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Winning the Lottery is Almost Impossible so Why Are So Many People Still Playing?

There is a saying that the Lottery is a Tax on the Stupid but are the odds of winning really that bad?

Ever dreamed of quitting your job after winning the lottery? Maybe it's a co-worker who talks about traveling the world or an aunt who buys tickets hoping to help the family. The lottery holds a magnetic pull, a chance to break free from the ordinary and step into a world of unimaginable wealth. But have you ever wondered why, despite the odds, people still play the lottery?

This article explores deeper than just becoming rich. We'll look at the lotteries with the best odds of winning, their histories, past winners, and even Mathematics.

What Are the Odds of Winning the Lottery and Why Do People Play?

Unlike other games of chance that might involve some skill, picking lottery numbers like birthdays, anniversaries, and lucky feelings is all random. Perhaps, it's this element of randomness, the chance to win big that feeds the dream and keeps the hope of winning alive.

This universal desire for financial luck is a major reason why people worldwide play regardless. The odds of winning the lottery can be compared to a giant bucket filled with all the possible number combinations.

To win the jackpot, you need to scoop out the exact combination the lottery machine spits out of that massive bucket. No wonder the odds are crazy low. They calculate them by taking the total number of combinations and dividing it by... well, by just one.

There's a more technical way to calculate odds for different lottery prizes, it's called "combinatorial probability". You don't need to be a math expert to understand the main idea, this method uses special formulas to determine the number of winning combinations for different prizes.

Popular Lotteries Worldwide

The first public lottery in the West can be traced back to the time of Roman emperor Augustus Caesar – that's somewhere between 27 BC and 14 AD, while the first lottery with actual prize money didn't appear until much later, in 1466, held in the charming city of Bruges, Belgium.

China, on the other hand, was way ahead of the curve. They've been playing a lottery-like game called Keno for over 2,000 years. This fascination with lotteries has evolved into the multi-million dollar jackpots and sophisticated systems we see today, proving that the thrill of the chase for a life-changing win is a timeless human desire.

While lotteries worldwide may differ, I found two main categories that are most played globally:

Daily Draws- Also known as Regional Draws in other countries. These quick-play options offer a chance to win a fast cash prize, similar to picking up a lottery ticket at the gas station.

National Lotteries- are the big games, run by countries or regions, with jackpots that can dramatically alter your life like these popular games:

6/49 Lottery

Region: US, Canada, UK

Format: Players choose 6 unique numbers from a pool of 49.

Odds: 1 in 13,983,816 (generally the best odds on this list).

Jackpot: Winning the jackpot requires matching all six drawn numbers.

History of the 6/49 Lottery

The history of the 6/49 lottery began in Germany and shows changing preferences and the rise of a single dominant format. Before Germany unified, each state had its lottery. Prussia convinced others to stop competing, leading to a nationwide Prussian lottery until 1938. After World War II, regional lotteries were reintroduced, but the 6/49 format, launched in Berlin in 1952, became popular. It spread across West Germany and became the dominant format we know today.

Chance of Winning the 6/49 Lottery

Imagine picking 6 lucky numbers out of 49 and you hit the jackpot. The odds of winning the 6/49 lottery depend on how many of your selected numbers match the actual winning numbers drawn.

  • Total Ticket Combination- There are a total of 13,983,816 different combinations possible because of how many ways you can choose 6 numbers from 49.
  • Winning the Jackpot- All 6 of your chosen numbers need to match the drawn numbers exactly. There's only 1 winning combination, so the chance of winning the jackpot is meager, it's 1 in 13,983,816 (which is roughly equivalent to saying there's a 0.00007% chance).

Matching fewer numbers has corresponding prizes as well. The methods to figure out the chance of winning are similar which is to calculate the number of winning combinations possible for that prize category and divide it by the total number of tickets which is 13,983,816.

Here's an example: The chance of matching 4 out of the 6 winning numbers is approximately 1 in 1,033.


Mega Millions

Region: US

Format: Two separate pools - 5 white balls, 1-70, and 1 gold Mega Ball, 1-25.

Odds: 1 in 302,575,350 (very low probability).

Jackpot: Matching all six drawn numbers (5 white balls + Mega Ball).

History of Mega Millions

Mega Millions launched in 2002, with two jackpots won in the first few drawings, and the biggest prize ever was a whopping $1.602 billion, which was won in Florida in 2023. Mega Millions holds the record for most billion-dollar jackpots with a total of 6. The State of Michigan led the Friday the 13th luck with four jackpots won in different years.

Chances of Winning Mega Millions

Total Ticket Combinations:

T = 70Cr5 * 25C1 

  • T: Total number of Mega Millions tickets
  • 70Cr5: Combinations of choosing 5 white balls out of 70 (white balls)
  • 25C1: Combinations of choosing 1 Mega Ball out of 25 (Mega Balls)

Probability of Matching 4 White Balls (P(4 WB))

P(4 WB) = W(4 WB) / T

  • P(4 WB): Probability of winning by matching 4 white balls
  • W(4 WB): Number of winning combinations where you match 4 white balls (needs calculation)
  • T: Total number of Mega Millions tickets (from equation 1)


Calculating W(4 WB):

Although not a simple combination like the jackpot, we can estimate it for illustration. Imagine you correctly guessed 4 specific white balls. There are 66 remaining white balls you don't need to guess correctly. For the fifth white ball, you have 66 choices left. Similarly, you still need to pick the correct Mega Ball (25 options).

