# Florida Lottery

## Introduction

The Florida Lottery opened for business on January 12, 1988. Revenue generated is supposed to benefit education, especially scholarships. As with many other state lotteries, there has been criticism that after enactment, education spending was cut from the general fund by amounts comparible to Lottery funding with that general fund money used to support other projects.

Florida offers a mix of games based on a live draw of balls, scratch offs, and "Fast Play" games. Fast Play games are mathematically equivalent to scratch offs, but are printed on the spot and don't require scratching.

Many draw games have an optional side bet. If find these extra games to be of better value than the base games they are tacked onto. In general, I find the best odds to be on the scratch off and Fast Play games, as opposed to the draw games. As usual, the return to player with scratch offs goes up as the bet amount increases.

As with all lotteries, the odds are terrible compared to most forms of casino gambling. Looking at the average return to player, all lottery games are a terrible bet. If you must play, I recommend playing the games that offer the best odds and do so in strict moderation.

## Florida Lotto

The Florida Lotto is the oldest lottery game in Florida. It is based on the draw of six balls from 1 to 53. The price of a bet is \$2. Following are the pertinent rules.

1. The player shall pick six different numbers from 1 to 53.
2. The Lottery shall do the same.
3. The player shall win a fixed base prize if he matches 3 to 5 of the numbers, as follows:
• Match 5 = \$3,000
• Match 4 = \$50
• Match 3 = \$5
4. A random multiplier shall be applied to fixed wins. This multiplier may range from 2 to 10 with an average of about 3.346. The probability of each multipliler appears below.
5. If the player matches all six numbers, then he shall win a progressive jackpot. This jackpot shall either be paid out as an annuity or reduced if the player chooses the instant win option. The jackpot will also be subject so sharing if two or more players win.
6. If the player matches two numbers, then he shall win a free game.

### Analysis

The following table shows the number of combinations of catching 0 to 6 numbers, the probability of each, the fixed win for catching 3 to 5 numbers, and the contribution to the return for fixed wins, before applying the multiplier. The return column has been divided by 2, to reflect the ratio of the return to the bet amount. The lower right cell shows the player can expect to win back 7.14% of his bet amount for catching 3 to 5 numbers, before the multiplier.

### Florida Lotto — Fixed Wins

Catch Avg. Win Combinations Probability Return
6 Jackpot 1 0.000000 ?
5 \$3,000 282 0.000012 0.018425
4 \$50 16,215 0.000706 0.017658
3 \$5 324,300 0.014126 0.035315
2 Free game 2,675,475 0.116540 ?
1 \$- 9,203,634 0.400899 0.000000
0 \$- 10,737,573 0.467716 0.000000
Total   22,957,480 0.000000 0.071398

The following table shows my best estimate of the weighting, probability, and contribution to the average for the multiplier. The weights are based on data from previous games. The lower right cell shows an average multiplier of 3.35.

### Florida Lotto — Fixed Wins

Multiplier Weight Probability Return
2 9 0.346154 0.692308
3 8 0.307692 0.923077
4 5 0.192308 0.769231
5 3 0.115385 0.576923
10 1 0.038462 0.384615
Total 26 1.000000 3.346154

The contribution to the return from fixed wins after the multiplier is the product of the average win and the multiplier, or 7.14% × 3.35 = 23.89%.

Sometimes, the player will match two numbers, for a free game, and then match three to five numbers in the free game. Considering wins that way, the ultimate win from catching 3 to 5 numbers, including as the result of a free game, is 27.04%.

Without adjusting for the annuity factor, the return to player is 2.47% per million dollars in the jackpot. This includes the possibility of winning a free game and then winning the jackpot in the free game.

For example, at the time of this writing on May 13, 2021, the jackpot is at \$8.75 million. That would make the return to player 27.04% + 8.75 × 2.47% = 48.61%. To reach breakeven, ignorring the likely event of jackpot sharing, the jackpot would need to reach \$29,594,481. This, again, does not factor in the time-value of money lost in taking the annuity and taxes.

## Double Play

Double Play is an optional \$1 bet that may be made after playing the Florida Lotto. Wins are based on the same numbers chosen by the player and multiplier from the Florida Lotto ticket. There is a separate ball draw immediately after the Florida Lotto draw. The following table shows the base prizes.

• Match 6 = \$250,000
• Match 5 = \$3,500
• Match 4 = \$60
• Match 3 = \$7
• Match 2 = Free ticket

Advantages of the Double Play over the Florida Lotto are: a ticket costs half as much, the wins are greater for catching 3 to 5 numbers, the multiplier applies to the prize for catching 6. The only downside is there is no progressive jackpot for catching all six.

The following table shows the probability and contribution to the return for all possible outcomes of the Double Play, before applying the multiplier. The base win for the free ticket is \$0.22, which is how much the player can expect to win if he keeps playing the free ticket until the bet is resolved.

