The odds of winning a jackpot in a national lottery are so slim (one in several hundred millions), that it’s often a better bet to play the state lotteries, like Fantasy Five, instead of the national ones.
Why are the Fantasy Five odds better?
Let’s take a look at the probabilities and compare your odds of winning national lotteries to your Fantasy Five odds. What’s important here is it does not matter how many people enter these games (other than the possibility you may have to share your winnings). The odds are calculated with a combinations formula and the multiplication rule; combinations are the number of ways the numbers can be arranged and the multiplication rule allows us to calculate probabilities for independent events. What matters is the number of balls in play and the number of balls you are allowed to choose.
- Mega Millions (Five numbers between 1 and 70; One number from 1 to 25; You choose 5 + 1): Odds of jackpot = 1 in 302.6 million and overall odds of a prize = 1 in 24. (How Mega Millions odds are calculated).
- Power Ball (Five numbers between 1 and 69; One number from 1 to 26; You choose 5 + 1): Odds of jackpot = 1 to 292 million [1] and overall odds = 1 to 24.7 (How Power Ball Odds are Calculated).
These odds are very long; even though you have reasonable odds of winning something (1 to 24 or 1 to 25), remember that a “win” is much more likely to be two dollars (about 1 to 37) than any of the higher value prizes. Now compare those odds to Fantasy Five odds:
- Florida Fantasy Five Odds: Jackpot = 376,992. Overall = 1 to 7.5 [2].
- California Fantasy Five Odds: Jackpot = 1 to 575,757. Overall = 1 to 9.
The top prize is small compared to national lotteries. For example, California’s Fantasy Five had a top prize of about $65,000 for February 2022, compared to Mega Millions $75 million. A brief glance at the numbers tells your probability of winning California’s Fantasy Five is over 500 times better than winning a national lottery. When deciding which game to play though, what’s really important is a statistic called expected value for lotteries, which tells you how much you can expect to gain (or lose) for how much money you put in.
How are Fantasy Five Odds Calculated?
Using California’s Fantasy Five as an example, the combinations formula represents how many ways 39 balls can be arranged if 5 balls are chosen:
One of the easiest ways to solve the formula is with Symbolab’s calculator, which I used here:
The odds of a jackpot (all 5 numbers) is 1 to 575,757.
The Florida Fantasy Five Odds are better because there are fewer balls to choose from (36 instead of 39):
The odds of a jackpot (all 5 numbers) is 1 to 376,992.
You can figure out the odds for any other Fantasy Five game by replacing the total number of balls (“n”) in the formula.
If you’re unfamiliar with the combinations formula, I go into more detail in How Lottery Odds are Calculated
References
[1] Odds and Prizes.
[2] Fantasy 5 FAQ. Retrieved February 20, 2022 from: https://www.flalottery.com/fantasy5-faq#:~:text=The%20overall%20odds%20of%20winning%20FANTASY%205%20are%201%20in%207.58.