'rule of the third' revisited.

[flukey luke]

I am going to dedicate this thread to the so called 'rule of the third' and my observations regarding it over my many years of studying roulette.
The document I will share comes in 2 parts. I will try and type up the second part tommorow evening. The first part should give you some food for thought.


Most of you will be aware of something called the 'rule of the third'.
This rule says that for every 37 spin cycle, you will roughly get 13 numbers that don't appear. Now there is no real dispute here. I have studied roulette for many years and this rule has ALWAYS manifested itself give or take a few numbers either way. The least original numbers I have seen come in a cycle of 37 spins is about 18 and the most I have seen is about 28. These two events are very extreme. It is uncanny how many times you will see the 13 missing numbers from a 37 spin cycle.
Now I am going to attempt to show you an unusual way of looking at it. It may take you a few times to understand where I am coming from but with a bit of patience you will get there.

I have just downloaded some numbers from the spielbank-wiesbaden Casino in Germany and will use them for reference.

4,31,30,15,16,26,29,8,0,23,23,6,14,12,13,33,8,29,15,14,14,25,3,21,23,1,23,31,7,34,27,35,
0,4,10,7,23,26.  There are 38 numbers there but I need an extra one for my purposes.

Now I am going to make a 'fabricated' cycle of 37 numbers from the list of numbers above.
How I am I going to do this?   I am going to use the wheel layout.
Take the first number in the list above which is 4 and I will work from there. Imagine the roulette wheel as a clock. This clock will always work clockwise (never anti-clockwise) I have to go from the first number in the list which is 4 to the second number which is 31.  Remember I am travelling clockwise, to do this, I just need to count the pockets from number 4 to number 31. I don't know about you, but I counted 22 pockets. So my very first number in this 'fabricated' cycle of 37 spins will be 22. An important aspect to consider is that if a number from the original list repeats, you can not then count any pockets moving clockwise, therefore the number will be a 0.
Now I will write out the complete 37 spin cycle from this fabricated set.

22,26,24,19,15,31,23,21,17,0,30,15,8,16,10,31,14,9,23,0,19,28,7,12,6,31,9,5,15,2,23,3,4,
14,13,23,19.
So there I have my 'fabricated' cycle of 37 spins. What you will find is that the 'rule of the third' applies to this set of 'fabricated' numbers as well.

Finally, I am going to make another set of 'fabricated' numbers (37 again) This time I want you just to imagine a clock with the numbers 0 ââ,¬â€œ 36 on it. I will be working clockwise again. (never anti-clockwise) I have to use the original set of numbers again to arrive at this second set of 'fabricated' numbers. I have to go from the first number in the list which was 4 to the second number which is 31. (An easy way to do this also is just subtract the 4 from the 31 = 27) So counting clockwise from number 4 to number 31 = 27.
Now I will write out the complete 37 spin cycle for this second set of 'fabricated' numbers.

27,36,22,1,10,3,16,29,23,0,20,8,35,1,20,12,21,23,36,0,11,15,18,2,15,22,8,13,27,30,8,2,4,6,34,16,3.
So there I have a second set of 'fabricated' numbers and you will find the 'rule of the third' also applies to these numbers as well.

I am going to go through the three sets of numbers now and find out how they stack up. (I will ignore the 4 from the original set and start from the 31 instead.)

31 (1)
30 (2)
15 (3)
16 (4)
26 (5)
29 (6)
8 (7)
0 (8
23 (9)
23 * (9)
6 (10)
14 (11)
12 (12)
13 (13)
33 (14)
8 * (14)
29 * (14)
15 * (14)
14 * (14)
14 ** (14)
25 (15)
3 (16)
21 (17)
23 ** (17)
1 (18)
23 *** (18)
31 * (18)
7 (19)
34 (20)
27 (21)
35 (22)
0 * (22)
4 (23)
10 (24)
7 * (24)
23 **** (24)
26 * (24)

So in that first group of 37 spins, there are 24 original numbers and 13 missing.

Now I want to look at my first set of 'fabricated' numbers.