### Double Play

Catch Avg. Win Combinations Probability Return
6 \$250,000 1 0.000000 0.010890
5 \$3,500 282 0.000012 0.042993
4 \$60 16,215 0.000706 0.042378
3 \$7 324,300 0.014126 0.098883
2 \$0.22 2,675,475 0.116540 0.025742
1 \$0 9,203,634 0.400899 0.000000
0 \$0 10,737,573 0.467716 0.000000
Total   22,957,480 0.000000 0.220885

The lower right cell of the table above shows an expected win of \$0.220885. The multiplier is the same 3.346154 is is for the Florida Lotto. The overal return of the game is the produt of the average base win and the multiplier, which equals 0.220885 × 3.346154 = 0.739117, which for a lottery game isn't bad.

For the Florida Lottery to equal the return of the Double Play game, the jackpot would need to be \$19,012,010.62. This figure does not consider the annuity reduction, taxes, and the chance of jackpot sharing. Unless the jackpot is significantly higher than \$19 million, the Double Player offers a much better bet than the Florida Lotto, thus I would recommend making the extra wager, if playing the Lottery anyway.

## Fantasy 5

The Fantasy 5 is a \$1 daily game based on the draw of five numbers from 1 to 36. The player chooses five and wins according to how many match the daily draw by the Lottery. The game is pari-mutual, which means the wins are not fixed, but winners share a cut of the prize pool. Following are the rules.

1. The cost of a ticket is \$1.
2. There is one draw per day.
3. The player shall select five distinct numbers from 1 to 36. There is also a quick-pick option, for the game to randomly do the picking.
4. The Lottery shall pick five random numbers, without replacement, from 1 to 36.
5. The Lottery shall take the total revenue from ticket sales, not counting any "free tickets" from past drawings, and divide it roughly as follows to pay winners:
• Catch 5 — 24.7%
• Catch 4 — 9.3%
• Catch 3 — 17.0%
6. If there are no catch 5 winners, then that portion of the prize poll shall roll down to the pool for catch 4 winners.
7. The maximum prize for catching 4 is \$555. If due to a roll down, this cap is reached, then the the excess money in the catch 4 pool, not paid out due to the prize cap, shall roll down to the catch 3 pool.
8. Catch 4 and catch 3 winnings are somehow rounded to be evenly divisible by \$0.50.
9. If the player catches two numbers, then he shall win a free ticket.

### Analysis

The following analysis shows the probability of winning, average prize, and contribution to the return for all possible number of catches. If the player catches 2 and gets a free ticket, I assume the player will keep playing the free ticket until the bet is resolved. The average win from such a free ticket is \$0.51. You will notice the return column for catching 3 to 5 is not the same as the revenue shares stated above. This is because some wins for catching 3 to 5 will be from free tickets. For purposes of the table below, I count those wins under catching 2.

### Fantasy 5 — Return per Bet Made

Catch Avg. Win Combinations Probability Return
5 \$82,102.07 1 0.000003 0.217782
4 \$199.30 155 0.000411 0.081943
3 \$12.14 4,650 0.012334 0.149687
2 \$0.51 44,950 0.119233 0.060839
1 \$- 157,325 0.417317 0.000000
0 \$- 169,911 0.450702 0.000000
Total   376,992 1.000000 0.510251

Another way to look at this game is to analyze it by bet resolved. If the player initially catches 2, he will get a free game, which will eventually resolve in a monetary win or loss as long as he keeps replaying free games. The following table breaks down the odds according to the final outcome. Doing the math this way, the contributions to the return match the revenue shares listed in the rules above. Either way, the return to player is 51.0%.

### Fantasy 5 — Return per Bet Resolved

Catch Avg. Win Combinations Probability Return
5 \$82,102.07 1 0.000003 0.247264
4 \$199.30 155 0.000467 0.093036
3 \$12.14 4,650 0.014004 0.169951
1 \$0.00 157,325 0.473811 0.000000
0 \$0.00 169,911 0.511715 0.000000
Total   332,042 1.000000 0.510251

## EZ Match

EZ Match is an opptional extra bet that may be placed for \$1 after making a \$1 Fantasy 5 bet. It may seem like a side bet where the player has control of his destiny, but it's not.

The way this bet is skinned is the game picks five random numbers, without replacement, from 1 to 36, immediately, and prints them on the ticket. If there is a positional match with one of the player's chosen numbers, then the player wins a random prize. Here is the example from the Florida Lottery web site.

Note how the player matched three numbers positionally for wins of \$25, \$50, and \$25, for a total of \$100. However, note how the probability distribution table doesn't list a prize of \$25. Based, in part, on an apparently outdated document titled Emergency Rule 53ER12-40, the prize distribution is for the sum of the prizes between the five positions.

What seems to be actually going on is the player has a 7/33 (21.21%) chance of winning anything. If it is determined he does win, then his prize is determined like a pull-tab or scratch-off game, where there is a pool of outcomes and the game randomly selects one from the batch. Here is my best estimate on the number of each total prize in a batch. This table also shows the probability of each win and the contribution to the return. The lower right cell shows an average win of \$3.35.

