That's just the way I'd do it. For me I think I would see the spaces for the diagonals and 2x4 and so on more clearly if the squares are blank.  There's absolutely no mathematical reason why this should work, and I am dubious, especially given the large drawdown that Dane reported - and then disappeared! But as far as   a system for selection is concerned, it is as good as any and does at least force some structure on your play. That by itself is a good thing.

Hope this is clear.
Well, I tried to insert an image rather than an attachment but couldn't figure out how to do it. See attachment.

Hey no worries Sam - I'll do a snip with some explanations for you.

Just work through his example in #5 and you'll get it.

I think I'd use blank and fill them in as they come. Makes it easier to see the un-hit numbers.

But I was wondering - is Dane still around? I see that there was a big down turn of around 400 units between games 140 and 155. I was wondering if he was still playing this, or perhaps had moved on.

Never meant to imply it was easy - and of course I know nothing of the finer aspects of the whole deal. I simply wanted to make the point that even in the circumstances you mentioned the journal or log idea was still valid.

Just out of interest, here in NZ when we have that type of incident on a freeway (we call them motorways) there are a whole host of things that happen. The first is that the police set up a "rolling block" which slows the traffic down which in turn causes queues which then become self-controlling. Then we have big trucks with a massive flashing "X" displayed on the back (in white) on the lane that is blocked. Then cones for lane control plus further amber lights and all that stuff.  It becomes quite a spectacle actually.

Al - you ask "how can writing that down in a journal help?". I'm surprised at you! You claim to be a professional at what you do and the fear you have expressed is based on real experience so - how can you NOT try to mitigate this circumstance? Writing it down in a journal is good for both you AND your peers and co-workers. It provides a record of experience, number 1, from which others in your business can learn. Number 2, consider mitigating factors - you can scan the scene with this particular fear in mind and do any number of things - put people on flag duty, put flashing lights in the direction of on-coming traffic, put wheel spikes after the barrier and before the scene, increase the brightness of lights.  Jeez - and I'm not even an expert in your business!

As I clearly stated Al, bear in mind that the answer to this question will be probabilistic, not "absolute". And I was merely presenting the mathematical truth.

People are endlessly creative and given this truth who knows what they may come up with? You have made an assumption that the only possible strategy that derives from this relates to, in your own words, "which one will hit in which order" and so you have failed to acknowledge the endless other possibilities. This is short-sighted in the extreme.

Never underestimate the power of human creativity and I would suggest to you that you should not insult the intelligence of the good folk who congregate here. Some are beginners looking for advice it is true, and some are extremely experienced and knowledgeable and, in my opinion, it would be unwise, not to mention insulting, to treat them in so condescending a manner.

A good strategy is not about guessing the next number to come out - this is fruitless as the maths of probability shows.  But it is not unreasonable to work on constructing a more sophisticated game strategy which is based around playing the statistical necessities that must be obeyed over a series. Roulette is a closed game in the sense that there are only 37 possibilities and all 37 exist each and every spin, and so over a series, since only these possibilities exist, if a distortion happens in a certain way then there is a consequential distortion elsewhere.

I'm not going to go into detail here as I do not want to limit or steer in any particular direction, people's thought processes, but consider for example if after 24 spins you have seen only 12 "shows", what do you think is likely to happen in the next 14 spins (making up a cycle of 38)?

Here's another example - what do think is most likely going to happen in the next 14 spins if, after the aforementioned 24 spins, you have 20 unique "shows" and these are imbalanced by 8 blacks and 12 reds?

There are endless possibilities.  Let people do what they must, which is to "create". Such is our nature and I can assure you that your attempt to shut them down by expounding your own particular version of the "truth" is fruitless - thank goodness!

Good to see that your simulation was accurate.  Here's the maths of it.

Generally speaking, what people usually mean by "the law of the third" is this – at a certain point in a series of spins, roughly one third of the numbers won't have shown, while two thirds will have been dominant.  The rather nebulous point of this is that the implication exists that if we can identify which ones are active, at the expense of certain others, then we are playing a game with only 2/3's of the numbers active and so we are getting "better than odds" payouts.

You have to be real careful about what you mean when using the phrase "law of third".  It is really not a law at all – it is merely an effect of standard probability maths – a "rule of thumb" if you like.  It is better called "rule of the third" really and probably was once, but over time things get warped and the significant difference between a "rule of thumb" and a "law" has been overlooked.  Furthermore, it is only a "third" at one specific point in a series of events.  Before this point, lots more than a third of the numbers haven't shown, and after that point there are less and less, asymptotically approaching, but never reaching, zero. 

To work out the maths, and hence derive a result, we have to carefully decide – what is the question?  I suggest that the proper question to ask is this – derive a general formula to determine how many numbers have not shown after a specified number of  events - and at the same time bear in mind that the answer to this question will be probabilistic, not "absolute".  This would then allow us to ask the more specific question – at what point in a series of trials do we have roughly 1/3 of the possible outcomes still to show?

The following refers to a single zero wheel.  It can be extended to a double zero wheel quite easily as shown in the examples at the bottom.

As previously discussed, the chance that a number won't come up is called the inverse (or negative) probability, and is 36 / 37.  To extend this for a variable number of spins is therefore going to be (36 / 37) ^N (also previously mentioned) where N represents the number of spins.  The next stage is to extend this for all numbers.  This is simply a matter of multiplying the above result by the number of numbers, i.e. 37.

