Can You Buy All Lottery Ticket Combos to Win? (Explained)

Purchasing every possible lottery ticket combination to guarantee a win is a concept often debated in the context of large jackpot lotteries.

To analyze whether this strategy is viable, let’s consider the factors that impact its feasibility and expected value.

Table of Contents

Factors to Consider

Lottery Mechanics: Lotteries like Powerball or Mega Millions have vast combinations. For instance, Powerball involves selecting five numbers from 1 to 69 and one Powerball number from 1 to 26, leading to 292,201,338 possible combinations.
Cost: The cost of buying every combination depends on the price per ticket (usually $2 for Powerball and Mega Millions). For Powerball, purchasing every combination would cost 292,201,338 combinations * $2 = $584,402,676.
Jackpot Size: To break even, the jackpot would need to exceed the total cost of purchasing all combinations. However, this doesn’t account for taxes or the potential of multiple winners.
Taxes: Lottery winnings are subject to federal and possibly state taxes, significantly reducing the net prize.
Split Jackpot: If another player also wins, the jackpot is divided, reducing the prize further. The feasibility of this strategy heavily depends on being the sole winner.

Analysis

Expected Value Calculation

The expected value (EV) of this strategy can be simplified as:

To have a positive EV, the adjusted jackpot value (after accounting for taxes and the probability of a split jackpot) must exceed the total cost of purchasing every combination.

Practical Challenges

Logistics: Buying every possible ticket is logistically challenging, requiring a system to ensure no combinations are missed and managing the physical process in time for a drawing.
Risk of Splitting the Jackpot: There’s no guarantee of being the sole winner, especially as jackpot sizes increase and attract more players.

Q&A – Can You Buy All Lottery Ticket Combos to Win?

How many combinations are there in major lotteries like Powerball or Mega Millions?

For major lotteries, the number of possible combinations varies:

Powerball: Players pick 5 numbers from a set of 69 and 1 Powerball number from a set of 26, resulting in 292,201,338 possible combinations.
Mega Millions: Players select 5 numbers from a set of 70 and 1 Mega Ball number from a set of 25, leading to 302,575,350 possible combinations.

What is the cost to buy every possible lottery ticket combination?

Powerball: At $2 per ticket, purchasing every combination would cost approximately $584,402,676.
Mega Millions: Similarly, at $2 per ticket, buying all combinations would cost about $605,150,700.

How does the jackpot size affect the feasibility of buying all lottery ticket combos?

The jackpot size significantly impacts the feasibility:

A jackpot must be substantially higher than the total cost of purchasing all combinations to potentially make this strategy profitable.
After accounting for taxes and the possibility of splitting the jackpot, the net gain must still exceed the investment for this approach to be considered feasible.

What are the tax implications on lottery winnings?

Lottery winnings are subject to federal taxes and, in some cases, state taxes, which can significantly reduce the net amount received. The top federal tax rate can be as high as 37%, and state taxes vary, with some states not taxing lottery winnings at all, while others may tax at rates over 10%.

Can you be the sole winner if you buy all combinations, or is there a risk of sharing the jackpot?

Even if you buy all combinations, there’s a risk of sharing the jackpot with other winners who happen to select the winning numbers independently. The more players there are, especially when the jackpot is high, the greater the likelihood of multiple winners.

What are the logistical challenges of purchasing every lottery ticket combination?

The logistical challenges include:

Time: Purchasing hundreds of millions of tickets would require an immense amount of time and coordination.
Errors: The risk of human error in ensuring every possible combination is purchased without duplication.
Retailer Capacity: The capability of lottery retailers to process such a high volume of ticket purchases within the timeframe before a drawing.

Is it legal to buy all the lottery ticket combinations?

Yes, it’s legal to buy all lottery ticket combinations, provided the purchases are made in compliance with the lottery rules and local laws. However, the practicality and logistics of doing so present significant barriers.

How do split jackpots affect the strategy’s expected value?

Split jackpots significantly reduce the expected value (EV) of this strategy:

The EV becomes negative if the jackpot must be shared with one or more winners, as the split reduces the return below the cost of buying all ticket combinations.

Has anyone ever attempted to buy all lottery ticket combinations?

There have been instances where groups or individuals have attempted to buy large quantities of lottery tickets, but purchasing every single combination is logistically and practically challenging. The most famous case involved an Australian syndicate in the 1990s attempting to buy all combinations in a Virginia lottery, but complete coverage is rare.

What alternatives are there to improve chances of winning the lottery without buying every combination?

Alternatives include:

Joining lottery pools to increase the number of tickets purchased collectively without significantly increasing individual investment.
Playing lotteries with better odds, even if they offer smaller jackpots.
Systematic playing, where players select a range of numbers across tickets to cover more combinations than random selection, though this doesn’t guarantee a win and still involves significant investment.

Conclusion

While theoretically possible, purchasing every lottery ticket combination to win is impractical due to the logistical challenges, the cost involved, the significant reduction in prize money due to taxes, and the risk of having to share the jackpot with other winners.

This strategy is not advisable due to the negative expected value when considering these factors.

Financially and practically, it’s not a sound investment, and the strategy becomes less feasible as the complexity and popularity of the lottery increase.