### EZ Match Prize Table

Win Number
per Batch
Probability Return
\$500 5 0.000056 0.027821
\$250 5 0.000056 0.013911
\$100 38 0.000423 0.042288
\$50 124 0.001380 0.068996
\$20 1050 0.011685 0.233697
\$15 470 0.005230 0.078455
\$10 4200 0.046739 0.467394
\$5 1400 0.015580 0.077899
\$4 7000 0.077899 0.311596
\$3 30792 0.342666 1.027999
\$2 44776 0.498286 0.996572
Total 89860 1.000000 3.346628

Taking the product of the probability of winning and the average win, (7/33) × 3.346628, gives the player an expected return of 0.680159 =~ 68.0%.

## Jackpot Triple Play

Jackpot Triple Play is a game based on picking 6 numbers from 1 to 46. For a \$1 bet, the player gets three tickets. For an extra \$1, the player may play the Combo game, which I will analyze separately. Following are the rules of Jackpot Triple Play.

1. The cost of a ticket is \$1.
2. The player shall choose six different numbers from 1 to 46, or select the quick-pick option for the numbers to be chosen randomly.
3. In addition to the ticket with the player's chosen numbers, the player will get two more quick-picks for free.
4. The numbers on the quicks picks are independent of the player's picks on the first game and to each other.
5. The following is the pay table for each game, according to the number of matches:
• Catch 6 — Jackpot
• Catch 4 — \$500
• Catch 3 — \$25 Catch 2 — \$1
•
6. The jackpot is paid in the form of an annuity over 25 years. As usual with lottery annuities, the player may also choose a lump sum payment for a reduced amount.
7. If the jackpot goes over \$2,000,000 and there is no winner, then any money in the jackpot in excess of \$2,000,000 will roll down to the lower prizes. How exactly this is done, I don't know.
8. The player has the option of betting an extra \$1 for the Combo bet, which is addressed separately on this page.

The following table shows my analysis of Jackpot Triple Play. The return column is the produce of the win, probability, and 3. The reason for multiplying by 3 is the player gets 3 games for \$1. The lower right cell shows the value of fixed wins is 19.54% of the amount bet.

### Jackpot Triple Play

Catch Avg. Win Combinations Probability Return
6 Jackpot 1 0.000000 ?
5 500 240 0.000026 0.038434
4 25 11,700 0.001249 0.093682
3 1 197,600 0.021096 0.063287
2 0 1,370,850 0.146352 0.000000
1 0 3,948,048 0.421493 0.000000
0 0 3,838,380 0.409785 0.000000
Total   9,366,819 1.000000 0.195403 + ?

Before considering the time value of money lost in the annuity, jackpot sharing, and taxes, the return to player for each \$1,000,000 in the jackpot is 32.03%. the breakeven meter, where the return to player is 100%, with the same cavaets, is \$2,512,173. By way of comparison, at the time of this writing, on May 14, 2021, the jackpot was at \$950,000.

## Pick 2

The Pick 2 game is played by picking two numbers, each from 0 to 9. The Lottery shall do the same as well as picking a Fireball. Individual bets cost \$0.50 or \$1.00. There are several types of bets, each of which offers a Fireball option. The Fireball serves as a second chance, replacing the first and/or second number drawn by the Lottery if it helps the player win. The player must double his bet to add the Fireball option.

### Straight

To win the Straight bet, the player must match both numbers in the draw in the correct order. Wins pay 50 for 1. The following table shows the return table for the pick-2 Straight bet. The lower right cell shows an expected return of 50%.

### Pick 2 — Straight Bet

Event Pays Combinations Probability Return
Win 50 1 0.010000 0.500000
Loss 0 99 0.990000 0.000000
Total   100 1.000000 0.500000

### Straight with Fireball

If the player makes a Straight bet, he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace the first and/or second ball drawn by the Lottery, if it helps the player win. The number of wins possible depend on whether the player makes a 1-way (for example 5-5) or 2-way bet (for example 3-7).

The following return table shows the possible outcome of a 1-way bet, for example choosing the number 5-5. The lower right cell shows an expected return of 60%.

### Pick 2 — Straight Bet with Fireball — One Way

Wins Pays Combinations Probability Return
2 60 1 0.001000 0.060000
1 30 18 0.018000 0.540000
0 0 981 0.981000 0.000000
Total   1000 1.000000 0.600000

The following return table shows the possible outcome of a 2-way bet, for example choosing the number 5-7. The lower right cell shows an expected return of 60%.

### Pick 2 — Straight Bet with Fireball — Two Way

Wins Pays Combinations Probability Return
1 30 20 0.020000 0.600000
0 0 980 0.980000 0.000000
Total   1000 1.000000 0.600000

### Box

To win the Box bet, the player must pick two different numbers and match both numbers in the draw in EITHER order. Wins pay 25 for 1. The following table shows the return table for the pick-2 box bet. The lower right cell shows an expected return of 50%.

### Pick 2 — Box Bet

Event Pays Combinations Probability Return
Win 25 2 0.020000 0.500000
Loss 0 98 0.980000 0.000000
Total   100 1.000000 0.500000

### Box with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace the first and/or second ball drawn by the Lottery, if it helps the player win.

The following return table shows the possible outcomes. The lower right cell shows an expected return of 60%.