22 (1)
26 (2)
24 (3)
19 (4)
15 (5)
31 (6)
23 (7)
21 (8
17 (9)
0 (10)
30 (11)
15 * (11)
8 (12)
16 (13)
10 (14)
31 * (14)
14 (15)
9 (16)
23 * (16)
0 * (16)
19 * (16)
28 (17)
7 (18)
12 (19)
6 (20)
31 ** (20)
9 * (20)
5 (21)
15 ** (21)
2 (22)
23 ** (22)
3 (23)
4 (24)
14 * (24)
13 (25)
23 *** (25)
19 ** (25)

So in that first 'fabricated' group of 37 numbers, there are 25 original numbers and 12 numbers missing.

Now I want to look at my second set of 'fabricated' numbers.

27 (1)
36 (2)
22 (3)
1 (4)
10 (5)
3 (6)
16 (7)
29 (8
23 (9)
0 (10)
20 (11)
8 (12)
35 (13)
1 * (13)
20 * (13)
12 (14)
21 (15)
23 * (15)
36 * (15)
0 * (15)
11 (16)
15 (17)
18 (18)
2 (19)
15 * (19)
22 * (19)
8 * (19)
13 (20)
27 * (20)
30 (21)
8 ** (21)
2 * (21)
4 (22)
6 (23)
34 (24)
16 * (24)
3 * (24)

So in that second 'fabricated' group of 37 numbers, There are 24 original numbers and 13 numbers missing.

So looking at all three sets of numbers which include the original set and the two 'fabricated' sets.

There is the following.

24 original  13 missing.
25 original  12 missing.
24 original  13 missing.

This fits in nicely with the 'rule of the third'.

PART 2 TO FOLLOW....... I will show you how to combine all three sets in a way which 'shrinks' the wheel and gives you a bet which produces some very nice results.

[flukey luke]

One important part that I should have added was the numbers that are missing from the three groups.

In the original set of numbers, there are 13 numbers missing.
2,5,9,11,17,18,19,20,22,24,28,32,36.

In the first set of 'fabricated' numbers, there are 12 numbers missing.
1,11,18,20,25,27,29,32,33,34,35,36.

In the second set of 'fabricated' numbers, there are 13 numbers missing.
5,7,9,14,17,19,24,25,26,28,31,32,33.

All these numbers that are missing can be left out on the actual physical wheel.

As an example, you know that in the first set of 'fabricated' numbers, the number 11 never appears. Now bare in mind this is not the actual physical number 11 that you see on the wheel. Remember how I worked it out. Let's say the current number on the actual physical wheel is 33. If you count clockwise 11 pockets, you will come to number 12. So if I want to leave out the 'fabricated' 11, I will not be playing the 12 on the following spin after the 33.
Now suppose the next number out is 10. Now if I want to leave out the 'fabricated' 11, I will need to count 11 pockets clockwise from the 10 and I arrive at 22. So if I want to leave out the 'fabricated' 11 on the next spin, I don't play the number 22.

If you add up all the missing numbers from the three sets, 13+12+13 = 38.
Now there are only 37 numbers on the wheel. Some of the missing numbers do overlap. But what you will find when I show you more details in PART TWO is that actually only around 8-12 numbers are what I would call 'playable' in any 37 spin cycle.

[flukey luke]

I am able to start PART TWO here.

If you digested the previous information, you will know that I am working with three sets of numbers.
One is the actual physical numbers as they appear on the wheel and the other two are sets of fabricated numbers.
(a full explanation of how I arrive at those is explained above)


I will be using the same set of numbers that I downloaded from the Spielbank-Wiesbaden Casino.

These were as follows. 4,31,30,15,16,26,29,8,0,23,23,6,14,12,13,33,8,29,15,14,14,25,3,21,23,1,23,
31,7,34,27,35,0,4,10,7,23,26.

This is now the hardest part and you will probably need to read this several times to get the hang of things.

Starting from the 4 and moving to 31 gives me the following results working out the three sets of numbers.
31, 22, 27,

Now, if I was wanting to find out if there is a bet on the next spin, how would I go about it?
For a start, the 31 just stays the same. The 22 means I need to count clockwise on the physical wheel from the 31 and move around 22 pockets. I arrive at 27. The 27 means I need to count clockwise on my 0-36 clock from 31 and move forward 27 numbers. I arrive at 21.

