What are the chances of winning the lottery?
A definitive guide, written with help from a mathematics professor.
⏰ 10 Minute Read
The odds of winning
Frequently Asked Questions
– Section 1 –
Have you ever wondered what the chances are of winning the lottery? Most often winning the lottery means winning the highest-tier prize in the lottery, the Jackpot. Some lotteries are so big that even winning the second-tier cash prize money could be a life-changing sum. For example, in the US Mega Millions, where the second tier prize is a cool $1,000,000. When players choose the Megaplier option, it can go up even further to $5,000,000!
The chances of holding the winning ticket depend on the size of the lottery. In general, the bigger the lottery, the bigger the top-tier prizes, the lottery jackpot, and the lottery winnings. There are exceptions and variations though.
The size of a jackpot depends on the rules of the lottery. For example, it depends on what part of the money pool is for the top-tier prize. It could also depend on other rules of the lottery, say, on whether the jackpot has rollovers. A rollover happens when the jackpot fund is not won in one or more consecutive draws. When the jackpot rolls over, the money transfers to the designated fund for the next draw. When this happens, a smaller lottery can develop the biggest lottery jackpot fund.
Some lotteries finance big future draws by allocating a small percentage of each prize fund from their regular draws. For example, Superdraws and Megadraws in the Australian Lotto.
In the following article, you will learn a lot more about the different types of lotteries. You will gain insight into the different ways of forming the top prize and how difficult it is to win the top prize. You will learn what affects the chances of winning a big prize and expert playing strategies.
At the end of the article, you will find the answers to frequently asked lottery questions.
Definitions you need to know before reading the rest of this article
– Section 2 –
The chances of winning the lottery depend on a lot of factors. Before we start looking at these in detail, it is important to offer some definitions:
1) Winning a lottery game
This means winning the highest-tier prize, or the jackpot.
2) Odds of winning a lottery game
This is the probability of winning the jackpot expressed as odds.
The odds of winning a lottery game usually given as 1 in N, where N is the number of all possible draws in the lottery. The number of all possible draws in the lottery – this depends on the type of lottery and is computed using a formula.
3) The type of the lottery
This defines the number of balls in the draw and the total number of balls used.
- If there are 5 balls drawn, then the lottery is a pick-5.
- If there are 6 balls drawn, then the lottery is pick-6.
- If the lottery has 35 balls, and 5 balls are drawn, we refer to it as being a 5/35 lottery.
Some lotteries also have bonus balls. These are drawn to determine extra tiers of prizes. Bonus balls/numbers can be drawn from the same set as the balls/numbers in the main draw, or from a different set. If the latter, then winning the jackpot requires hitting one or both bonus balls.
Here we focus only on simple lotteries. These are indicated as m/n, where m is the number of balls in the draw, and n is the number of all balls. For example, a 6/49 lottery would be one where 6 balls are drawn out of a set of 49, and that is what forms the (main) draw.
There is a math formula for computing the odds of winning the jackpot in a simple lottery. For lotteries that require players to match exactly all the drawn numbers, the odds in an m/n lottery are 1 in C(n,m).
The table below in the next section shows how the odds change between lotteries of different types and sizes.
Which lottery Is the hardest to win?
The type of lottery (from the table on this page) with the worst chances of winning is 20/90. The odds of winning this type of lottery are the staggering 1 in 50,980,740,277,700,939,310.
Which lottery has better odds of winning?
The type of lottery (from the table on this page) with the best chances of winning is the 10/20 lottery. The odds of winning it are 1 in 184,756.
The odds of winning the lottery
Compare the odds of winning almost any type of lottery available.
– Section 3 –
The table below ranks different types of lotteries. The lotteries are arranged in order by the odds of winning. The odds of all lotteries in this table have been verified by lottery expert Dr. Iliya Bluskov. He is a former Mathematics professor, a researcher in Combinatorics, and the author of lotto strategies books. You can use the table to find out the chances of winning online lottery games.
