United States Lottery Games: Odds, Analysis, and Comparisons

Last updated on April 7, 2024

United States lottery games are a staple of the gaming industry and American culture, offering a mix of traditional draws, instant-win scratch cards, and innovative multi-state games that captivate millions of participants each week.

This article will explore lottery games throughout the United States, highlighting major mathematical calculations crucial for decision-making.

In this list, we deliberately exclude keno-style games, instant scratch-offs, and any draw games involving ten or fewer numbers. We want to concentrate on traditional lottery draw games for a more meaningful comparison.

Important Metrics To Compare United States Lottery Games

When comparing lottery games to make an informed decision, it’s crucial to consider a variety of metrics. These metrics provide insight into each game’s potential benefits and drawbacks, enabling you to weigh your options based on what matters most.

Here are some metrics you might consider when choosing a lottery game.

• Probability of winning – This figure is crucial for understanding the odds of winning the lottery. Since there’s only one way to win the jackpot, we calculate this metric using the expression P = ¹/n, where n is the total number of combinations. This metric helps players understand the scale of the odds against them. The higher the number of combinations, the lower the probability of winning because more possible outcomes could occur. We use the combination formula to calculate the total number of combinations in a game.¹
• Overall odds – This metric gives you an idea of how likely you are to win something, not necessarily the top prize, but any prize the game offers. For example, if a lottery game has an overall odds of 1 in 9, it means that, on average, there is one winning ticket for every nine tickets you purchase. This information is typically available in the Odds and Prizes table on each game’s official website.
• 50/50 chance – This is the number of tickets needed to achieve a 50/50 chance of winning. Again, it does not necessarily mean the top prize, but it means any prize. ²
• Expected Value – It is crucial to understand that lottery games are not created equally. The expected value of a ticket gives an idea of the average amount of money you can expect to win (or lose) per ticket purchased, considering the probability of winning various prizes. This article only considers the top prize for simplicity, ignoring smaller prizes and the effect of jackpot sharing among multiple winners. We don’t need to review all the odds and prizes to illustrate how lottery odds work.
• Minimum prize – Most lottery games start with a minimum and increase until someone wins. We will use the minimum prize to calculate important metrics such as expected value and cost-to-prize ratio, but it’s worth noting that as the top prize increases, the EV improves.
• Cost per ticket – This information can be useful for comparing the cost of the ticket relative to the potential jackpot prize. It gives a glance at the “bang for your buck.” For example, New Jersey Pick 6 cost $2 per ticket. With a prize that starts at $2 million and grows until someone wins, the cost-to-prize ratio is $2 to $2 million. The ratio means that for every $2 spent on a ticket, you are entering for a chance to win a jackpot prize of $2 million.

Based on the above factors, we aim to compare and organize the list of lottery games in the United States into various categories to guide you in selecting the game that best suits your risk preferences.

How to Choose the Best Lottery Games?

Choosing a lottery game based on your risk preference involves understanding different metrics that align with your comfort with risk and the desired level of potential reward.

For example, to compare Virginia’s Bank a Million and Mega Millions games in an informed way, we can look at the odds of winning the jackpot and the expected value of a ticket. Depending on your priorities, these metrics can help evaluate which game might offer better relative value or a higher chance of winning.

Besides the expected value, you might also consider looking at the overall odds and the number of tickets to achieve a 50/50 chance of winning.

^* Let me remind you that our EV calculation is unusual; we use only the starting top prize for simplicity.

EV_(jackpot) = (P×J)−C

Where:

EV represents the Expected Value,
P is the Probability of winning the jackpot,
J is the Jackpot value,
C is the Cost of the ticket.

This EV calculation is enough to provide hints of average return (or loss) for a particular outcome. In this case, we are calculating the EV for winning the jackpot. For this particular analysis, we ignore other prize tiers, taxes, the possibility of jackpot sharing, and the non-monetary value you might place on the excitement of playing for larger jackpots.

Positive Expected Value (+EV): Imagine you have a lottery game where, on average, you get more money back than you put in every time you play. If the game costs $1 to play, and you get $1.20 back on average, you’re in a good game. This situation is what we call having a positive EV.

Negative Expected Value (-EV): On the flip side, suppose there’s another game where, even though you might win sometimes, you lose more money than you win in the long run. Let’s say it also costs $1 to play, but you only get back 80 cents on average this time. Playing this game means you’re slowly but surely losing money. This situation has a “Negative EV.” It’s akin to a leaking bucket where, no matter how much water (or money) you put in, you end up with less because it keeps leaking out.³

Positive EV means you’re on a path to gain more than you lose over time, making buying a lotto ticket desirable. Negative EV means you’re likely to lose more than you gain if you keep playing the lotto, making it something you might want to avoid if you want to come out financially.

