66,666 Random Numbers, Volume 1

A while ago I posted about gambling at roulette, and explained that whatever strategy you adopt – excluding the possibility of using electronic equipment to monitor the wheel and ball speeds, and improve prediction of where the ball will land – no strategy can overcome the edge that casinos offer by giving unfavourable odds on winning outcomes. Now, believe it or not, I do a fair bit of research to keep this blog ticking over. And in the course of doing the research for a potential casino/roulette post, I came across this book:

That’s right: 66,6666 random numbers. But not just any numbers: the numbers on a roulette wheel, 0-36. The numbers are also colour coded as per a standard roulette wheel. Here’s a typical page:


But there’s more:

  1. The book includes a bonus set of an extra 10,000 random numbers. (Question: why not just call the book 76,666 random numbers?)
  2. There’s also an American Edition, which is almost identical, but accounts for the fact that in American casinos, the wheel also includes a 00.
  3. This is just Volume 1. Further volumes don’t seem to have gone into production yet, but the title suggests it’s just a matter of time.

Now, tables of random numbers have their place in history. As explained in an earlier post, simulation is a widely-used technique in statistical analysis, when exact mathematical calculations for statistical problems are too complicated. And before computers were widely available, it was commonplace to use tables of random digits as the basic ingredient for simulation routines.

But, hello! This is 2019. Chances are there’s a reasonable random number generator in the calculator on your phone. Or you can go here and fiddle around with the settings in the dialog box. Or you can fire-off 66,666 random numbers with a one-line code in R or any other statistical language. You can even do it here:

# simulate the results numbers <- sample(0:36, 66666, replace=T) # tabulate the results table(numbers) # show results as a barplot library(ggplot2) df<-data.frame(table(numbers)) colnames(df)<-c('number','frequency') ggplot(data=df, aes(x=number, y=frequency)) + geom_bar(stat="identity", width=0.5, fill='lightblue') +ggtitle('Frequencies of Results in 66,666 Roulette Spins')

Just hit the ‘run’ button. This may not work with all browsers, but seems to work ok with Chrome.

The simulation is all done in the first non-comment line. The rest is just some baggage to tabulate the frequencies and show them graphically.

This approach has the advantages that:

  1. You get different numbers every time you repeat the exercise, just like in real life;
  2. The numbers are stored electronically, so you can analyse them easily using any statistical functions. If you ran the R session above, you’ll have seen the results in tabulated summary form, as well as in a barplot, for example. But since the data are stored in the object ‘numbers’, you can do anything you like with them. For example, typing ‘mean(numbers)’ give you the mean of the complete set of simulated spins.

So, given that there are many easy ways you can generate random numbers, why would anybody possibly want to buy a book with 66,666 random numbers? Well, here’s the author to explain:

After gaining a moderate amount of experience playing roulette, I discovered how easy it was to master the rules of the game – and still lose!

He goes on…

Having lost my bankroll and now distrusting my knowledge of statistics as they pertained to roulette, I scoured the Internet for more information on the game. My findings only confirmed what I already knew: that statistics can only define the shape and character of data and events that have already taken place and have no real bearing over the outcome of future spins.

And finally…

I chose to compile a book of 66,666 random numbers for two reasons: One, I’ve paid my dues – literally, I’ve lost thousands of dollars playing this game, and I don’t want you to suffer the same consequence; two, as roulette is a game played against the house and not against my fellow gamblers, I knew I wanted to provide you with the same opportunity to study these numbers and learn something that might just make a difference in the way you play the game.

In summary, despite having lost a fortune believing there is some system to win at roulette, and despite sincerely wishing that you avoid the same fate, having learned through experience that no roulette system can possibly work, the author has provided you with 66,666 spins (plus a bonus 10,000 extra spins) of a roulette wheel so that you can study the numbers and devise your own system.(Which is bound to fail and almost certainly cost you a fortune if you try to implement it).

Now, just to emphasise:

  1. The random properties of a roulette wheel are very simply understood from basic probability;
  2. A study of the outcome of randomly generated spins of a roulette wheel is a poor substitute for these mathematical properties;
  3. Biases in the manufacture or installation of a roulette wheel, which could make some numbers, or sequences of numbers, more frequent than others, are likely to be vanishingly small. But if there were such biases, you’d need to study a very long series of the outcomes of that particular wheel to be able to exploit them;
  4. You might choose to play roulette for fun. And you might even get lucky and win. But it is a game with negative expected winnings for the gambler, and if you play long enough you will lose with 100% certainty.