So now we have a general formula for determining the statistical expectation of how many numbers will NOT appear in N spins –

[(nbr of possible outcomes - 1) / nbr of possible outcomes] ^ (nbr of spins) * nbr of possible outcomes.

Or : ((X-1)/X) ^N) * X    where   X = nbr of possible outcomes, and
               N = nbr of spins

So let's now ask the question – after how many spins will we have 12 numbers not shown? (12 is roughly one third of 37 for a single zero wheel.  I'd use 13 for a double zero wheel).

Or     12 = (36 / 37) ^N * 37

We could use logs to solve it, but it is simpler to just plug in a few numbers to N and work it out by trial and error – after all, we don't really want anything other than a whole number for N since you can't have 36.245 spins!

By experimenting you will find that N = 41 gives the closest result to a nice round number of 12.  To be precise, (36 / 37) ^41 * 37 = 12.03.  So, for a single zero wheel, after 41 spins we should have, on average, 12 numbers not shown yet and therefore 25 which have been busy.

So for a double zero wheel (X = 38) and nbr of spins (N) = 40 we get 13.07.  Work it out for yourself – it's quite easy really.

In terms of playing on a single zero wheel it is probably better to find a number closer to 37 spins – just because we kind of consider 37 spins to be a "cycle".  By experimentation with the numbers in the formula it is easy to show that the best result, i.e. one that gives closest to a whole number, is 38 spins.  This produces 13 numbers that have not shown (13.06 actually) and so it is expected that by spin 38, on average, we should have 24 numbers shown.

Other useful results (for a single zero wheel) are:
•   13.13 shows at spin 16
•   14.40 shows at spin 18
•   17.29 shows at spin 23
•   17.83 shows at spin 24
•   23.94 shows at spin 38

See - that wasn't so hard was it?

I'm not as experienced in the other casinos as XXVV, but I can tell you that Skycity Auckland's culture has not changed. It is completely corporate, automation is everywhere (even to the free non-alcoholic drinks), and the majority of dealers are a-holes. Because tipping is illegal in this part of the world you would think that the dealers could be a little more dispassionate about the whole thing, but no, they revel in taking you down. Most dealers now are either asian or indian. These people fear for their jobs and so are completely corporate brain-washed. There is one particular (asian) dealer who I am sure they consider to be their ball-breaker. He spins barely 3 rotations before the ball drops - all the time. I recall one trainee dealer who was an absolute delight - she was full of personality and joined in the fun to a degree that made everybody smile. Guess what? Never saw her again after that first night!  What a crazy mentality these corporate people have.

I would disagree with XXVV on one thing - Mr Dotcom is a piece of garbage and the sooner he gets deported to face the music for his crimes in America the better - in my view.  He is attempting to sabotage our elections for his own selfish purposes and because of the money he can inject into his campaign he has managed to buy a couple of rather (again - in my view) sleazy politicians who I wouldn't trust to feed my dog!

Ah - right - of course. You have allowed for it in the determination of your expected spread - I should have realised that. Yep - it is just another outcome really so that it figures as a loss just the same as the opposite EC coming out would do. Cool. Be interesting to see how it works out over time. Thanks.

Well done Leapyfrog - what a fascinating concept! I guess you were a little bit lucky with this group of numbers - no zero. On average I would anticipate at least one zero in the mix for a 35 number selection. Have you got an example with a zero in it? And how do you handle it? Just take the loss and ignore it in the sequence? I think that is what I would most likely do.

Um - a small point Dane - what do you mean by

QuoteRight after 24 different numbers repeating.

24 unique numbers will typically appear by spin 37.

QuoteQuote by palestis *****You walk up to a roulette and decide in advance to bet on black. With a twist. First you wait until you lose 3 times in a row. Meaning RRR. (Of course you don't lose actual money. Only in the virtual loss mode). If the probability of the 4th spin to bring yet another red is 1/16,  then the probability of black should be 15/16. Overwhelmingly  in your favor. The question is this. With 50:50 chances, betting randomly, is it possible to keep on losing spin after spin after spin? How many times? And is there a limit after which, a 50:50 chance finally comes your way? ******

Yet when you do this you only win 50% of your attempts, not 15/16. If it were that easy we would all be doing it. For example, by extension of the above principle I predetermine the following - if I see 2 reds I will bet black and if I see 2 blacks I will bet red. On the principle above I should win 3 out of every 4 bets placed. Doesn't happen. I win 50%! Always! Virtual betting gives no advantage, changes nothing - wish it did, but it doesn't. Period. End of story. Use your creativity to look elsewhere - this one is a dead duck.

Nicely stated.  I would contend, however, that the context we are in is the gambling one and in common parlance when we talk about odds we are really meaning "the odds on offer" which is different to the probability of the outcome. However your point is well made about the logical equivalence. It's just this type of difference in meaning that causes problems in communication.

I confess I always think of odds in terms of what is on offer because I am aware that the game is unfair and the only way to measure the degree of "unfairness" is to compare the odds with the probabilities. The point was made to me quite categorically when I was demonstrating the game "penny ante" to a well experienced gambler friend of mine and once he understood the game his immediate question was "what are the odds"?

Anyway, thanks for your detailed response - very interesting.