|Lottery Type||Odds of Winning a Jackpot|
|10/20||1 in 184,756|
|5/35||1 in 324,632|
|5/40||1 in 658,008|
|5/49||1 in 1,906,884|
|5/50||1 in 2,118,760|
|6/42||1 in 5,245,786|
|7/34||1 in 5,379,616|
|7/35||1 in 6,724,520|
|6/45||1 in 8,145,060|
|7/36||1 in 8,347,680|
|6/47||1 in 10,737,573|
|5/69||1 in 11,238,513|
|5/70||1 in 12,103,014|
|6/48||1 in 12,271,512|
|6/49||1 in 13,983,816|
|7/39||1 in 15,380,937|
|5/90||1 in 43,949,268|
|6/59||1 in 45,057,474|
|7/47||1 in 62,891,499|
|6/90||1 in 622,614,630|
|20/62||1 in 9,206,478,467,454,345|
|20/70||1 in 161,884,603,662,657,876|
|20/80||1 in 3,535,316,142,212,174,320|
|20/90||1 in 50,980,740,277,700,939,310|
A 5 35 loto is a lottery where 5 numbers are drawn from a total of 35 balls.
What is the chance of winning a 5/35 lottery?
The odds of winning a 5-number, 35-ball lottery is 1 in 324,632.
A 5 40 loto is a lottery where 5 numbers are drawn from a total of 40 balls.
What is the chance of winning a 5/40 lottery?
The odds of winning a 5-number, 40-ball lottery is 1 in 658,008.
A 5 49 loto is a lottery where 5 numbers are drawn from a total of 49 balls.
What is the chance of winning a 5/49 lottery?
The odds of winning a 5-number, 49-ball lottery is 1 in 1,906,884.
A 5 50 loto is a lottery where 5 numbers are drawn from a total of 50 balls.
What is the chance of winning a 5/50 lottery?
The odds of winning a 5-number, 50-ball lottery is 1 in 2,118,760.
A 5 69 loto is a lottery where 5 numbers are drawn from a total of 69 balls.
What is the chance of winning a 5/69 lottery?
The odds of winning a 5-number, 69-ball lottery is 1 in 11,238,513.
A 5 70 loto is a lottery where 5 numbers are drawn from a total of 70 balls.
What is the chance of winning a 5/70 lottery?
The odds of winning a 5-number, 70-ball lottery is 1 in 12,103,014.
A 5 90 loto is a lottery where 5 numbers are drawn from a total of 90 balls.
What is the chance of winning a 5/90 lottery?
The odds of winning a 5-number, 90-ball lottery is 1 in 43,949,268.
A 6 42 loto is a lottery where 6 numbers are drawn from a total of 42 balls.
What is the chance of winning a 6/42 lottery?
The odds of winning a 6-number, 42-ball lottery is 1 in 5,245,786.
A 6 45 loto is a lottery where 6 numbers are drawn from a total of 45 balls.
What is the chance of winning a 6/45 lottery?
The odds of winning a 6-number, 45-ball lottery is 1 in 8,145,060.
A 6 47 loto is a lottery where 6 numbers are drawn from a total of 47 balls.
What is the chance of winning a 6/47 lottery?
The odds of winning a 6-number, 47-ball lottery is 1 in 10,737,573.
A 6 48 loto is a lottery where 6 numbers are drawn from a total of 48 balls.
What is the chance of winning a 6/48 lottery?
The odds of winning a 6-number, 48-ball lottery is 1 in 12,271,512.
A 6 49 loto is a lottery where 6 numbers are drawn from a total of 49 balls.
What is the chance of winning a 6/49 lottery?
The odds of winning a 6-number, 49-ball lottery is 1 in 13,983,816.
A 6 59 loto is a lottery where 6 numbers are drawn from a total of 59 balls.
What is the chance of winning a 6/59 lottery?
The odds of winning a 6-number, 59-ball lottery is 1 in 45,057,474.
A 6 90 loto is a lottery where 6 numbers are drawn from a total of 90 balls.
What is the chance of winning a 6/90 lottery?
The odds of winning a 6-number, 90-ball lottery is 1 in 622,614,630.
A 7 34 loto is a lottery where 7 numbers are drawn from a total of 34 balls.
What is the chance of winning a 7/34 lottery?
The odds of winning a 7-number, 34-ball lottery is 1 in 5,379,616.
A 7 35 loto is a lottery where 7 numbers are drawn from a total of 35 balls.
What is the chance of winning a 7/35 lottery?
The odds of winning a 7-number, 35-ball lottery is 1 in 6,724,520.
A 7 36 loto is a lottery where 7 numbers are drawn from a total of 36 balls.