All lottery games are generally designed to have a negative expected value. ⁴ The lower the value, the less favorable the game is for the player, indicating a greater average loss per ticket purchased.

^**The calculation of overall odds greatly depends on the odds and prizes each game offers. Normally, a lottery game that offers more ways to win improves the game’s overall odds, allowing players to win any prize by buying fewer tickets.

^***This 50/50 chance does not necessarily indicate winning the jackpot. It could be any prize from the top down to the lowest tier. For example, in Mega Millions, the probability that a single ticket is not a prizewinner is 0.9583. If you buy more tickets, the probability of losing with n number of tickets is this number raised to the nth power.

P_(losing) = 0.9583^{Number of tickets}

So, if we calculate 0.958317 and subtract the result from 1, the probability of winning any prize is higher than 50%.

P_{(50-50 chance of winning any prize)} = 1 – 0.9583¹⁷ = 0.5152

However, winning the lowest-tier prize is more likely because the probability does not favor the jackpot.

Notice how Virginia’s Bank a Million beats the Mega Millions in this department.

Decision Factors

Based on the table above that compares Bank a Million and Mega Millions, here are the factors you might want to consider.

• If you prioritize better odds of winning the jackpot over the size of the jackpot, Bank a Million is more attractive.
• If you seek a more favorable expected value per ticket, Bank a Million appears more favorable. Aiming for a lower value would be best, which signifies a reduced average loss per ticket.
• If the size of the prize is the most important factor, despite the significantly lower odds, Mega Millions might be more appealing due to its larger jackpot.
• If you’re thinking of buying lottery tickets, you might want to consider Bank a Million over Mega Millions. To have a 50/50 chance of winning any prize in Mega Millions, you need to purchase 17 tickets. On the other hand, Bank a Million only requires 12 tickets for the same chance. So, if you want to maximize your chances of winning, Bank a Million is the clear winner.

Now, without further ado, we would like to present a list of United States lottery games that offer different perspectives on lottery gaming.

If you’re ready, let’s dive into the list.

United States Lottery Games with Better Odds of Winning Than Being Killed by a Shark

The World Animal Foundation states that the odds of being killed in a shark attack are 1 in 4,332,817.⁵ Below are lottery games in the United States that give you more favorable odds of winning than being killed by a shark. The data is listed in order of probability, starting with the easiest.

Top United States Lottery Games According to Overall Odds

The probability of winning is an important factor. But it’s also crucial to understand the probability of losing. The following games below offer less probability of losing, which means you have more opportunity to win any prize with fewer tickets.

The overall odds column indicates the average number of tickets you must buy if you expect one ticket to win a prize.

Notice how Tri-State Megabucks and Hoosier Lotto stand out compared to other lottery games based on the prizes they offer.

For example, the probability that a single ticket will not win a prize in Idaho Cash is 0.8246. Therefore, you must buy four tickets for a 50/50 chance of winning any prize.

P_{(winning any prize)} = 1 – 0.8246^{4 tickets} = 0.54

Idaho Cash offers a jackpot prize that starts at $20,000 and increases each draw until it’s won. Comparatively, buying four tickets for Tri-State Megabucks and Hoosier Lotto will give you the same 50/50 chance of winning any prize, and both games offer a prize that starts at $1 million and grows until someone wins.

The following lottery games below give you a 50/50 chance of winning any prize by buying five tickets.

Based on the table above, the Illinois Lotto and Lotto America stand out as they offer prizes beyond $1 million. Note that with Extra Shot, you can improve your overall odds of winning any prize in Illinois Lotto to 1 in 5.38.

However, be mindful that winning the jackpot in Illinois Lotto and Lotto America proves to be very difficult. With a probability of 1 in 15,890,700 for Illinois Lotto and 1 in 25,989,600 for Lotto America, you might consider Hoosier Lotto and the Tri-State Megabucks as better games.

Lottery Games Requiring Players to Match an Extra Number

An extra number is a great idea for playing a lottery game as this provides extra prize tiers, so players have more ways to win.

However, an extra number is a tricky one.⁶

And here’s why.

You can play a lottery game with an extra number in two ways: either the extra number is drawn from the same drum as the primary balls or a separate drum.

The most difficult lottery games require picking an extra number from a separate drum. Examples of these games are the Powerball and the Mega Millions.

So, an extra number drawn from a separate drum is designed to trick you into believing that your overall odds of winning improve significantly. The reality is that the probability of winning the jackpot becomes increasingly impossible.

Luckily, not all games are created equally.