### Pick 2 — Box Bet with Fireball

Wins Pays Combinations Probability Return
2 30 2 0.002000 0.060000
1 15 36 0.036000 0.540000
0 0 962 0.962000 0.000000
Total   1000 1.000000 0.600000

### Front/Back

The Front and Back are two separate bets, which win if the player correctly predicts the first and second number drawn by the Lottery respectively. Wins pay 5 for 1. The following table shows the return table for the pick-2 Front and Back bets. The lower right cell shows an expected return of 50%.

### Pick 2 — Front/Back Bets

Wins Pays Combinations Probability Return
Win 5 1 0.100000 0.500000
Loss 0 9 0.900000 0.000000
Total   10 1.000000 0.500000

### Front/Back with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace the first and/or second ball drawn by the Lottery, if it helps the player win. Each win pays 3 for 1.

The following return table shows the possible outcomes. The lower right cell shows an expected return of 60%.

### Pick 2 — Front/Back with Fireball

Wins Pays Combinations Probability Return
2 6 1 0.010000 0.060000
1 3 18 0.180000 0.540000
0 0 81 0.810000 0.000000
Total   100 1.000000 0.600000

## Cash for Life

Cash for Life is a \$2 game, based on the draw of five balls out of 60 and a Cash Ball from 1 to 4. The top two wins are paid as \$1,000 per day or per week for the lifetime of the winner. Following are the detailed rules.

1. The cost of a ticket is \$2.
2. The player should picks five different numbers from 1 to 60.
3. In addition, the player should pick a Cash Ball from 1 to 4.
4. Daily, at 9:00PM, the Lottery shall have a drawing, which shall also pick balls on the same basis as the player.
5. The following are the wins based on how many numbers matched and whether the Cash Ball matched.
• Catch 5 and Cash Ball — \$1,000 per day for life
• Catch 5 without Cash Ball — \$1,000 per week for life
• Catch 4 and Cash Ball — \$2,500
• Catch 4 without Cash Ball — \$500
• Catch 3 and Cash Ball — \$100
• Catch 3 without Cash Ball — \$25
• Catch 2 and Cash Ball — \$10
• Catch 2 without Cash Ball — \$4
• Catch 1 and Cash Ball — Free ticket
6. The top two prizes are paid for at least 20 years. If the winner dies before 20 years of payments, the balance owed can be paid to the designated heirs.
7. The top two prizes may be paid on an annual basis.

The following table shows the probability and contribution to the return for all fixed wins. The return column is the product of the win, probability, and 1/2. The reason for dividing by 2 is to show the ratio of the win to the bet amount of \$2. The lower right cell shows that fixed wins have an immediate value of 21.68% of the amount bet.

### Cash for Life

Catch Avg. Win Combinations Probability Return
5 Yes \$1000 per day 1 0.000000 ?
5 No \$1000 per week 3 0.000000 ?
4 Yes \$2,500 275 0.000013 0.015735
4 No \$500 825 0.000038 0.009441
3 Yes \$100 14,850 0.000680 0.033988
3 No \$25 44,550 0.002039 0.025491
2 Yes \$10 262,350 0.012009 0.060045
2 No \$4 787,050 0.036027 0.072054
1 Yes Free ticket 1,705,275 0.078059 ?
1 No \$- 5,115,825 0.234176 0.000000
0 Yes \$- 3,478,761 0.159240 0.000000
0 No \$- 10,436,283 0.477719 0.000000
Total     21,846,048 1.000000 0.216754 + ?

The rest of this analysis of Cash for Life shall assume if the player wins a Free Ticket, then he shall keep playing it until the bet is resolved. That said, the value of the fixed wins goes up to 0.235106, to include fixed wins won after winning a Free Ticket.

The return to player from the top prize is 0.008360 per year the winner collects. The return to player from the second to top prize is 0.003583 per year the winner collects. Combined, the top two awards have a return to player of 0.011942 per year the winner collects. These figures include the possibility of winning a Free Game and then winning one of the top two awards in a free game.

For the expected return to equal 100%, the winner would have to live 65.6 years. Wins are not adjusted to inflation, so this figure does not consider the time value of money lost.

For more information, see the Florida Lottery page on Cash for Life.

## Pick 3

Pick 3 games are played by picking three numbers, each from 0 to 9. The Lottery shall do the same as well as picking a Fireball. Individual bets cost \$0.50 or \$1.00. There are several types of bets, each of which offers a Fireball option. The Fireball serves as three second chances, replacing each ball, one at a time, drawn by the Lottery, if it helps the player win. The player must double his bet to add the Fireball option.

### Straight

To win the Straight bet, the player must match all three numbers in the draw in the correct order. Wins pay 500 for 1. The following table shows the return table for the pick-3 Straight bet. The lower right cell shows an expected return of 50%.

### Pick 3 — Straight Bet

Event Pays Combinations Probability Return
Win 500 1 0.001000 0.500000
Loss 0 999 0.999000 0.000000
Total   1000 1.000000 0.500000

### Straight with Fireball

If the player makes a Straight bet, he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace the first and/or second ball drawn by the Lottery, if it helps the player win. The number of wins possible depend on whether the player makes a 1-way (for example 5-5-5), 3-way bet (for example 3-3-7), or 6-way bet (for example 2-8-4). Each win pays 200 for 1.

