Who are we?

This website was developed by a team led by Michał Krawczyk, PhD, that is Joanna Rachubik and Raman Kachurka.

Michał Krawczyk obtained his doctoral degree in economics at the University of Amsterdam and he’s currently a professor at the University of Warsaw.

Professor Krawczyk is an expert on risk and decision making. Some of the publications in this field that he has (co-)authored can be found here:

• “The representativeness heuristic and the choice of lottery tickets: A field experiment”
(Judgment and Decision Making 14(1), 51, 2019)

• “Catastrophic risk: social influences on insurance decisions”
(Theory and Decision 82.3, 2017)

• “Common components of risk and uncertainty attitudes across contexts and domains: Evidence from 30 countries”
(Journal of the European Economic Association 13.3, 2015)

• "Let me dream on!' Anticipatory emotions and preference for timing in lotteries”
(Journal of Economic Behavior & Organization 98, 2014)

• “Investment, resolution of risk, and the role of affect”
(Journal of Economic Psychology 32.6, 2011)

• “Give me a chance! An experiment in social decision under risk”
(Experimental economics 13.4, 2010)

• “Experiments in Decision-Making Under Risk” (Rozenberg Publishers vol. 464, 2009)

• “Dictating the risk: Comment" (American Economic Review 106.3, 2016)

Why can you trust us?

As you can see, this website is also hosted by a university (the University of Warsaw in this case, dr Krawczyk’s alma mater and current employer). You can therefore be confident that what you are told here is based on solid scientific research (but then again we made it as easy to follow as possible). Specifically, this website was developed as (a tiny) part of a public-funded scientific research project on lotteries.

Note also that all of this is completely free and we are not trying to make money here in any way.


The main purpose of developing this website was to give you a helping hand when making decisions about lottery play. In particular, we want to offer some guidance through the jungle of countless books, websites and software platforms that allegedly can help you get rich by playing lotto, Pick 3, Pick 4, scratch cards etc. Sadly, these materials are typically useless. Some are highly misleading, creating completely unrealistic expectations and contributing to excessive lottery play. Many will cost you quite a bit. Some may be credit card scams. The software may come with viruses.

We have gone through a lot of this material and we offer some general advice, some warnings, and some clarifications. We also make comments on specific books and websites and rank them on how helpful vs. dangerous they are. Obviously, we sometimes quote some rubbish they say. To make it easier for the readers, incorrect or misleading statements are always displayed in magenta, like this: this is the most beautiful color!!!

Note: there are many other websites that can be more helpful if you start having real gambling problems. If you spend much more than you should, you go in debt, your professional activities or your personal relations suffer because of your lottery play, please contact Gamblers Anonymous.


The key notion when playing lotteries is that of expected return: how much you will earn, on average, per one dollar/euro/pound etc. spent on the coupons. Sadly, this is invariably negative: you will not earn–you will lose. How much? Well, typically, you will lose a bit more than half of the money you spend to buy the tickets. It is completely understandable that on average you must lose (a lot): if the winnings were higher than the cost of the ticket, the lottery would go bankrupt. In fact, lotteries are very profitable, despite considerable operating cost, which means the players must lose a large fraction of their money on average. Basically, the same is true for any type of gambling, although state lotteries happen to pay out a particularly low fraction of the money they collect.

For example, if you play roulette in a casino, you only lose 1/37=2.7%, rather than more than 50% of what you invest. Of course, this is true for a single roulette play and most patrons play many times each night, so they end up losing much more.

But back to the lotteries.

By playing lotteries you lose money on average, full stop. The only exception is a scam in which the lottery wheel is rigged, and you happen to be an insider. If that is your case, you need advice from a defence attorney, not from us.

Else, you will lose money on average, which means that you should not treat a lottery as a form of investment. That would be a very bad investment indeed. On average, playing lottery, will always make you poorer. If a book or website tells you that, with their help, lotteries will make you rich, it is a serious reason to start being suspicious.

Then again, if you find it enjoyable AND you can control the cost, feel free to play! All the best!

But remember: it can only be understood as consumption, not investment. In other words, you need to calculate how much it costs you (about half the amount you spend on the coupons) and ask yourself if perhaps other consumption goods you could buy with this money would not make you happier.


Here are some other very important things to know:

Lottery is NOT a game of skill

It is pure luck. You cannot affect the numbers to be drawn. "Laws of attraction", "positive thinking", "visualising the victory", "manifesting the millions" and similar terms you will often encounter in books and websites are sheer nonsense. It is just voodoo, superstition, magical thinking, rain summoning. Yes, “positive thinking” may sometimes help you recover from illness, land a job, create a solid relationship etc. but it is only because your attitude can affect YOU (and how you feel and behave is of course important for your health, wealth, and happiness). Your attitude CANNOT affect the lotto balls in a machine a thousand miles away from you. Nor a machine next door. Well, if you do have psionic powers so that you can move physical objects, like lotto balls, just by thinking about them, we are all ears. But then you don’t need to bother to buy the lottery ticket, right? Just use the law of attraction to unearth some zillion-carat diamond and land it in your pocket. That said, some of the materials we have reviewed do offer some helpful advice how not to miss the winning if you are lucky enough to win in the first place: keep your tickets safe, sign them, carefully check if you have won (also consolation prizes available) etc. We concur. If you do play, do not miss a victory.