What is the chance of winning a 7/36 lottery?
The odds of winning a 7-number, 36-ball lottery is 1 in 8,347,680.
A 7 39 loto is a lottery where 7 numbers are drawn from a total of 39 balls.
What is the chance of winning a 7/39 lottery?
The odds of winning a 7-number, 39-ball lottery is 1 in 15,380,937.
A 7 47 loto is a lottery where 7 numbers are drawn from a total of 47 balls.
What is the chance of winning a 7/47 lottery?
The odds of winning a 7-number, 47-ball lottery is 1 in 62,891,499.
A 10 20 loto is a lottery where 10 numbers are drawn from a total of 20 balls.
What is the chance of winning a 10/20 lottery?
The odds of winning a 10-number, 20-ball lottery is 1 in 184,756.
A 20 62 loto is a lottery where 20 numbers are drawn from a total of 62 balls.
What is the chance of winning a 20/62 lottery?
The odds of winning a 20-number, 62-ball lottery is 1 in 9,206,478,467,454,345.
A 20 70 loto is a lottery where 20 numbers are drawn from a total of 70 balls.
What is the chance of winning a 20/70 lottery?
The odds of winning a 20-number, 70-ball lottery is 1 in 161,884,603,662,657,876.
A 20 80 loto is a lottery where 20 numbers are drawn from a total of 80 balls.
What is the chance of winning a 20/80 lottery?
The odds of winning a 20-number, 80-ball lottery is 1 in 3,535,316,142,212,174,320.
A 20 90 loto is a lottery where 20 numbers are drawn from a total of 90 balls.
What is the chance of winning a 20/90 lottery?
The odds of winning a 20-number, 90-ball lottery is 1 in 50,980,740,277,700,939,310.
– Section 4 –
This FAQ section has comprehensive answers to the most frequently asked questions about the odds of winning the lottery.
The odds of winning the lottery are different for each type of lottery and depend on the number of balls drawn and on the total number of balls used in it. If one plays the same lottery and the lottery does not change its rules, such as the total number of balls in the lottery and the possible numbers of balls drawn, then the odds of winning the top prize remain the same. The payoff might vary though. Some lotteries have a fixed amount top tier prize; others have a varying amount Jackpot, say due to rollovers. In any case, winning the Jackpot is a life changing event. However, the odds of winning the lottery differ between different lotteries, and are always determined by the total number of balls used and the number of balls drawn.
There is one sure way to increase your odds of winning the lottery, or the chances of hitting a jackpot. That is to play more tickets than just one. For example, the odds of winning a jackpot in Lotto 6/45 are 1 in 8,145,060. Playing 10 different tickets would improve the odds to 1 in 814,506. If you further increased the number of tickets, it would further improve the odds. For a 6/56 lottery, playing 8,145,060 different tickets will cover all possible draws. This will guarantee you the jackpot (and a large number of lower-tier prizes). This leads us to a related question, which has something to do with the size of the top prize, or the jackpot. If the jackpot is large, then it makes sense to aim for a part of it by being a member of a lottery syndicate. A syndicate can buy a much bigger number of tickets than an individual player. This improves further the odds of a big win. Keep reading for more information about playing in a lottery syndicate.
The odds of winning the lottery using the same numbers are the same as the odds of winning the lottery using different numbers every time you play. This is the case if all the other conditions of playing are the same. In other words, if you play the same numbers in a draw or the same set of tickets and numbers in every draw you play, your result would be comparable to the results of a player who plays the exact same draws, with the same number of tickets as you, but uses different numbers every time. The reason is that the odds of winning the jackpot for every particular lottery ticket are the same. These are the odds of winning the lottery, and they do not change from draw to draw. In addition, what happens in a previous draw does not affect what will happen in the next draw. This assumes that the lottery is unbiased; which to a great extent is the case nowadays.
Some people believe that the chances of winning the lottery are much worse than the chances of being struck by lightning. This is a myth that is easily debunked. People who don't enjoy playing the lottery say, "You are more likely to get struck by lightning than win the lottery.". It is just a way of telling you: "You should not be playing either..." Well, let us see how much truth is there in such a comparison.