Therefore, in this simplified scenario, the estimated number of winning combinations for matching 4 white balls (W(4 WB)) would be:

W(4 WB) = 66 * 25 (This is an underestimate of the actual number of winning combinations)

Putting it all together:

  • We know T (total tickets) from equation 1 (around 302,575,350).
  • We have an estimated W(4 WB) (number of winning combinations for 4 white balls).

Plugging into the probability equation:

P(4 WB) = (66 * 25) / 302,575,350 (This is an underestimate of the actual probability)

This simplified calculation gives you an estimated chance of winning by matching 4 white balls. However, the actual calculation for Mega Millions prize tiers would involve more complex combinations considering order doesn't matter (e.g., you can pick ball A then B or B then A, and it's still considered 4 white balls).

This example emphasizes the concept - you calculate the specific winning combinations for a prize tier (W) and divide it by the total tickets (T) to get the odds (P) of winning that prize tier.


Region: US

Format: Similar to Mega Millions - 5 white balls (1-69) and 1 red Powerball (1-26).

Odds: 1 in 292,201,338 (extremely low probability).

Jackpot: Winning the jackpot requires matching all six drawn numbers (5 white balls + Powerball).

Powerball History

Powerball was launched in 1992 and was initially offered in just 15 states. It quickly gained popularity with its attractive jackpots. One of the first big wins came in 1993 when a Wisconsin teacher won a staggering $111 million, the first nine-figure jackpot ever awarded.

Jackpots kept climbing, with a record-breaking $1.58 billion split between three winners in 2016. But in 2022, there was a mind-blowing $2.04 billion win in California. Most recently, someone in Oregon joined the Powerball billionaire club with a $1.32 billion win in April 2024.

Chances of Winning the Powerball

Imagine two separate containers for a clearer picture of the Powerball:

  • Container 1: Holds 69 white balls, each with a unique number from 1 to 69.
  • Container 2: Holds 26 red Powerballs numbered 1 to 26.

To win the jackpot, you need to correctly guess the exact winning combination: 5 white balls drawn from Container 1 and 1 red Powerball drawn from Container 2.

Powerball Calculation

Here's a simplified explanation of how the odds are calculated for different prize tiers.

Number of Winning Combinations: Matching 4 out of 5 white balls and the Powerball is calculated by first finding the number of ways to choose 4 out of 5 white balls. This can be done using the following formula:

P(4 white + Powerball) = (C(69, 4) * C(26, 1)) / (Total Tickets)


  • P(4 white + Powerball): This represents the probability of winning by matching 4 white balls and the Powerball.
  • C(69, 4): This is the combination formula. It calculates the number of ways to choose 4 white balls out of 69 total.
  • C(26, 1): This calculates the number of ways to choose 1 Powerball out of 26 total.
  • Total Tickets: This is the total number of possible unique tickets in Powerball (292,201,338).



Region: Pan-European lottery

Odds: 1 in 139,838,160 (very low probability).

Jackpot: Winning the jackpot requires matching all 5 main numbers (1-50) and 2 Lucky Star numbers (1-12)

History of EuroMillions

EuroMillions started in 2004 and has held over 1,700 draws across Europe. There are two main combos to consider- the main and the lucky stars:

  • Main Numbers: To play EuroMillions, you must select 5 numbers out of a pool of 50.
  • Lucky Stars: Additionally, you need to select 2 numbers out of 12 as your Lucky Stars.

How to Win the EuroMillions

To calculate the odds of winning the jackpot, you can use the formula for combinations. The formula for combinations is:

C(n, r) = n! / (r! * (n - r)!)


Here's a breakdown:

C(n, r): This represents the number of combinations you can choose when selecting r items from a set of n items, where order doesn't matter.

Main Numbers:  (n = 50, r = 5)

Lucky Stars:  (n = 12, r = 2)

The formula calculates the total number of ways or combinations and not the actual odds of winning.

To get the odds, you'd need to divide the number of winning combinations (1) by the total number of possible combinations. Here's where the explanation stops and the additional calculation comes in:

Calculate the number of possible combinations for main numbers:

  • C(50, 5) = 50! / (5! * (50 - 5)!)

Calculate the number of possible combinations for lucky stars:

  • C(12, 2) = 12! / (2! * (12 - 2)!)

Multiply both to get the total number of possible combinations:

  • Total Combinations = C(50, 5) * C(12, 2)

Divide 1 (number of winning combinations) by the total combinations to get the odds of winning which is very small, around 1 in 139 million.