Winning the grand prize in games such as lotto, Powerball, Megamillions, EuroMillions etc. is extremely unlikely

Again, if it were not, the lottery would go bankrupt. Now, it is very difficult to intuitively grasp just how unlikely it is, because, obviously, we just don’t experience it.

The odds of winning the main prize in the 6/49 lotto are about 1 to 13,983,816. In the case of EuroJackpot, itis about 1 to 95,344,200 for the main prize and 1 to 5,959,013 for the second prize. In Megamilions it’s 1 to 258,890,850. But, let's say that we want to win "only" the third prize (5,000$). The odds are still against us: 1 to 739,688.

So, yes, it is very unlikely indeed. But what do these numbers mean, how do they compare to other rare events?

As "The Economist" notes, winning the jackpot in Powerball was around four times less likely than being killed by an asteroid impact in 2016. Of course, you can die in many different ways. For example, according to the website problemgambling.ca, you are 250 times more likely to be killed by lightening (1 in 56,439) than winning the jackpot. If you’re driving more than 8 km to buy a lottery ticket, it is also more likely that you’ll be killed in a traffic accident than that you’ll win with that ticket.

You can also imagine a football field fully covered with ants. There will be around 15 million of them, so more or less as many as there are possible number combinations in Lotto.

“But I see so many pictures of lottery winners!”

Well, lotteries are very popular. There are some winners out there. They get photographed and these images stick in your mind so it feels like winning is quite possible. Psychologists Amos Tversky and Daniel Kahneman called this mistake “availability heuristic”. Sadly, nearly nobody bothers to document billions of losing tickets around the world. Here is our modest attempt to counter this imbalance:

“But what about all these people who have won a lot of money using a system? I have seen testimonials on these websites!”

Well, testimonials are not that hard to come by. Look, we’ve got some too about this website:

"LOTTO FACTS is the coolest website ever made." – Judge John Fake, Alabama.

The pictures below show some cases of misleading pictures of lottery winners:

Screenshot of lotto-destroyer.org with fake testimonials
Original source of a photo
Original source of a photo

Screenshot of smartluck.com with a fake testimonial
Original source of a photo with a lottery winner

Please note that “Mazey says his numbers are just lucky and don’t really have any personal significance, such as birthdays or an anniversary. “I just mix the numbers around” Mazey said.”

Screenshot of thelottoblackbookrevealed.com with a fake testimonial

Please note that winning ticket was a scratchoff ticket, while on the thelottoblackbookrevealed.com number betting strategy is discussed.

Original source of a photo with a lottery winner

Screenshot of winninglottobooks.com with a fake testimonial
Please note “SPECIMEN ONLY” notice
in the middle of a printed "check"

Every number is equally likely to be drawn

Some people like betting on the "lucky numbers" like 7, on low rather than high numbers, on their birth dates, on the numbers that are "due" because they have not been drawn for a while, numbers that have been drawn a lot in the past etc. Many "systems" recommend one such strategy or another, often claiming that some numbers are more likely to be drawn than others. That is NOT true. Many studies have been conducted to check it; some of them were published in scientific journals, which means they have been verified by competent reviewers and are known to use solid statistical analysis. The large majority of cases concluded that lottery drawings are not biased. The examples include "The statistics of the national lottery" by John Haigh, published in the Journal of the Royal Statistical Society: Series A in 1997, analysing the UK data and “A Statistical Analysis of Popular Lottery “Winning” Strategies” by Alber C. Chen and colleagues, published in the Case Studies In Business, Industry And Government Statistics in 2010, using the data from California SuperLotto.

In each drawing any number has the same chance to be drawn as any other number. That means in particular that history does not matter. There is absolutely no point in analysing "trends" and "patterns". There are no trends. There are no patterns. Past drawings are completely irrelevant. It is impossible to "predict" or “forecast” the numbers to be drawn. No numbers are "due". "Hot" numbers are as likely to be drawn as "cold" numbers etc.

Also within a drawing, the fact that a number has been drawn, does not make any other number more likely than some yet another number. The fact that we already have 2 and 4 does not make picking 3 more or less likely than picking 21 or 39. Any combination is exactly as likely to be drawn as any other combination. For example, contrary to common intuition, (1,2,3,4,5,6) is as likely to be drawn as (13,19,21,28,38,41).

“But nobody has ever seen (1, 2, 3, 4, 5, 6) to be drawn! That cannot happen!

Well… it can happen, but the odds are against it in any single drawing, something like 1 to 14 million in 6/49 lotto games. Have you ever seen (13, 19, 21, 28, 38, 41) drawn? Well, you would not remember, so you're not sure (but we bet you haven’t, because the odds are, well, something like 1 to 14 million in any single drawing). And that is the thing--there are few "special" combinations like (1, 2, 3, 4, 5, 6) and millions of unspecific combinations like (13, 19, 21, 28, 38, 41). So it seems like you know that (1, 2, 3, 4, 5, 6) has not happened, so presumably cannot possibly happen but (13, 19, 21, 28, 38, 41)--who knows? Again: there is no evidence that the machine is biased, so every combination is exactly as likely as any other combination.