It is certainly easier to win the lottery than to die from being struck by lightning. In fact, it is actually easier to win the lottery than to be struck by lightning. Of course, we should keep in mind that there are over 600 lotteries in the world. The odds of these lotteries vary wildly from very low to very high. So, it might be true for some of the most difficult-to-win lotteries. In general, there is a better chance to win the lottery.
The statistics for people struck by lightning are collected over an entire year. Lottery draws happen many times every week and some lotteries have draws every day. So to compare the chances we should first answer some questions on what we are comparing. Do we focus on one particular lottery, or on one particular country, or a state, or, perhaps an online lottery? If so, which country, which state, which lottery? We might choose a lottery with very good odds in a country where lightning storms are very rare. In which case it will be a very easy comparison in favour of winning the lottery. We must also consider the lottery player. Do they stay at home and avoid risks or do they like adventure and the outdoors?
For this argument, lets look at the USA. There is lots of real data to use. The USA has many lotteries. It is also a place with many storms and reliable storm and casualty monitoring. The USA has a large population, so it is a sufficiently big sample of data.
According to the National Weather Service, there are 270 lightning victims per year. This is data taken over the period 2009 - 2018. The average number of fatalities is 27 per year and the number of injuries is 243 per year.
1600 new lottery millionaires are created each year. This is According to the TLC TV show “The Lottery Changed My Life".
In 1996, 1,136 people won a million dollars or more from a US lottery. This statistic appeared in an article by Duane Burke. It is from the North American Association of State and Provincial Lotteries.
This shows that there are over a thousand lottery winners of a million or more each year. During the same time, there are 270 victims of lightning. This is in a country with a population of approximately 330,000,000.
This comparison shows that winning the lottery is much easier.
There are other, quite essential differences between being struck by lightning and winning the lottery. One is a highly desirable event, the other is to be avoided at all costs. To be fair to the supporters of the myth though, we can finish this lightning argument with a comment from a reader of Burke's article. "The truth is: There are way less people trying to be struck by lightning (than those trying to win a Jackpot). If you were really trying, your odds are pretty good!"
The chances of winning the lottery are better if you play every than if you only play once a week. for the same amount. Of course, it also matters how much money you play and for how long.
Lottery Tip: If you play more than one lottery ticket each day, your lottery odds will be further improved. The odds will be reduced by a factor equal to the number of tickets you play, as long as all the tickets are different.
For illustration, let's consider a 5/35 lottery over a period of one year. We will assume the lottery has a draw every day, and you play one single ticket per draw. Let us see how the different odds of winning change with any new day of play you add.
Your odds of winning this lottery are 1 in 324,632, and these are your odds of winning it on the first day you play. Playing two days will reduce (improve) your odds of winning the lottery to 1 in (324,632)/2 or 1 in 162,316. Playing three days will further reduce the odds of winning the lottery to 1 in (324,632)/3 or 1 in 108,210.7. After N days of playing (if N is not too big) your odds of winning the lottery would be 1 in (324,632)/N.
After one year of playing, you would have played 365 tickets. Your odds of winning the lottery over one year of playing every day would be 1 in (324,632)/365 or 1 in 889.4. which already looks much better than the odds of winning the lottery by playing one ticket at one time.
These computations provide very close approximation to the exact lottery odds. At least when the number of draws is small in comparison to the number of all possible draws. 365 is still small in comparison to 324,632. Computing the exact odds requires more sophisticated maths. The precise odds for winning the 5/35 in 365 days of playing are 1 in 889.9. You can see that this number is only slightly different from the one we computed by the simple approximation formula.
A hint that the approximation formula may not be good over a large number of draws is the fact that after playing 324,632 draws your odds of winning the lottery are still not the certain 1 in 1, or 1 in (324,632)/(324,632); the reason, well, being unlucky... The odds of winning the lottery are the same if instead of one player playing 324,632 draws we have one draw in which 324,632 players played one random ticket. This is close to what might happen in a real draw. There could be many pairs, and triples, etc. of players who chose the same common numbers. As a result of the overlapping numbers, the draw can produce no winner. This is why rollovers happen most of the time. Even if the number of tickets sold is larger than the number of all possible draws in the lottery. Rollovers are more likely when the number of tickets sold is less than the number of possible draws.