However, we’ve seen a similar mis-use of simulation before. In this post a newspaper did 100 random simulations of the NBA lottery draft in order to predict the lottery outcome. The only difference with the roulette simulation is that 66,666 is a rather bigger number – and therefore greater waste of time – than 100.

Moral: simulation can often be avoided through a proper understanding of the randomness in whatever process you are studying. But if you really have to simulate, learn the basics of a language like R; don’t waste time and money on books of random tables.

10 thoughts on “66,666 Random Numbers, Volume 1

  1. Hello. Thanks for critiquing my book. I appreciate your honesty. When I published this random numbers book, I was also working on a much larger work. Inside, you will see the greater context in which my random numbers book should be viewed. I would be interested in your opinion on my most recent book, American Roulette – An Observational Study & Frequency Analysis of Spin Trials, Runs & Trends, and Wheel Dynamics. Looking forward to hearing from you. Thanks.


    1. Hi Michael… sorry for not replying sooner. I’ve only just noticed your comment. Thank you for writing. I hope my original post didn’t cause you any offence. My blog is meant to be at least partly entertainment, introducing statistical ideas and thinking to mostly non-statisticians, and I try to use many different types of source material to achieve that. Your book was a great opportunity for me to comment on the wider issue of data simulation.

      I was cynical about your previous book because it wasn’t anything fundamentally different from a book of random number tables. These are redundant now that we can easily simulate random numbers on a phone, calculator or computer. I appreciate the reference to your new book, and agree it puts the whole argument in a much wider context: the identification of potential gambling strategies.

      These have to fall into one of two categories: strategies that are based on a roulette wheel that is perfect, so that in every spin each number is equally likely; or strategies that try to exploit possible discrepancies/biases in the wheel. Standard mathematics proves that there is no hope of finding a winning strategy in the first of these cases. If you are playing on a perfect wheel, you are bound to lose. Well, you might get lucky and win, but if you keep playing by any strategy, you will eventually lose all your money. Nothing else is possible. To be fair, I don’t think you are proposing strategies under the assumption of a fair roulette wheel, though your discussion about probabilities in Chapter 6 is completely wrong and misguided.

      It seems to me the the real essence of your book is to try to develop strategies based on perceived patterns in roulette data. There are several points here. First, casinos go to great lengths to do 2 things: 1. to make sure their roulette wheels are as close to perfect as possible; 2. to stop people trying to notice patterns that might derive from non-perfect wheels. But to be honest, they are so successful with 1, they don’t need to bother much with 2. So, first any biases in roulette data are likely to be really small and you’d need a lot of data to detect them (and be able to risk a lot of money in trying to exploit them); but then they wouldn’t let you collect that data anyway.

      So, I’m still doubtful a strategy can be found. But let’s suppose a wheel has some defect and it’s possible to derive a strategy to exploit this. Then such a strategy would depend on the precise characteristics and biases of that particular wheel. It would be necessary to study the data from that particular wheel. It’s pointless telling me you’ve done simulations or encouraging me to look at data from your previous book. I have to have data from that wheel.

      Kindly, I have to tell you, that your book is a complete waste of time for anyone thinking of playing roulette. You have all sorts of statistical analyses to explain why your methods work. If you wish to send me a copy, I will write back and explain the faults in your analyses.

      Roulette is great fun, and that can be a good enough reason for playing. Sometimes someone might even get lucky and win. Usually they won’t, however, and it’s simply wrong for you to suggest that if they buy your book, and follow the strategies you suggest, they have an improved chance of winning. The truth is they don’t.

      With best wishes…

      1. Hi Stuart. Thanks for writing. I was hurt a bit. But that’s the risk anyone takes when they put themselves or something they’ve debeloped out there. Do you have an Amazon account? I’d be happy to send you a copy. Im wondering if I didn’t make my point clear in my book now. I dont specifically vlaim that my strategies will improve anyone’s chances of winning; odds and probabilities are what they are (mathematical results) and as such they cannot be improved or made worse. I only claim the based on frequency analysis results, the potential for winning is much greater than previously thought.