“But I have heard that the sum of winning numbers is typically in the range of 120-180 or so. So combinations that are outside of this range have a lower chance to be drawn and should not be bet on, right?"

Wrong. Indeed, many “systems”, for instance those promoted by Gail Howard, recommend avoiding coupons with all-low or all-high numbers, sticking to the intermediate sum of numbers. But this advice does not really increase your chances. It is very simple: the sum of numbers in MOST combinations of 6/49 numbers is within this range (and similar “typical ranges”, or “most probable ranges” exist for other games). So it is not surprising that the sum of numbers of combinations ACTUALLY DRAWN is typically in this range. Think about it: in Pick 3 any number between 000 and 999 can be drawn. To be sure, numbers below 700 are typically drawn (70% of the time). Does it mean that betting on 253 gives you a better chance than betting on 873? No, they are equally likely. The only reason that numbers below 700 are usually drawn is that there are more of them. By the same token, combinations in which the sum of numbers is between 120 and 180 are typically drawn in lotto just because there are so many of them, not because any of them is more likely to be drawn than any other combination. In other words, restricting yourself to the 120-180 sum range means that you still have to guess which one of millions of combinations within this range is going to be drawn. In the end, your chance of winning is exactly the same as for any other combination.

The only way to increase your chances of winning is to buy more tickets (but we don’t advise it).

Of course, you also proportionally increase the costs in such a way, so that, again, you just cannot make money. In fact, you lose about half the money you spend. More tickets bought, more money lost (on average of course: you may get lucky; or less lucky and lose it all).

"Does it mean it does not matter at all which numbers are picked?"

Well, it depends on the game:

In Pick 3, Pick 4, Keno: YES, it doesn’t matter.

In Lotto, PowerBall, EuroMillions: NO, it does matter.

“Hey, didn't you just say that any number is as likely to be drawn as any other number and the same goes for combinations?” Yes, but probability of winning is not the only thing that matters. Lotto is a parimutuel game, which means that if you win the jackpot/the grand prize you have to share it with others who won. That may not sound too terrible—after all who wouldn't be happy about winning the jackpot, never mind sharing with a few other players. Yet, the more other winners there are in expectation, the lower your expected winnings. Now, while the distribution of winning numbers is uniform (each combination is as likely as any other) it is NOT true for players' betting strategies. Some numbers are bet on more than others.

For example the “lucky” number 7, is typically bet on more often than other numbers in Europe and America. The same is true for number 8 in China. Even more importantly, not all combinations seem equally attractive. While most players wouldn't like to play with a very special combination such as (1, 2, 3, 4, 5, 6), some do pick it. And because there are few characteristic combinations, each of them will be picked by several players for each drawing. That means that if you are one of them and you happen to win, you will have to share with (many) others. Therefore:

  • • avoid equally spaced sequences such as (1, 2, 3, 4, 5, 6) or (5, 10, 15, 20, 25, 30)
  • • avoid sequences that correspond to any regular geometric figure on the lotto card
  • • avoid special numbers that are meaningful to many others (corresponding to the date of the drawing for example)
  • • do not follow specific advice of "strategies"—other players may have seen the same advice
  • • do not bet on a previously drawn combination (since many others might bet on it as well); well a combination drawn in 1983 a zillion miles away from your place is probably safe, as long as you selected it yourself and did not advertise it on fb.

If you were to do one of these things, you could end up sharing the jackpot with many other players, in the worst case hundreds or even thousands of them. And while making $5 thousand is great, is not exactly as great as making $5 million.

Again, it is not that any of the “strategies” just mentioned decrease your chances of winning. It will, however, decrease your expected winnings, conditional on winning the grand prize/jackpot (if you win, you get less money).

As a side note: some books and websites, like “Win The Lottery, My Story: I Did, You Can Too” by J.L. Williams, recommend buying more than one ticket with the same numbers for the same drawing. Unless you know for a fact that these are the numbers to be drawn (you are a part of an illegal conspiracy, as considered before), that is a very bad strategy. Suppose for example that you are the sole winner (which is quite possible, under the condition that you win at all of course, if you stick to the suggestions given before). Then having the second ticket with the same numbers on it will not increase your winnings by much: you may only get additional 2nd or 3rd prizes from your second ticket, while the chance and amount of the grand prize stays put. And yet, you had to pay for it of course.

Review of particular "systems"

Below we provide a list of webpages and books containing systems that we have reviewed. You will find a short description of each of them and a "misinformation score" which gives a sense how reliable it is.

DISCLAIMER: Please note that we cannot recommend following any specific advice you could find even in the sources with a relatively positive score and we certainly cannot take responsibility if you do. Most of this stuff is rubbish anyway. Also, while we have spared no time to read these materials and assess their validity, we are not infallible either. We sincerely apologise if some description or some score is incorrect. If you think so, please let us know using the contact form below.

Anyway, HERE IT IS: the websites and the books. Enjoy descriptions... and avoid (nearly all of) them.

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