The 500X the Cash scratch-off lottery game is one of the most popular games offered by the Florida Lottery. With a $50 price point and a top prize of $25 million, it offers players the chance to win life-changing sums of money. But what are the actual odds of winning the top prize or any prize for that matter? Let’s take a closer look at how scratch-off lottery games work and the published odds for 500X the Cash.
How Scratch-Off Lottery Games Work
Scratch-off lottery tickets, also known as instant win games, offer the chance to instantly win cash prizes by revealing hidden symbols or numbers under the covering on the ticket. Games like 500X the Cash have a finite number of tickets printed for each game with a predetermined number of winners at each prize level. The tickets are randomly distributed and no one knows where the winning tickets are located. Players scratch off the covering on their ticket to reveal symbols or numbers and check these against the winning combinations listed for the game. Any ticket matching one of the published winning combinations wins the corresponding prize.
Odds of Winning 500X the Cash
The Florida Lottery publishes the overall odds of winning any prize in a particular scratch-off game. For 500X the Cash, the overall odds printed on the ticket state:
Overall Odds | 1 in 4.50 |
This means that on average, 1 in every 4.50 tickets sold for this game will be a winning ticket. So for every 4.5 tickets purchased, 1 player can expect to win some type of prize.
The lottery also publishes more detailed prize odds showing the chances of winning at each prize level in the game. The prize odds for 500X the Cash are:
Prize Amount | Odds | Winners |
$50 | 1 in 8.33 | 120,000 |
$100 | 1 in 60 | 10,000 |
$200 | 1 in 60 | 10,000 |
$500 | 1 in 85.71 | 7,000 |
$1,000 | 1 in 2,400 | 250 |
$5,000 | 1 in 4,800 | 125 |
$10,000 | 1 in 19,200 | 31 |
$25,000 | 1 in 38,400 | 16 |
$500,000 | 1 in 120,000 | 5 |
$1 million | 1 in 240,000 | 2 |
$25 million | 1 in 600,000 | 1 |
Looking at the $25 million top prize, the odds show it has a 1 in 600,000 chance of being won. This means that out of all 600,000 tickets printed for the 500X the Cash game, there is expected to be just 1 top prize winner. Compared to some other prizes like $50 with odds of 1 in 8.33, the top prize has significantly worse odds. But it offers the chance for an incredibly life-changing payout.
Calculating the Probability of Winning
Now that we know the published odds, we can calculate the probability of winning each prize. Probability represents the likelihood of an event happening expressed as a number between 0 and 1. The higher the probability, the more likely an event is to occur.
We calculate probability by taking the inverse of the odds. For example, the odds of winning $50 in 500X the Cash are 1 in 8.33. To find the probability, we take 1 divided by 8.33.
Prize Amount | Odds | Probability |
$50 | 1 in 8.33 | 0.12 |
Doing this results in a 0.12 probability or 12% chance of winning the $50 prize. The probability of winning each 500X the Cash prize based on the stated odds is:
Prize Amount | Odds | Probability |
$50 | 1 in 8.33 | 0.12 |
$100 | 1 in 60 | 0.017 |
$200 | 1 in 60 | 0.017 |
$500 | 1 in 85.71 | 0.012 |
$1,000 | 1 in 2,400 | 0.00042 |
$5,000 | 1 in 4,800 | 0.00021 |
$10,000 | 1 in 19,200 | 0.000052 |
$25,000 | 1 in 38,400 | 0.000026 |
$500,000 | 1 in 120,000 | 0.0000083 |
$1 million | 1 in 240,000 | 0.0000042 |
$25 million | 1 in 600,000 | 0.0000017 |
As expected based on the long odds, the probability of hitting the $25 million jackpot is extremely small at just 0.0000017 or roughly 1 in 600,000. Still, while highly unlikely, someone has to win the top prize.
Determining the Expected Value
Another useful calculation we can do is determining the expected payout value on a 500X the Cash ticket. Expected value accounts for both the probability and the prize amount to help you understand how much a ticket might be “worth” on average. This can give you a better sense of whether the cost of the ticket is justified.
To find the expected value, you multiply the probability of winning each prize by the prize amount. Then add up these values for all the prize levels. Let’s walk through an example:
The probability of winning $50 is 0.12 and the prize amount is $50.
0.12 x $50 = $6
The probability of winning $25 million is 0.0000017 and the prize amount is $25 million.
0.0000017 x $25,000,000 = $425
Doing this for every prize level and then summing the results gives an overall expected value of $19.37.
Running through the calculations for all 500X the Cash prizes gives a total expected value of $19.37. This means that on average, the value of a $50 ticket will be $19.37 taking into account the probabilities and amounts of all possible prizes.
Conclusion
In the end, while the $25 million top prize in the 500X the Cash game offers the allure of an incredible payout, the actual probability is extremely small at just over 1 in 600,000. The much more likely outcome is winning a smaller prize like $50 or $100 which still beats the cost of the ticket. With odds of 1 in 4.50 of any win, players have a decent chance of winning something. But due to the long odds on the jackpot, purchasing a single $50 ticket is very unlikely to change your life with an enormous payout. Playing the lottery is all about the thrill of the unknown, however, and you simply never know when you might just hit it big and defy the odds.