        If you send me your email address, I’ll send you a copy via Amazon.

      2. Hi again Michael, I’ve mailed you, so we can continue this conversation in private.

  2. Thanks for that pictures of 1.000 random numbers. Really apreciate the work.
    I can see a lot of probabilities now in it. If you circle in red the Nrs. like (35 and 2) and blue (1-19) or green (0 and 4) you will get a picture out of it. Vali

    1. Hi Vali… thanks for your comment. You probably realise, but the point I was trying to make is pretty much the opposite of what you imply in your comment. Sure, if you look at a run of 1000 random numbers you can convince yourself there are some patterns there. But the point is that in a different set of 1000 random numbers you’d see a different set of ‘patterns’. So, you can’t learn anything from random numbers that would be useful in predicting what might happen in the future. In other words, unless a roulette wheel has some bias, and you can learn about the bias from studying the sequence of spins from that particular wheel, there is no strategy that can help you win at roulette. It’s totally pointless looking at random numbers and trying to hunt for patterns. Best wishes… Stuart

  3. Hi Stuart, I do agree that the randoms numbers are tricky and can make anyone think tha theret is a patern somewhere like an imaginary sistem and so it makes very dificult. I have been playing for 4 years roulette sometimes hours afters hours day by day on online casino trying to figure it out a way of wining for long term and sometimes I won and many times I lost and sometimes very much so in the end casino wins but i also realise that when I was playing carefully starting with small bets and continue carefullly in those time I always had a win in the end but the always then changed the bets in biger bets and have got lost all of it very fast. I like random numbers because they are like a mistery and it was become to be a passion for me a hobby to hunt random wining numbers in a strategig way. I know it sounds naiv to say so but there is always a way out for an exit in everything. we all know that because of so many combinations and roullete has to do with matematic algoritm amound of bets spins and probabilities so thats ok to accept that 1+1 will always be 2 and never 3. thats ok, but we deal with an unknow probabilieties so an exit for wining must be somewhre like how much peopel know these days about universu,black holes, quantum mecanic and so much about galaxies just by puting in time piece by piece. Sorry my english is not so good, what I wanna say that we are talking just about 37 numbers on european roulete wich depends on how much is the bet, the limits on the table and the speed and probabilieties so there are many factors involved. what I realized is that in 1.000 spins there is always a number that comes between 16-32 times and one time or two times it hapens to come the same number close to eachother in less the 5 spins between them. its interesting cause I can win for free 100 spins without puting bet on it just observing till the favorite numbers comes out and then also beting more 180 spins staring with 0,1 cent for one spin in penny roullete for exampe so in the end I can catch a ramdom wining number in 280 spins anyway wich means in the end it is a win,sometimes small win sometimes biger win but win is a win and so it is ok. there must be a patern of probabilities in random numbers for a win. Just like in chess if there is no checkmate there is pat like no wining and no losing so if there is no losing and so in time there may be a win, is just a step farther just like sience. Even random numbers can get in a trap.

    1. Hi Vali…. Thanks again for your mail. I don’t have as much experience at playing roulette as you, and I admire your search for a winning strategy. All I can say is that if the roulette wheel is genuinely generating random numbers, there is no hope of winning in the long run. You might win in the short term, but you are guaranteed to lose eventually if you keep playing, whatever strategy you adopt. It might be that if you study the sequences of numbers of a particular wheel you can detect some pattern in the numbers which suggests the wheel is not generating random numbers. (For example, if even numbers were occurring more often than odd numbers). And in that case you could place bets in a way that would allow you to win in the long run. But casinos are very careful to eliminate this possibility, so this also seems unlikely to provide you with a winning strategy. So, I am very skeptical that you can find any way of winning money at roulette. You might get lucky and win, but more often than not you won’t. If your experience has been different from that, then I’m very happy for you. If you wish to carry this conversation on further it might be easier for you to write to me directly at stuart.coles1111@gmail.com. Best wishes… Stuart

      1. Thank you Stuart for your replay. I really apreciate it and I will e-mail you, if in time, I find something worth it.
        Best Regards

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