The following return table shows the possible outcome of a 1-way bet, for example playing 5-5-5. The lower right cell shows an expected return of 60%.

### Pick 3 — Straight Bet with Fireball — One Way

Wins Pays Combinations Probability Return
3 600 1 0.000100 0.060000
1 200 27 0.002700 0.540000
0 0 9,972 0.997200 0.000000
Total   10,000 1.000000 0.600000

The following return table shows the possible outcome of a 3-way bet, for example choosing the number 3-3-7. The lower right cell shows an expected return of 60%.

### Pick 3 — Straight Bet with Fireball — Three Way

Wins Pays Combinations Probability Return
2 400 1 0.000100 0.040000
1 200 28 0.002800 0.560000
0 0 9,971 0.997100 0.000000
Total   10,000 1.000000 0.600000

The following return table shows the possible outcome of a 6-way bet, for example choosing the number 3-5-7. The lower right cell shows an expected return of 60%.

### Pick 3 — Straight Bet with Fireball — Six Way

Wins Pays Combinations Probability Return
1 200 30 0.003000 0.600000
0 0 9,970 0.997000 0.000000
Total   10,000 1.000000 0.600000

### Box

To win the Box bet, the player must pick three numbers and match both numbers in the draw in ANY order. The player should pick either two (example 3-9-3) or three (example 8-5-2) different numbers. 3-way wins pay 160 and 6-way wins pay 80.

The following table shows the return table for the 3-way pick-3 box bet. The lower right cell shows an expected return of 48%.

### Pick 3 — Box Bet — 3 Ways

Event Pays Combinations Probability Return
Win 160 3 0.003000 0.480000
Loss 0 997 0.997000 0.000000
Total   1000 1.000000 0.480000

The following table shows the return table for the 6-way pick-3 box bet. The lower right cell shows an expected return of 48%.

### Pick 3 — Box Bet — 3 Ways

Event Pays Combinations Probability Return
Win 80 6 0.006000 0.480000
Loss 0 994 0.994000 0.000000
Total   1000 1.000000 0.480000

### Box with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each ball drawn by the Lottery one at a time, if it helps the player win. Each win pays 68 on a 3-way bet and 34 on a 6-way.

The following return table shows the possible outcomes of a pick-3 3-way box bet with the Fireball. The lower right cell shows an expected return of 61.2%.

### Pick 3 — Box Bet with Fireball — 3 Way

Wins Pays Combinations Probability Return
3 204 1 0.000100 0.020400
2 136 6 0.000600 0.081600
1 68 75 0.007500 0.510000
0 0 9,918 0.991800 0.000000
Total   10,000 1.000000 0.612000

The following return table shows the possible outcomes of a pick-3 6-way box bet with the Fireball. The lower right cell shows an expected return of 61.2%.

### Pick 3 — Box Bet with Fireball — 6 Way

Wins Pays Combinations Probability Return
2 68 18 0.001800 0.122400
1 34 144 0.014400 0.489600
0 0 9,838 0.983800 0.000000
Total   10,000 1.000000 0.612000

### Front/Back Pair

The Front Pair and Back Pair are two separate bets, which win if the player correctly predicts the first two numbers and last numbers, respectively. Wins pay 50 for 1. The following table shows the return table for the pick-3 Front Pair and Back Pair bets. The lower right cell shows an expected return of 50%.

### Pick 3 — Front Pair/Back Pair Bets

Wins Pays Combinations Probability Return
1 50 1 0.010000 0.500000
0 0 99 0.990000 0.000000
Total   100 1.000000 0.500000

### Front Pair/Back Pair with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each ball drawn by the Lottery, one at a time, if it helps the player win. Each win pays 20 for 1. The number of possible wins depend on whether the two numbers chosen by the player are the same (one way) or different (two ways).

The following return table shows the possible outcomes of a one-way (for example 6-6) front/back pair bet. The lower right cell shows an expected return of 60%.

### Pick 3 — Front/Back with Fireball — One way

Wins Pays Combinations Probability Return
3 60 10 0.001000 0.060000
1 20 270 0.027000 0.540000
0 0 9,720 0.972000 0.000000
Total 0 10,000 1.000000 0.600000

The following return table shows the possible outcomes of a two-way (for example 3-6) front/back pair bet. The lower right cell shows an expected return of 60%.

### Pick 3 — Front/Back with Fireball — Two Way

Wins Pays Combinations Probability Return
2 40 20 0.002000 0.080000
1 20 260 0.026000 0.520000
0 0 9,720 0.972000 0.000000
Total 0 10,000 1.000000 0.600000

## Pick 4

Pick 4 games are played by picking four numbers, each from 0 to 9. The Lottery shall do the same as well as picking a Fireball. Individual bets cost \$0.50 or \$1.00. There are several types of bets, each of which offers a Fireball option. The Fireball serves as four second chances, replacing each ball, one at a time, drawn by the Lottery, if it helps the player win. The player must double his bet to add the Fireball option.

