The math behind Florida Lotto

Florida Lotto is a complex lottery game offering a rolling jackpot and fixed prizes in the base draw, along with several add-ons. It shares many features with Michigan Lottery's Lotto 47, but has different parameters. Florida Lotto is among the few lotteries offering something for matching two numbers in the base draw. The jackpot starts from $1 million after the reset.

Category

Florida Lotto is a combinatorial lottery game that draws from one pool: six numbers from 1–53 (the base draw).

• Size of the draw: 6.
• Size of a played line: 6.
• Cost of a line: $2 

The game has two add-ons: The Double Play, allowing the same ticket to participate in a second similar draw (additional cost $1), and the EZmatch, based on an instant number draw at the ticket purchase and a prize draw, assigning random prizes to the EZmatch numbers (additional cost $1).

There are 5 multipliers (2x, 3x, 4x, 5x, 10x) that apply to prizes, except the jackpot, and one is automatically drawn for each ticket before the base number draw.

Prizes

There are five tiers of prizes in the base draw, defined as matching 2 to 6 numbers. They are all fixed prizes, except the top prize (6 numbers matched), which is a rolling jackpot, and the Match 2 prize, which is not a money prize, but an additional free line for you to play in the next draw. In the Double Play option, the same five tiers are defined, the fixed prizes get slightly increased (unlike in Lotto 47, where they get doubled), and the top prize is fixed at $250,000 for the Double Play draw.

The prizes do not increase uniformly from the lowest to the highest. There is an abrupt jump between the first two tiers, i.e., from jackpot to $3,000, and for the corresponding odds of winning.

There are 11 possible fixed prizes assigned at the EZmatch draw, from $3 to $500.

Florida Lotto has been available for Florida Lottery players since April 29, 1988. Photograph credit: Scott Habermann / Shutterstock.com.

The odds of winning

The odds of winning in the base draw with one line range from 1 in 22,957,480 (for the jackpot) to 1 in 8.58 (for the lowest tier). The overall odds of winning any prize (including the free ticket prize) in the base draw are 1 in 7.61. The overall odds of winning any money prize in the base draw are 1 in 67.36.

The same odds stand for the Double Play draw. If the Double Play is activated, the odds of winning in at least one of the two draws are noted in the next table:

The odds of winning any prize in EZmatch or any prize in the base draw are 1 in 3.39 (29.49%).

The odds of winning any prize in EZmatch or any prize in any of the two draws in Double Play are 1 in 2.58 (38.76%).

The odds of winning any prize in EZmatch or any money prize in the base draw are 1 in 4.99 (20.03%).

The odds of winning any prize in EZmatch or any money prize in any of the two draws in Double Play are 1 in 4.71 (21.22%).

The next table shows the odds of winning each possible money prize in the base draw, by taking into account the prize odds and the multiplier odds. These should be interpreted as a priori odds, before any information is available (before the ticket is printed).

Average win and fairness

The next table lists the average win for each money prize in the base draw (no multiplier applied):

*This is for an average jackpot win of $10.83 million.

Example of use and interpretation of the table: Over the long run, a win in the 5 of 6 match tier is distributed as $0.03685 average win per line played (assuming the prize is won with the relative frequency of about 1 in 81,409 draws).

The next table lists the fairness of each prize in the base draw relative to its probability:

For an average jackpot of $10.83 million*, its fairness would be 23.58%. However, this only applies in the circumstance where such a jackpot is actually won, as rollovers actually mean zero prizes in this tier.

Fairness is lower, both individually and overall, than in Michigan Lotto 47, which is explainable by the lower odds of winning (due to a larger pool of numbers in Florida Lotto) relative to similar prize amounts.

*Note: The average jackpot was chosen as the average of the jackpots won over the last 10 years, per the Florida Lottery.

Florida Lotto has to compete on shelves with popular state games such as Pick 3 and Pick 4, as well as multi-state powerhouses like Powerball and Mega Millions. Photograph credit: Scott Habermann / Shutterstock.com.

Expected value and house edge

The exact expected value of the Florida Lotto game cannot be determined because the first-tier prize is variable. It is still relevant to estimate it for two particular cases, associated with two assumptions:

• A: The first case is taking the jackpot amount as zero in the base draw (case justified by a long series of draws when the jackpot is not won, given its probability).
• B: The second case is taking an average amount for the jackpot won over a period of time (say, the last 10 years).

In case A, the expected value is –$1.4591, or –72.96% as a percentage of the line cost. The house edge of the game is 72.96%.

In case B, the expected value is –$0.925147, or –46.26% as a percentage of the line cost. The house edge of the game is 46.26%.

One way to interpret this is that in case A, you are expected to lose an average of $1.4591 for every $2 invested over the long run.

The above values correspond to the base play. 

With the Double Play option and no EZmatch option activated:

In case A, the expected value is –$1.5590, or –51.97% as a percentage of the line cost. The house edge of the game is 51.97%.

In case B, the expected value is –$ 0.9438, or – 31.46% as a percentage of the line cost. The house edge of the game is 31.46%.

One way to interpret this is that in case A, you are expected to lose on average $1.5590 at every $23 invested, over the long run.

With the EZmatch option and no Double Play activated:

In case A, the expected value is –$1.7079, or –56.93% as a percentage of the line cost. The house edge of the game is 56.93%.

In case B, the expected value is –$1.17395, or – 39.13% as a percentage of the line cost. The house edge of the game is 39.13%.

This means that in case A, you are expected to lose on average $1.7079 at every $3 invested, over the long run.

With both EZmatch and Double Play activated:

In case A, the expected value is –$1.9974, or – 49.94% as a percentage of the line cost. The house edge of the game is 49.94%.

In case B, the expected value is –$1.4634, or – 36.59% as a percentage of the line cost. The house edge of the game is 36.59%.

One way to interpret this is that in case A, you are expected to lose an average of $1.9974 for every $4 invested, over the long run.

Final remarks

Syndicating for this game carries a high risk, as the second-tier prize is very low relative to its odds and compared to the jackpot. This is also reflected in the fairness associated with that prize.

Having the Double Play option activated increases the odds of winning and also reduces the house edge of the game. The EZmatch option contributes to a high probability of winning any prize (almost 30%).

As far as individual long-run play is concerned, the lowest house edge is obtained when both EZmatch and Double Play are activated. 

House edge is not much different from that in Michigan Lotto 47; however, the odds of winning any prize are about twice as high as in that game due to those additional 6 numbers in the poll. Therefore, overall, Florida Lotto is preferable with respect to the odds between these two similar games.