Virginia’s Bank a Million offers more ways to win with bonus numbers, yet your probability of winning the jackpot doesn’t change. This is possible because Bank a Million draws the bonus number from the same drum as the primary number.

Players of Bank a Million pick six numbers from 40 and enjoy significant improvement in the overall odds of winning any prize without changing the probability of winning the jackpot.

Interestingly, an extra number is not the only way a lottery game provides more ways to win. For example, Oregon’s Win for Life offers 46 ways to win. At $2 per game, you are entering a chance to win $1,000 a week for life with a 1 in 1,353,275 probability and overall odds of 1 in 4.63.

The table below shows lottery games in the United States that require lotto players to match an extra ball to win the top prize.

Multi-State Lottery Games

Cash4Life (5 from 1-60 + 1 from 1-4)

Lotto America (5 from 1-52 + 1 from 1-10)

Lucky for Life (5 from 1-48 + 1 from 1-18)

Gimme 5 (5 from 1-39)

Tri-State Megabucks (5 from 1-41 + 1 from 1-6)

Powerball (5 from 1-69 + 1 from 1-26)

Mega Millions (5 from 1-70 + 1 from 1-25)

State-Specific Lottery Games

The following list features unique lottery games offered by each state. Many of these states participate in multi-state lottery games, so there’s no need to repeat the data for the above games. We will include only the unique and specific games for each state.

We excluded the Expected Value (EV) calculation in this list because the jackpot prize increases over time. Additionally, we omitted the cost per game, as these figures can change.

Since all lottery games have negative expected values, we deem it more relevant to base your decisions on the probability of winning the jackpot and other lesser-known factors, such as overall odds and the number of tickets needed to get a 50/50 chance of winning any prize.

Check out the complete list below.

Arizona

Fantasy 5 (5 from 1 to 41)

The Pick (6 from 1 to 44)

Arkansas

Arkansas Lotto (6 from 1 to 40)

Natural State Jackpot (5 from 1 to 39)

California

Fantasy 5 (5 from 1-39)

SuperLotto Plus (5 from 1-47 + 1 from 1-27)

Colorado

Cash 5 (5 from 1-32)

Colorado Lotto+ (6 from 1-40)

Connecticut

Cash5 (5 from 1-35)

Lotto! (6 from 1-44)

Delaware

Multi-Win Lotto (6 from 1-35)

District of Columbia

District of Columbia doesn’t have its own lottery game. It participates in multi-state games such as Lucky for Life, Mega Millions, and Powerball. Official page: https://dclottery.com/

Florida

Fantasy 5 Midday/Evening (5 from 1-36)

Florida Lotto (6 from 1-53)

Jackpot Triple Play (6 from 1-46)

Georgia

Fantasy 5 (5 from 1-42)

Jumbo Bucks Lotto (6 from 1-47)

Idaho

5 Star Draw (5 from 1-45)

Idaho Cash (5 from 1-45)

Weekly Grand (5 from 1-32)

Illinois

Illinois Lotto (6 from 1-50)

Lucky Day Lotto Midday/Evening (5 from 1-45)

Indiana

Ca$h 5 (5 from 1-45)

Hoosier Lotto (6 from 1-46)

Iowa

Iowa doesn’t have its own lottery game. It participates in multi-state games such as Lotto America, Lucky for Life, Mega Millions, and Powerball. Learn more

Kansas

Super Kansas Cash (5 from 1-32 + 1 from 1-25)

Kentucky

Cash Ball 225 (4 from 1-35 + 1 from 1-25)

Kentucky 5 (5 from 1-39)

Louisiana

Easy 5 (5 from 1-37)

Louisiana Lotto (6 from 1-42)

Maine

Maine participates in all six multi-state lottery games, including Gimme 5, Lotto America, Lucky for Life, Mega Millions, Powerball, and Tri-State Megabucks. Learn more

Maryland

Bonus Match 5 (5 from 1-39)

Multi-Match (6 from 1-43)

Massachusetts

Massachusetts participates in four multi-state lottery games, including Lotto America, Lucky for Life, Mega Millions, and Powerball. Learn more

Michigan

Fantasy 5 (5 from 1-39)

Lotto 47 (6 from 1-47)

Minnesota

Gopher 5 (5 from 1-47)

North 5 (5 from 1-31)

Mississippi

Match 5 (5 from 1-35)

Missouri

Missouri Lotto (6 from 1-44 (2x))

Show Me Cash (5 from 1-39)

Montana

Big Sky Bonus (4 from 1-31 + 1 from 1-16)

Montana Cash (5 from 1-45)

Nebraska

Pick 5 (5 from 1-40)