### Straight

To win the Straight bet, the player must match all three numbers in the draw in the correct order. Wins pay 5000 for 1. The following table shows the return table for the pick-4 Straight bet. The lower right cell shows an expected return of 50%.

### Pick 4 — Straight Bet

Event Pays Combinations Probability Return
Win 5000 1 0.000100 0.500000
Loss 0 9,999 0.999900 0.000000
Total   10,000 1.000000 0.500000

### Straight with Fireball

If the player makes a Straight bet, he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each of the four numbers drawn by the Lottery, one at a time, if it helps the player win. The number of wins possible depend on whether the player makes a 1-way (example 5-5-5-5), 4-way bet (example 3-3-7-3), 6-way bet (example 2-8-4-8), 12-way (example 1-3-5-1), or 24-way (example 3-9-7-5). Each win pays 1500 for 1.

The following return table shows the possible outcome of a 1-way straight with Fireball bet, for example playing 5-5-5-5. The lower right cell shows an expected return of 60%.

### Pick 4 — Straight Bet with Fireball — One Way

Wins Pays Combinations Probability Return
4 6000 1 0.000010 0.060000
1 1500 36 0.000360 0.540000
0 0 99,963 0.999630 0.000000
Total   100,000 1.000000 0.600000

The following return table shows the possible outcome of a 4-way straight with Fireball bet, for example choosing the number 3-3-7-3. The lower right cell shows an expected return of 60%.

### Pick 4 — Straight Bet with Fireball — Four Way

Wins Pays Combinations Probability Return
3 4500 1 0.000010 0.045000
1 1500 37 0.000370 0.555000
0 0 99,962 0.999620 0.000000
Total   100,000 1.000000 0.600000

The following return table shows the possible outcome of a 6-way straight with Fireball bet, for example choosing the number 3-5-3-5. The lower right cell shows an expected return of 60%.

### Pick 4 — Straight Bet with Fireball — Six Way

Wins Pays Combinations Probability Return
2 3000 2 0.000020 0.060000
1 1500 36 0.000360 0.540000
0 0 99,962 0.999620 0.000000
Total   100,000 1.000000 0.600000

The following return table shows the possible outcome of a 12-way straight with Fireball bet, for example choosing the number 3-5-3-0. The lower right cell shows an expected return of 60%.

### Pick 4 — Straight Bet with Fireball — 12 Way

Wins Pays Combinations Probability Return
2 3000 1 0.000010 0.030000
1 1500 38 0.000380 0.570000
0 0 99,961 0.999610 0.000000
Total   100,000 1.000000 0.600000

The following return table shows the possible outcome of a 24-way straight with Fireball bet, for example choosing the number 3-5-0-7. The lower right cell shows an expected return of 60%.

### Pick 4 — Straight Bet with Fireball — 24 Way

Wins Pays Combinations Probability Return
1 1500 40 0.000400 0.600000
0 0 99,960 0.999600 0.000000
Total   100,000 1.000000 0.600000

### Pick 4 Box with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each ball drawn by the Lottery one at a time, if it helps the player win. Each win pays 380 on a 4-way, 252 on a 6-way, 126 on a 12-way, and 62 on a 24-way.

The following return table shows the possible outcomes of a pick-4 4-way box bet with the Fireball. The lower right cell shows an expected return of 59.28%.

### Pick 4 — Box Bet with Fireball — 4 Way

Wins Pays Combinations Probability Return
4 1520 1 0.000010 0.015200
3 1140 4 0.000040 0.045600
2 760 6 0.000060 0.045600
1 380 132 0.001320 0.501600
0 0 99,857 0.998570 0.000000
Total   100,000 0.999990 0.592800

The following return table shows the possible outcomes of a pick-4 6-way box bet with the Fireball. The lower right cell shows an expected return of 60.48%.

### Pick 4 — Box Bet with Fireball — 6 Way

Wins Pays Combinations Probability Return
3 756 8 0.000080 0.060480
2 504 12 0.000120 0.060480
1 252 192 0.001920 0.483840
0 0 99,788 0.997880 0.000000
Total 0 100,000 1.000000 0.604800

The following return table shows the possible outcomes of a pick-4 12-way box bet with the Fireball. The lower right cell shows an expected return of 60.48%.

### Pick 4 — Box Bet with Fireball — 12 Way

Wins Pays Combinations Probability Return
3 378 8 0.000080 0.030240
2 252 48 0.000480 0.120960
1 126 360 0.003600 0.453600
0 0 99,584 0.995840 0.000000
Total 0 100,000 1.000000 0.604800

The following return table shows the possible outcomes of a pick-4 24-way box bet with the Fireball. The lower right cell shows an expected return of 59.25%.

### Pick 4 — Box Bet with Fireball — 24 Way

Wins Pays Combinations Probability Return
2 124 144 0.001440 0.178560
1 62 672 0.006720 0.416640
0 0 99,184 0.991840 0.000000
Total 0 100,000 1.000000 0.595200

### Front/Middle/Back Pair

The Front Pair, Middle Pair and Back Pair are three separate bets, which win if the player correctly predicts the first two numbers and last numbers, respectively, in the chosen pair. Wins pay 50 for 1. The following table shows the return table for the pick-4 Pair bets. The lower right cell shows an expected return of 50%.

