John Lottery's Bimonthly Lottery Articles: Florida Lotto Plus Analysis. Should you buy the $2 or $3 Option?

Friday, October 31, 2008

Florida Lotto Plus Analysis. Should you buy the $2 or $3 Option?

Introduction
The Florida Lottery enhanced the Florida Lotto by introducing the $2 and $3 LOTTO PLUS jackpot levels on March 2, 2008. This gives players of that game the option to "Super Size" their jackpot winnings. This means that rather than strictly buying a single $1 ticket, players can instead:

Spend $2 per ticket, and increase the base jackpot payout by $10 Million if that combination wins; or
Spend $3 per ticket, and increase the base jackpot payout by $25 Million if that combination wins.

Shortly after these options became available, the first $2 Lotto Plus jackpot winner increased his winnings from $6 million to $16 million in the May 10th 2008 drawing. However, since that time to date, there have been no additional Lotto Plus winners.

The lure of increasing the size of the Jackpot purse for only $1 or $2 more seems to be very attractive on the surface. Thus, we asked ourselves two questions:

Would We Buy the Lotto Plus Option?
And, If so, Which One?

Our analysis found that:

Yes, We Would Buy
the Lotto Plus Option
in Certain Instances

but it would depend on the size of the Base Jackpot being offered. As for which one to buy, we found that:

The $3 Lotto Plus Option is the Best
(If You Can Afford It)

How would you know when to buy the Florida Lotto Plus Option?
You should always buy the plus option whenever the current jackpot value is below its Jackpot Breakeven level.

For $2 Lotto Plus, Breakeven is $5.8 million: Buy the $2 Lotto Plus Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
For $3 Lotto Plus, Breakeven is $8.3 million: Buy the $3 Lotto Plus Option whenever the Jackpot is below this value. Never above this. Buy 3 tickets instead.

Why is that?
The reason these levels can be calculated is because ONLY the Jackpot prize is increased for those winners who purchased the option. No other lower level prizes are increased. So, as the Jackpot increases above its minimum, only the probability weighted amount of jackpot money returned to players increases. At some point, which we call Jackpot Breakeven, the Single $1 Ticket jackpot return outweighs the increased Jackpot payments per dollar spent. Once this point is reached, buying the Lotto Plus option is not a good investment. Remember, because the option costs $1 or $2 more, it is necessary to divide these probability weighted returns by 2 or 3 before comparing them to single $1 tickets. When the jackpot is above the breakeven level, the per dollar return of Florida Lotto Plus tickets becomes less and less valuable compared to that of a regular $1 ticket.

As lottery players, we want to play the option that returns the most money back to us, the players. As you will see below, your option changes depending on the jackpot level.

Florida Lotto Plus

When a player buys the Florida Lotto Plus Option only the Jackpot will be increased. For the $2 option, jackpot payout increases by $10 Million. For the $3 option, jackpot payout increases by $25 Million.

However, the Florida Lotto has 22,957,480 unique combinations. Only one of these will be selected in any particular drawing. Excluding duplicates, there will be only 1 winning combination.

To play, the Florida Lotto requires a player to select 6 numbers from a set of 53 (there is no bonus ball). Prizes are only paid out to players who correctly match 3, 4, 5, or 6 of the numbers. This means that of the nearly 23 million combinations, only 340,798 will return any prize payout.

The graph below illustrates both the expected Lotto Plus $3 Return (in blue) and the Lotto Plus $2 Return (in red) against the expected return of a Single Ticket (in green).

When the advertised jackpot is set to the minimum $3 million, the $3 Lotto Plus returns the most money, $0.467 of each dollar received, back to the players. By comparison, the $2 Lotto Plus returns the $0.374 of each dollar received, and a Single $1 Ticket returns $0.313.

When the jackpot level reaches $5.8 million, the returns of the $2 Lotto Plus and a Single Ticket are equal, at $0.436 each. However, both of these are substantially below the $3 Lotto Plus's $0.508 return. (Note that above this breakeven level, the single ticket returns out pace that of the $2 option.)

When the advertised jackpot level reaches $8.3 million, the $3 Lotto Plus and a Single Ticket returns are equal, at $0.544 each. This jackpot level is the $3 Lotto Plus breakeven. From the graph, it is clear that either of these two scenarios are preferable to the $2 Lotto Plus option which only returns $0.490 per dollar spent.

Above the $3 Lotto Plus breakeven point, single tickets purchased without either option return more to the players. When the jackpot grows to $23 million, $1.184 is returned to single ticket holders, compared to only $0.810 for $2 Lotto Plus, and $0.758 for $3 Lotto Plus.

Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Florida Lotto jackpot is below $8.3 million, the $3 Lotto Plus should be purchased. Above $8.3 M, always buy single tickets. If you cannot afford the $3 option, you should consider the $2 Lotto Plus. In this case, breakeven is at $5.8 million. Buy the $2 option below this level, and single tickets above it.

Alternate Analysis
Since the only prize that is increased by $2 and $3 Lotto Plus is the actual Jackpot paid to winners, we can alternately analyze the jackpot payout on a per dollar basis. For this, a simple algebraic relationship is defined as:

JackpotAmount = (JackpotAmount + OptionPayout)/CostPerTicket

As seen, the OptionPayout and CostPerTicket variables are fixed but depend upon whether we are analyzing the $2 or $3 option. This means that we can solve for the optimal Jackpot amount for either of these options.

Solving for the $2 Lotto Option, our formula changes to: JackpotAmount = (JackpotAmount + 10)/2 which implies the $2 Plus JackpotAmount of $10 Million.

Similarily solving for the $3 Lotto Plus Option, our formula changes to: JackpotAmount = (JackpotAmount + 25)/3 which implies a $3 Plus JackpotAmount of $12.5 Million.

If you prefer this analysis to breakeven returns, we advise that you NEVER purchase either option when the base jackpot is above $12.5 million. At this level, go for the Jackpot, and purchase multiple combinations, giving yourself increased chances of winning.

Conclusion
To conclude, the decision to buy the Florida Lotto Plus option is dependent upon the jackpot size. When the jackpot is below its breakeven level, players are encouraged to buy the plus option. But, when the jackpot is above its breakeven level, players should forego this option, and buy 2 or 3 straight tickets instead (depending on whether you are considering the $2 or $3 option).

Our belief is that both of these options have value to the Florida Lottery player and should be considered.

Looking back at the May 10th 2008 $2 Lotto Plus winner, we believe the player made a very good choice, not only for his winnings, but because the base jackpot level was approximately equal to the $2 breakeven level of $5.8 million. Rounding this number to the nearest million, the player was indifferent to buying the option or not. Having purchased the option and having the winning combination, the player won a $16 million annuity jackpot, consisting of the $6 million base amount plus the $10 million option payout. Well done!

Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.