UK National Lottery

Region: United Kingdom

Odds: Varies by game, but roughly 1 in 45,057,474

History of the UK National Lottery

The UK government established the National Lottery in 1994 and has become a fixture in British life. The first draw took place on November 19th of that year, and proceeds from the lottery continue to support good causes across the country. The Lotto's record jackpot currently stands at a staggering £66,070,646, a life-changing sum for any lucky winner.

Calculation on How to Win the Jackpot

As mentioned earlier, the chance of winning the UK National Lottery is approximately 1 in 45,057,474. This seemingly complex number arises from considering the total number of possible combinations you can draw the 6 winning numbers from the pool of 59, divided by the number of ways to order those same numbers.

Here's the breakdown:

  • Total Combinations (without regard to order)- There are 59 possibilities from 1 to 59. For the second ball, since the first isn't replaced, there are only 58 possibilities left. This continues for all 6 balls, resulting in a multiplication of all the possibilities: 59 x 58 x 57 x 56 x 55 x 54. While it may be a large number, it represents the countless unique combinations that exist for drawing the 6 winning numbers (without considering their order).
  • Number of Ways to Order the Numbers- However, drawing 1-2-3-4-5-6 is the same scenario as drawing 6-5-4-3-2-1. Both win the jackpot. So, we need to account for the overcounting due to order. There are 6! (6 factorial) ways to order 6 distinct objects. So, in this case, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
  • Jackpot Probability- To get the actual probability, we divide the total number of combinations (without regard to order) by the number of ways to order those same numbers:

Probability (Jackpot) = Total Combinations / Number of Orderings = (59 x 58 x 57 x 56 x 55 x 54) / 720 ≈ 1 / 45,057,474

How Many Tickets Do You Need to Win the UK National Lottery according to Math


image credit: University of Manchester


A study by Drs. Stewart and Cushing and mathematicians at the University of Manchester suggest that you need 27 sets of tickets minimum to guarantee a win on the UK National Lottery's 'Lotto' game.

Using a mathematical system called finite geometry, they found that this approach ensures at least two numbers in common in one of the tickets for each of the possible draws. Despite the guarantee of a win, making a profit is unlikely as shown by a test where they matched only two balls on three tickets.

The study utilized Prolog, a programming language, for the analysis. However, it's unlikely to be a profitable win.

Lucky Lottery Winners Who Went Public

You hear about lottery winners in the news sometimes, but it's hard to get a real sense of how many there are and what happens to them after they win because of privacy and lottery anonymity rules.

However, some winners go public and proudly wave off their cash. Here are some of them:

  • Joe and Jess Thwaite (UK)- This couple won the EuroMillions jackpot of £184 million in 2022.
  • Edwin Castro (US)- Although he declined to publicly appear, he won the largest lottery prize of around $997.6 million.
  • Colin and Chris Weir (UK)- In 2011, the couple won £161 million in EuroMillions jackpot and became known for their philanthropic endeavors.
  • Adrian and Gillian Bayford (UK)- Another couple won the £148 million EuroMillions jackpot in 2012 and publicly shared their winnings with family and relatives.

Did Anyone Win the Lottery Twice or More?

Stefan Mandel, a Romanian economist with a gambler's spirit, defied the odds by winning the lottery not once, but a staggering 14 times. His secret? Not luck, but Math. He identified a loophole in lotteries with smaller number pools.

He devised a method called combinatorial condensation. This reduces the number of tickets to win.

Mandel tested his strategy in Romania, winning enough to flee. In Australia, he targeted lotteries where the jackpot was more than the cost of buying all tickets. He convinced people to invest and built a machine to pick and print tickets.

His biggest win involved printing millions of tickets (almost all possible combinations) for a Virginia lottery in February 1992 with a jackpot of $27,036,142 and having them processed at stores. He won the jackpot despite some tickets missing, making headlines.

Lottery officials saw this as cheating the system and launched investigations. Though no wrongdoing was found, Mandel faced backlash from some investors and new lottery laws prevented similar tactics.

Mandel made a profit but some investors felt shortchanged. He eventually declared bankruptcy and faced legal troubles for later investment schemes. Today, he lives a quiet life on a remote island.

Maybe It's Not About Winning, But the Dream

Lotteries are a big deal around the world! People love to play, and it's not just about becoming a millionaire. The exciting chance of winning big money and making dreams come true keeps many people buying tickets, even though the odds are very low.

The future looks bright for lotteries as they transition into the digital arena and make it easier to play from anywhere in the world. In the end, whether lotteries stay popular or not might depend on how well they change with the times and how people choose to spend their money on games of chance.

If you're thinking about playing lotteries online, remember to play responsibly. We at GameChampions only recommend safe and legal lottery sites, so if you do choose to play, you can be sure you're doing so safely.

About the author

Angel Cabal

Ex-soccer player for Real Oviedo Football Club and long-time casino enthusiast with a profound understanding of the iGaming industry. I'm constantly on the lookout for the latest bonuses, leveraging my 10+ years of expertise to maximize your gambling returns.