### Pick 3 — Front Pair/Back Pair Bets

Wins Pays Combinations Probability Return
1 50 1 0.010000 0.500000
0 0 99 0.990000 0.000000
Total   100 1.000000 0.500000

### Front/Middle/Back Pair with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each ball drawn by the Lottery, one at a time, if it helps the player win. Each win pays 15 for 1. The number of possible wins depend on whether the two numbers chosen by the player are the same (one way) or different (two ways).

The following return table shows the possible outcomes of a one-way (for example 6-6) front/back pair bet. The lower right cell shows an expected return of 60%.

### Pick 3 — Front/Back with Fireball — One way

Wins Pays Combinations Probability Return
4 60 1 0.001000 0.060000
2 30 9 0.009000 0.270000
1 15 18 0.018000 0.270000
0 0 972 0.972000 0.000000
Total   1,000 1.000000 0.600000

The following return table shows the possible outcomes of a two-way (for example 3-6) front/back pair bet. The lower right cell shows an expected return of 60%.

### Pick 3 — Front/Back with Fireball — Two Way

Wins Pays Combinations Probability Return
3 45 2 0.002000 0.090000
2 30 8 0.008000 0.240000
1 15 18 0.018000 0.270000
0 0 972 0.972000 0.000000
Total 0 1,000 1.000000 0.600000

## Pick 5

Pick 5 games are played by picking five numbers, each from 0 to 9. The Lottery shall do the same as well as picking a Fireball. Individual bets cost \$0.50 or \$1.00. There are several types of bets, each of which offers a Fireball option. The Fireball serves as five second chances, replacing each ball, one at a time, drawn by the Lottery, if it helps the player win. The player must double his bet to add the Fireball option.

### Straight

To win the Straight bet, the player must match all five numbers in the draw in the correct order. Wins pay 50000 for 1. The following table shows the return table for the pick-5 Straight bet. The lower right cell shows an expected return of 50%.

### Pick 5 — Straight Bet

Event Pays Combinations Probability Return
Win 50000 1 0.000010 0.500000
Loss 0 99,999 0.999990 0.000000
Total   100,000 1.000000 0.500000

### Pick 5 Straight with Fireball

If the player makes a Straight bet, he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each of the five numbers drawn by the Lottery, one at a time, if it helps the player win. The number of wins possible depend on whether the player makes a 1-way (example 5-5-5-5-5), 5-way bet (example 3-3-7-3-3), 10-way bet (example 2-8-2-8-2), 60-way (example 5-9-7-3-5), or 120-way (example 3-9-7-5-0). Each win pays 12,000 for 1.

The following return table shows the possible outcome of a pick-5 1-way straight with Fireball bet, for example playing 5-5-5-5-5. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — One Way

Wins Pays Combinations Probability Return
5 60000 1 0.000001 0.060000
1 12000 45 0.000045 0.540000
0 0 999,954 0.999954 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a pick-5 5-way straight with Fireball bet, for example choosing the number 3-3-7-3-3. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — Five Way

Wins Pays Combinations Probability Return
4 48000 1 0.000001 0.048000
1 12000 46 0.000046 0.552000
0 0 999,953 0.999953 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a 10-way straight with Fireball bet, for example choosing the number 3-5-3-5-3. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — Ten Way

Wins Pays Combinations Probability Return
3 36000 1 0.000001 0.036000
2 24000 1 0.000001 0.024000
1 12000 45 0.000045 0.540000
0 0 999,953 0.999953 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a pick-5 20-way straight with Fireball bet, for example choosing the number 3-0-7-7-7. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — 20 Way

Wins Pays Combinations Probability Return
3 36000 1 0.000001 0.036000
1 12000 47 0.000047 0.564000
0 0 999,952 0.999952 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a pick-5 30-way straight with Fireball bet, for example choosing the numbers 5-1-1-9-9. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — 30 Way

Wins Pays Combinations Probability Return
2 24000 2 0.000002 0.048000
1 12000 46 0.000046 0.552000
0 0 999,952 0.999952 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a pick-5 60-way straight with Fireball bet, for example choosing the numbers 4-8-0-8-5. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — 60 Way

Wins Pays Combinations Probability Return
1 12000 48 0.000048 0.576000
0 0 999,951 0.999951 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcome of a pick-5 120-way straight with Fireball bet, for example choosing the numbers 4-8-0-7-5. The lower right cell shows an expected return of 60%.

### Pick 5 — Straight Bet with Fireball — 120 Way

Wins Pays Combinations Probability Return
1 12000 50 0.000050 0.600000
0 0 999,950 0.999950 0.000000
Total   1,000,000 1.000000 0.600000

### Pick-5 Box

To win the Box bet, the player must pick five numbers and match all numbers in the draw in ANY order. The player should not pick the same number all five times, because it would be the same thing as a straight bet. 5-way wins pay 1198, 6-way wins pay 800, 12-way wins pay 400, and 24-way wins pay 200.