The chances of someone winning the lottery if exactly 324,632 random tickets were sold are 63.21%. This is due to the above-mentioned overlapping which happens under random choices. Each player who bought a ticket knows their numbers but does not know what the other players chose to play. For this reason, repetitions are quite possible. The chances of 63.21% are less than 100%, but not that bad. Note that the chances would easily change if the tickets are not chosen randomly.
If one lottery player buys 324,632 tickets corresponding to all possible draws, then their chances of winning the lottery are 100%. This is because one of their tickets must contain the drawn numbers. But, "Buying the lottery" is very expensive. Also, winning a jackpot is not a guarantee of a profitable venture. This is because there is the possibility of splitting the jackpot fund if there is more than one winner.
If you are interested in further improving your odds of winning a jackpot, you could check what happens if you play not one but two different tickets. Your odds will be further improved by a factor of two. If you play three tickets, your odds will be improved by a factor of 3. For example, if you play five tickets per draw, your odds of winning the lottery over one year of playing would become 1 in (889.4)/5 or 1 in 177.88. These are quite decent odds compared to the odds of winning the lottery with one ticket. Of course, you have to put more money into your playing over the year.
The odds of winning could be further improved by becoming a part of a syndicate play or by playing for more than a year.
The chances of winning the lottery if you play every week are better than a player who plays once a month. But, they are definitely worse than the chances of a player who plays the same amount as you but plays every day. The same considerations are in place as in the previous FAQ question. In a 5/35 lottery game, the odds of winning for any particular week of playing are 1 in 324,632. If you play for two weeks, then your odds are reduced to 1 in 162,316. If you play for three weeks the odds are reduced to 1 in 108,210.7. Playing this way for one year gives you odds 1 in (324,632)/52 or 1 in 6242.9 of winning the lottery. These odds are just a very close approximation to the real odds. The precise odds require more complicated mathematics.
We mentioned that the amount you play also matters. Playing $20 a week gives a better chance of winning the lottery than playing $2 every day. Generally, the odds of winning the lottery are proportional to the money you put into it. The frequency of play does not matter, although the idea of the lottery is to have some fun more often. Let's imagine a lottery whee the odds of winning are 1 in N. Player A buys $1,000 of tickets over a lifetime. Player B spends $1,000 on tickets for one draw. Both players have almost the same chances of winning - 1 in N/1000. and plays a dollar every week has almost the same chances as a player who plays once for the same amount. This assumes that playing one draw costs $1, and that player B plays different tickets. We used "almost" here, because, these odds are approximations. In real terms, player A will have marginally worse than the stated odds. Player B will have exactly the stated odds.
Given this information, a player might choose to wait for a big jackpot to play. Whilst the odds of winning are similar, in the event of a win they could receive more money. In draws like Superdraw and Megadraw in the Australian lotto 6/45, extra funds are added by the lottery. In the USA, the jackpot can grow immensely in some of the big lotteries like Powerball, Mega Millions.
We know that the chances of winning the lottery in one particular draw are not too high. However, the chances of winning the lottery in your lifetime are much better (unless you only play once in your lifetime...). Of course, it depends on your playing habits. Namely, how often you play and how much you put in any particular draw on average.
The following odds have been taken from two books by Dr. Bluskov. These are rough computations on how difficult is to be a big jackpot winner over a lifetime of playing. For more information, you should read the following books:
Combinatorial Lottery Systems (Wheels) with Guaranteed Wins LINK: www.amazon.com/dp/B09DGTT516
Combinatorial systems (wheels) with guaranteed wins for pick-5 lotteries including Euromillions and the Mega lotteries. LINK: www.amazon.com/dp/B08KPLJNNY
Let's take an example where over a lifetime a player spends $20 a week for a lottery that has a draw once a week. We can come up with approximately a 2% chance of winning a $1,000,000 jackpot or higher.
For each big jackpot winner over a lifetime of playing, there must be roughly 49 other players who don't win. These 49 players pay for the lottery tickets and possibly end up with a small loss over time. When we talk about “small loss", we mean it relatively. There would be many small wins in the process, even though there could be no major jackpot win. These smaller wins will partially cover the cost of playing. A player could end up being a winner even without winning jackpots along the way. For example, they could hit, say a 5+1-win, or several 5-wins (in a pick-6 lottery) over the years.
