Probability of Winning Florida Lotto with XTRA

TR Smith is a product designer and former teacher who uses math in her work every day.

Florida Lotto is one of seven draw games offered by Florida's lottery commission. After the multi-state lottery games Powerball and Mega Millions, Florida Lotto is the most popular jackpot game in the state. Drawings are held every every Wednesday and Saturday, with jackpots that start in the several millions of dollars. Tickets cost just \$1 per play.

Many players wonder how Florida Lotto compares to other games and how the prize odds are figured. Here is a more detailed explanation than what is provided on the official lottery website.

How to Play

To play Florida Lotto, select 6 different numbers from 1 to 53. For \$1 more, you can purchase the XTRA option, which will multiply non-jackpot prizes by either 2, 3, 4 or 5. The XTRA multiplier is randomly selected during main drawing. Each of the four different multiplier values has an equal chance of being selected. This is different from Powerball and Mega Millions where the multiplier values are weighted with some engineered to occur more frequently than others.

For instance, suppose the multiplier chosen is 3, and your lottery ticket has partial match and you have purchased the XTRA option on your ticket. Then you win the base prize times 3 for that partial match. Adding XTRA to your Florida Lotto ticket does not increase your odds of winning, it only increase the amount you could win. If you want to improve your overall chances of winning, you should spend the extra \$1 on a separate ticket with different numbers. And if you really want to decrease your chances of losing, don't buy lottery tickets in the first place.

Odds and Probability of Winning

The likelihood of matching n out of 6 numbers in the Florida Lotto drawing is given by the lottery probability formula

Prob(n) = (6 C n)(47 C 6-n)/(53 C 6)

where the function (x C y) is "x choose y," the combination function. The odds of winning are the reciprocal of the probability. The table below shows the exact probability of matching n of 6 balls, as well as the odds rounded to the nearest integer. Cash prizes are only awarded for matching at least 3 out of 6 numbers.

Match
Probability
Odds
6/6
1/22957480
1 in 22,957,480
5/6
141/11478740
1 in 81,409.5
4/6
3243/4591496
1 in 1,416
3/6
16215/1147874
1 in 71
2/6
535095/4591496
1 in 9
1/6
4601817/11478740
1 in 2.5
0/6
1533939/3279640
1 in 2
any cash prize
170399/11478740
1 in 67

Florida Lotto Payouts

If you match 3, 4, 5, or 6 out of 6 numbers in the official Florida Lotto drawing, you win a cash prize. The jackpot is awarded to the lottery player(s) with a perfect 6/6 match, and jackpots start at \$1,000,000. By paying \$1 more for the XTRA option, your prizes for the the 4/6 and 5/6 matches will be multiplied by the XTRA factor, which is randomly selected from the set {2, 3, 4, 5}. In the case of match 3 out of 6, purchasing the XTRA option always multiplies the base prize by 5. The jackpot prize is never multiplied.

Match
Prize
X2
X3
X4
X5
6/6
JP
JP
JP
JP
JP
5/6
~\$5,000
~\$10,000
~\$15,000
~\$20,000
~\$25,000
4/6
~\$70
~\$140
~\$210
~\$280
~\$350
3/6
\$5
\$25
\$25
\$25
\$25
2/6
\$0
free ticket
free ticket
free ticket
free ticket

In the table above, JP stands for jackpot. The base prizes for matching 5/6 and 4/6 balls are approximate since they are awarded on a pari-mutuel basis, meaning they depend on the number of winners for each level and the available pool of prize funds. The table shows the average estimated amounts. Typically, you win \$3,500 to \$6,500 for matching 5/6 balls. For matching 4/6 balls you typically win \$60 to \$80.

The base prize for matching 3 out of 6 is usually \$5, but occasionally it may be \$5.50 or \$6. If you match 3 out of 6 with the XTRA, you win a minimum of \$25. If you purchase the XTRA option and match 2 out of 6, you win a free quick-pick ticket with XTRA.

Miscellaneous Florida Lotto Probabilities

The probability that the 6 numbers drawn are all even or all odd, i.e., the same parity:

(27 C 6)/(53 C 6) + (26 C 6)/(53 C 6)
= 1012/44149
= 0.022922
= odds of 1 in 44

The probability that the 6 numbers drawn consist of 3 even numbers and 3 odd numbers is

(27 C 3)*(26 C 3)/(53 C 6)
= 14625/44149
= 0.33126
= odds of 1 in 3

Florida Lotto Expected Return

The expected return on a \$1 bet is computed by multiplying each approximate prize by its probability, adding the results, and then dividing this sum by the price of a ticket. Because the jackpot amout is so variable, and the likelihood is so low as to make this an extreme outlier event, we can safely leave the jackpot out of this calculation to simplify things.

For the plain \$1 Florida Lotto ticket without XTRA, the expected return on a \$1 wager is \$0.1815.

For the \$2 Florida Lotto with XTRA ticket, the expected return on a \$1 wager is \$0.3706. This is calculated using an average multiplier value of 3.5 for the second-tier and third-tier prize levels, since the average of 2, 3, 4, and 5 equals 3.5.

As you can see, the XTRA options increases your expected return per \$1 lottery bet. On the other hand, buying two regular tickets at \$1 apiece with different numbers will double your overall chances of winning a cash prize.

How Florida Lotto with Xtra Compares to Other Lotteries

Florida Lotto is easier to win than mutli-state games such as Powerball, Mega Millions, Hot Lotto, and Lucky for Life. In comparison, the likelihood of winning Florida Lotto is

• 1.27 times better than the likelihood of winning Hot Lotto
• 1.34 times better than the likelihood of winning Lucky for Life
• 11.28 times better than the likelihood of winning Mega Millions
• 12.73 times better than the likelihood of winning Powerball

If you're going to buy lottery tickets and you don't care that it's a sucker's bet, you're still better off playing a state lotto game rather than a big multi-state game, at least if your goal is to increase your chances of winning.

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