The following table shows the return table for the 4-way pick-4 box bet. The lower right cell shows an expected return of 50%.

### Pick 5 — Box Bet — 5 Ways

Event Pays Combinations Probability Return
Win 10000 5 0.000050 0.500000
Loss 0 9,996 0.099960 0.000000
Total   10,001 0.100010 0.500000

The following table shows the return table for the 10-way pick-5 box bet. The lower right cell shows an expected return of 50%.

### Pick 5 — Box Bet — 10 Ways

Event Pays Combinations Probability Return
Win 10000 5 0.000050 0.500000
Loss 0 999,995 9.999950 0.000000
Total   1,000,000 10.000000 0.500000

The following table shows the return table for the 20-way pick-5 box bet. The lower right cell shows an expected return of 48%.

### Pick 5 — Box Bet — 20 Ways

Event Pays Combinations Probability Return
Win 2500 20 0.000200 0.500000
Loss 0 999,980 9.999800 0.000000
Total   1,000,000 10.000000 0.500000

The following table shows the return table for the 30-way pick-5 box bet. The lower right cell shows an expected return of 49.8%.

### Pick 5 — Box Bet — 30 Ways

Event Pays Combinations Probability Return
Win 1660 30 0.000300 0.498000
Loss 0 9,999,970 99.999700 0.000000
Total   10,000,000 100.000000 0.498000

The following table shows the return table for the 60-way pick-5 box bet. The lower right cell shows an expected return of 49.8%.

### Pick 5 — Box Bet — 60 Ways

Event Pays Combinations Probability Return
Win 830 60 0.000600 0.498000
Loss 0 9,999,940 99.999400 0.000000
Total   10,000,000 100.000000 0.498000

The following table shows the return table for the 120-way pick-5 box bet. The lower right cell shows an expected return of 49.92%.

### Pick 5 — Box Bet — 120 Ways

Event Pays Combinations Probability Return
Win 416 120 0.001200 0.499200
Loss 0 9,999,880 99.998800 0.000000
Total   10,000,000 100.000000 0.499200

### Pick 5 Box with Fireball

If the player makes a Box bet, then he may add the Fireball option by doubling the bet amount. This adds an additional bet. The Fireball, drawn by the Lottery, shall replace each ball drawn by the Lottery one at a time, if it helps the player win. Each win pays 2400 on a 5-way, 1200 on a 10-way, 600 on a 20-way, 400 on a 30-way, 200 on a 60-way, and 100 on a 120-way.

The following return table shows the possible outcomes of a pick-5 5-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 5 Way

Wins Pays Combinations Probability Return
4 48000 1 0.000001 0.048000
1 12000 46 0.000046 0.552000
0 0 999,953 0.999953 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcomes of a pick-5 10-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 10 Way

Wins Pays Combinations Probability Return
3 36000 1 0.000001 0.036000
2 24000 1 0.000001 0.024000
1 12000 45 0.000045 0.540000
0 0 999,953 0.999953 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcomes of a pick-5 20-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 20 Way

Wins Pays Combinations Probability Return
3 36000 1 0.000001 0.036000
1 12000 47 0.000047 0.564000
0 0 999,952 0.999952 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcomes of a pick-5 30-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 30 Way

Wins Pays Combinations Probability Return
2 24000 2 0.000002 0.048000
1 12000 46 0.000046 0.552000
0 0 999,952 0.999952 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcomes of a pick-5 60-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 60 Way

Wins Pays Combinations Probability Return
1 12000 48 0.000048 0.576000
0 0 999,951 0.999951 0.000000
Total   1,000,000 1.000000 0.600000

The following return table shows the possible outcomes of a pick-5 120-way box bet with the Fireball. The lower right cell shows an expected return of 60%.

### Pick 5 — Box Bet with Fireball — 120 Way

Wins Pays Combinations Probability Return
1 12000 50 0.000050 0.600000
0 0 999,950 0.999950 0.000000
Total   1,000,000 1.000000 0.600000

## Scratch Offs

The Florida Lottery offers scratch off tickets in bets from \$1 to \$30. To get an estimate of the value, I sampled the odds of one game for each bet level. The following table shows the return to player for each game.

### Scratch Off Game Returns

Denomination Game Return
\$1 Loose Change 62.04%
\$2 Money Roll 66.17%
\$3 Scrabble 69.55%
\$5 Pay Me 70.45%
\$10 Cash Club 75.49%
\$20 200x the Cash 77.32%
\$30 Billion Gold Rush Surprise 77.03%

## Fast Play

Fast Play games are essentially like scratch cards, but don't require scratching. They are printed on the spot at a Lottery retailer. Much like scratch cards, they are created in large batches with a specified number of tickets for each monetary win. At the time of this writing, in May 2021, there were three games available. The return of each is listed below. As you can see, the returns are comparible to those of scratch cards for the same denomination.

### Scratch Off Game Returns

Denomination Game Return
\$1 Fast Cash 61.05%
\$2 Honeycomb 67.06%
\$5 Lucky 7s 70.01%

## Other Games

The Florida Lottery also participates in Powerball and Mega Millions.