The above computation is just an approximation on what could happen in reality. Extra factors have to be included to precisely evaluate the chances of winning a jackpot. These factors include:
- if a player misses any draws
- if a player plays different amounts on different draws
- the small wins which would come along the way and how they would be used to finance future participation
- how the lottery distributes the money for different prize tiers
- changes to lottery rules over time
There is one sure way to increase the chances of winning the lottery and that is to play more tickets than just one. For example, the odds of winning a Jackpot in Lotto 6/45 are 1 in 8,145,060. Playing 10 different tickets would improve the odds to 1 in 814,506. Playing 100 different tickets would further improve the odds to 1 in 81,450.6. Further increasing the number of tickets would further improve the odds. Playing a larger number of tickets is more appropriate for a syndicate.
The chances of winning a Jackpot as a part of a lottery syndicate are better than the chances of playing alone. Spending $X on one syndicate share gives more chances of winning than spending $X on playing alone.
It is difficult to be a jackpot winner if you play individually and easier if you play in a syndicate. Earlier on this page, we looked at the chances of winning the lottery over a lifetime. The approximate chance of being a lifetime winner through individual play is 2%.
What happens if you play the same amount for the same time, but now you are a part of a 50-person syndicate? Let's take an example where each person puts the same amount into playing as you ($20 per week). In this situation, the chances become close to 100% that you will be part of a big win over your lifetime! You will be splitting the big win with other people, but many players would prefer exactly that. Would you prefer to be an almost-sure winner of a portion of a jackpot? Or would you rather play individually and have a tiny 2% chance of hitting it alone? Unfortunately, playing alone comes with a 98% chance to be a lifetime down on the lottery. Another factor to consider (or to think about) is that you might not need a lifetime. The big win might come much earlier; as early as the next draw, and then you will have the choice to stop playing.
The chances of winning the lottery twice are much smaller than the chances of winning it once. The complete answer to this question depends on several things. How often you play and how many tickets you play on average are key factors. Whether you are a part of a syndicate or not and the size of the syndicate has to be considered. It also depends on whether we talk about playing in two particular draws and winning a Jackpot in each of them. Or if we talk about playing over a period of time (or even a lifetime of playing). To keep it simple, we will address the simplest situation. A player plays one ticket in a simple lottery with odds of 1 in M of winning it. They also play another ticket in a simple lottery with odds of 1 in N of winning it. The odds of winning a Jackpot twice under these conditions are 1 in M*N. Let's say the odds of winning a lottery are 1 in 1,000,000. The odds of winning it twice (but only playing one ticket in each of two particular draws) are 1 in (1,000,000)*(1,000,000). This is 1 in 1,000,000,000,000 (one in a trillion). Given these odds, perhaps the best strategy is to stop playing after winning a Jackpot. However, the history of lotto playing has recorded cases of players who won a Jackpot more than once. In fact, the chances of a repeated Jackpot win become much better under a long play. In other words, if we drop the requirement of two particular draws. Instead, we look at two draws over a lifetime of playing instead. Whilst the odds of winning a Jackpot twice are still long, they become feasible. This proves it is quite possible to happen, in support of the recorded history. Let's assume that playing a ticket is $1, and that a player has put $10,000 into playing the lottery over their lifetime. The odds of two jackpots in that lottery would be improved approximately 10,000 times to 1 in 100,000,000. These are still very long odds. But, with billions of tickets played, winning a jackpot twice becomes a possible event.
Surprisingly, the answer is different if we ask a different question. How likely is it that the same numbers are drawn twice in a particular lottery? We won't actually specify the numbers in this calculation. For example, let us take a 5/44 lottery, which has 1,086,008 possible draws. Suppose we look at the 5 numbers drawn in the last draw. The chances of the same 5 numbers being drawn in a particular draw in the future are 1 in 1,086,008. If we consider the same lottery over say 50 years, then these odds will improve thousands of times. This makes the event of repeating the same 5 numbers more feasible. We can drop the condition that we are trying to match the 5 numbers of the last draw. Instead, just leave the condition of matching the 5 numbers of any draw so far. This will significantly improve the odds of a match even further. Now consider the number of lotteries in the world, and the odds. Repeating all numbers in two different draws of the same lottery. Somewhere in the world, is almost certain to have happened already, and it has. For example, in the Bulgarian Lotto 6/49. In 2009, the six numbers drawn on September 6 were repeated in the very next draw (albeit drawn in a different order).