New Hampshire

New Hampshire participates in multi-state games such as Gimme 5, Lucky for Life, Mega Millions, Powerball, and Tri-State Megabucks. Learn more

New Jersey

Jersey Cash 5 (5 from 1-45)

Pick-6 (6 from 1-46)

New Mexico

Roadrunner Cash (5 from 1-37)

New York

New York Lotto (6 from 1-59)

Take 5 Midday/Evening (5 from 1-39)

North Carolina

Cash 5 (5 from 1-43)

North Dakota

North Dakota is a participant in Lotto America, Lucky for Life, Mega Millions, and Powerball. Learn more

Ohio

Classic Lotto (6 from 1-49)

Rolling Cash 5 (5 from 1-39)

Oklahoma

Cash 5 (5 from 1-36)

Oregon

Lucky Lines (8 from 1-32)

Oregon’s Game Megabucks (6 from 1-48)

Win for Life (4 from 1-77)

Pennsylvania

Cash 5 (5 from 1-43)

Match 6 (6 from 1-49)

Treasure Hunt (5 from 1-30)

Puerto Rico

Loto Cash (5 from 1–35 + 1 from 1–10)

Revanchax2 (5 from 1–35 + 1 from 1–10)

Rhode Island

Wild Money (5 from 1-38)

South Carolina

Palmetto Cash 5 (5 from 1-38)

South Dakota

Dakota Cash (5 from 1-35)

Tennessee

Daily Tennessee Jackpot (5 from 1–38)

Tennessee Cash (5 from 1-35 + 1 from 1-5)

Texas

Cash Five (5 from 1-35)

Lotto Texas (6 from 1-54)

Texas Two Step (4 from 1-35 + 1 from 1-35)

Vermont

Vermont participates in multi-state lottery games, including Gimme 5, Lucky for Life, Mega Millions, Powerball, and Tri-State Megabucks. Learn more

Virginia

Bank a Million (6 from 1-40)

Cash 5 (5 from 1-45)

Washington

Hit 5 (5 from 1-42)

Washington Lotto (6 from 1-49 two tickets)

Match 4 (4 from 1-24)

West Virginia

Cash 25 (6 from 1-25)

Wisconsin

Badger 5 (5 from 1-31)

Megabucks (6 from 1-49)

SuperCash! (6 from 1-39)

Wyoming

Cowboy Draw (5 from 1–45)

What are the Best United States Lottery Games For You?

From the list above, notice how Colorado Lotto+ and Virginia’s Bank a Million stand out in winning odds compared to other lottery games offering the same prizes.

Comparing Colorado Lotto+ with Virginia’s Bank a Million, it becomes clear that the latter is preferable. Not only does it offer a substantial prize, but it also covers the tax on winnings. Furthermore, Bank a Million presents more favorable odds of winning, with a 1 in 18.3 chance compared to Colorado Lotto+’s 1 in 30. Hence, Bank a Million stands out as the superior choice.

When comparing Bank a Million with Powerball, it’s evident that Powerball offers a larger jackpot. However, from another perspective, both Powerball’s second and Bank a Million’s top prizes are valued at 1 million dollars. Despite this similarity, the odds of winning differ significantly. Winning 1 million in Bank a Million is more likely, with odds of 1 in 3,838,380, compared to the more challenging odds of 1 in 11,688,053.52 for Powerball.

Many United States lottery games have prizes that continue to grow until someone wins. When choosing a lottery game, it’s crucial to consider the prize and the odds of winning.

Also worth mentioning are lottery games that offer big prizes yet allow you to win any prize with fewer tickets. Among the list are Hoosier Lotto and the Tri-State Megabucks. With four tickets, you are entering a chance to win any prize, including the jackpot prize of $1 million.

However, be careful when choosing a lottery game with improved overall odds, as this can be tricky.

For example, in the Illinois Lotto, buying five tickets gives you a 50/50 chance to win something. For Lotto America, you need seven tickets for the same odds. But winning the jackpot in both games proves to be very difficult. The chances are 1 in 15,890,700 for Illinois Lotto and 1 in 25,989,600 for Lotto America. This information shows Hoosier Lotto and Tri-State Megabucks are better lottery games.

Additional Resources

1. Combinations in Probability | Equation, Formula & Calculation    [↩]
2. How to Achieve a 50/50 Chance of Winning the Lottery    [↩]
3. The Truth About Winning Small Prizes in the Lottery    [↩]
4. Expected Value in Lotteries: Exposing Its Significance and Impact    [↩]
5. Shark Attack Statistics & Trends in 2024: What the Latest Data Reveals?    [↩]
6. How to Handle the Tricky Extra Ball    [↩]