTY for fifty. But these have also been discontinued.
In our search for truth, we sorted through a pile of 236 winners, looking for markers like White lines or numerical patterns. We collected our data then ran a hypothesis test. Were the differences random, or statistically significant? The result was that any imperfections or patterns were likely due to random fluctuations during production. In other words, if your winning card looks different (e.g., it has a white line) it’s just a random event.
Let’s say we’re wrong. You crack the secret number code and figure out that winners do look different. You can’t see the cards you’re buying, because they are on a roll. The conclusion? Winning cards do not look different. And even if they do, it won’t up your odds of winning
The next tip increases your odds a little bit. Buy groups of cards: 10 in a row of the same game, or even an entire roll of cards (this may cost you several hundred dollars or more!). There’s actually some pretty good science behind this tip. Scratch off ticket prizes are not random and tend to be evenly spaced throughout the rolls. The manufacturer has an certain dollar amount, say 1 million dollars, that they have to disperse for a game. If they printed the prizes in a truly random fashion, they could award tens of millions in prizes, just by random chance. They have to limit the number of winning cards to a set amount, like 250 winners in every 1000 card run. There WILL be some randomness—but every fourth or fifth card is not going to be a winner. You can increase your chances by buying 10 at a time, but it’s not a guarantee of a win. Scratch offs are very much a game of chance: I bought ten in a row. And they were all losers.
There is another very good reason for buying cards all from the same game. The probability of winning increases every time you buy more tickets for the same game. Imagine there’s a million tickets in a game with one big prize:
- If you bought 10 tickets, the odds of you winning are 1 in 100,000.
- If you bought 100 tickets, your odds increase to 1 in 10,000.
- 1000 tickets, and you have a 1 in 1000 chance of winning.
This is the logic that likely got Joan Gunther her millions. However, she didn’t buy 10 in a row or even a thousand.
Experts estimate she purchased 80,000 tickets worth more than 2 million dollars. But she did win more than 15 million;
That’s not a bad investment!
I’m assuming you don’t have 2 mill to plonk down on cards, so you can use another of Ms. Gunther’s tricks: play cards with higher expected value. The calculation is the total amount of remaining prizes divided by the total amount of money it would cost to buy all remaining tickets. For example, at the time of writing, Florida’s “Fastest Road to $1,000,000 has about 8 million tickets remaining. At $30 per ticket, it would cost just over $241 million to buy all remaining tickets. There are about 200 million dollars in remaining prizes. Divide the remaining prizes by the cost to buy
and you get about 83%. In other words, if you spent 241 million on buying all the tickets you’d only get back 82% of your money and you would lose 18% of it ($43 million dollars). That’s actually pretty good odds for scratch offs. Some tickets are as low as an expected value of 40%. Yyou’ll have a much greater chance of a win if you play cards with higher expected value.
And Now for The Bad News
Overall, the vast majority of people who play scratch off cards will lose, over the long run, about 70% of the money
that they spend on scratch off cards. The odds are heavily stacked against you winning. The “winners” are the states, who keep about 30% of the 60 billion spent on the lottery every year. So back to that statistician who had a pretty good trick for reading the cards. He had some wise words for scratch off ticket players. In an NPR interview, he said that he didn’t think any one could make a living off of scratch off tickets. So if scratch off tickets are your hobby, then enjoy. But if you’re in it to win big, But if you’re in it to win big—play a game with better odds.