So I am left with 31/ 27/ 21. Do any of these numbers match up in all three sets? The answer is no, therefore there will be no bet. Only if a number matches up in all three groups, will you bet that number/s.

So let's move on and look at the 31 to the 30. Working out the three sets of numbers gives me 30, 26, 36.

I combine these with the first group giving me 30-31, 22-26, 27-36.

Now using the 30, 26, 36 to see if there is a bet on the next spin. Once again the 30 just stays the same. The 26 means I need to count clockwise on the physical wheel from the 30 and move around 26 pockets. I arrive at 4. The 36 means I need to count clockwise on my 0-36 clock from 30 and move forward 36 numbers. I arrive at 29.

An important procedure to note here is that you also need to repeat the calculations with the 31, 22, 27 as well.

So after doing this, I am left with 30,31/ 0,4/ 20,29. Do any of these numbers match up in all three sets. The answer is no and therefore there is no bet.

So let's move on and look at the 30 to the 15. Working out the three sets of numbers gives me 15, 24, 22.

I combine these with the first and second group giving me 15-30-31, 22-24-26, 22-27-36.

Now using the 15, 24, 22 to see if there is a bet on the next spin. Once again the 15 just stays the same. The 24 means I need to count clockwise on the physical wheel from the 15 and move around 24 pockets. I arrive at 31. The 22 means I need to count clockwise on my 0-36 clock from 15 and move forward 22 numbers. I arrive at 0.

Once again, I need to repeat this procedure with the 30+31 from the first set of numbers, with the 22+26 from the second set of numbers and with the 27+36 from the third set of numbers.

So after doing this, I am now left with 15-30-31/ 20-22-31/ 0-5-14. There is no match up of any number in these three groups and therefore there is no bet. (a number has to match in all three groups)

So I hope you are starting to get the idea of how things are calculated.

I will stop here and wait for any questions!

[flukey luke]

It would be great if some kind soul could develop a programme which can calculate these steps. The important thing here is that it would eliminate any mistakes for the bet that I am going to suggest. There truly is a brilliant way to take advantage of this and I am happy to share but it would be really nice if everyone had access to it. I think it would be really appreciated if someone could help.

[chrisbis]

Interesting stuff at 7 in the morning, which was 11 last night, counting round the clock face till I get to 7 which gives me 8 hours kip!

Ok, fun over .

John. Where did this ZERO pop up from in Ur calcs?
I can Not find reference to it anywhere, previously?

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[Normy2000]

An important aspect to consider is that if a number from the original list repeats, you can not then count any pockets moving clockwise, therefore the number will be a 0.

[flukey luke]

Good try Normy but not correct.

Let's start from the top.

Number 4 goes to 31 on the physical wheel. On your second set, you count around the physical wheel from the 4 to the 31=22. On your third set using the 0-36 clock, you count around from the 4 to the 31=27.
So you are left with 31,22,27. Now here is the part I think you are having trouble understanding. The 31 is from the physical wheel. Remember the 22 and the 27 are not. They are fabricated using movement. This means for every subsequent number that appears, all these fabricated numbers from sets 2 and 3 are going to need to be readjusted.
Let's assume you wanted to have a bet on the 31,22,27 on the next spin. You would bet on the physical 31. You certainly would not bet on the physical 22 and 27. So let me show you how to adjust these. You need to use the current physical number which has appeared to make the adjustments. This is 31. Now from the 31, count around 22 pockets clockwise on the wheel (remember this is for the second set) you will arrive at 27. Now from the 31, count around 27 pockets on your 0-36 clock (this is for the third set) you will arrive at 21.
So your original 31,22,27 has now morphed into 31,27,21 because of the adjustments.
You need to keep making these adjustments after every number appears (except the first set number which is from the physical wheel)
This explains why the 31,22,27 morphs into 31,27,21 and why the 30-31, 22-26, 27-36, morphs into 30-31, 0-4, 20-29.

[flukey luke]

What I am going to do is wait and see if anybody wants to help and create a programme for this. I feel that if I go right into things, it will just get very complicated and messy and I am then wasting everybody's time.
Let's face it, this is not something you would ever have the time to calculate in a real casino unless you understood everything like the back of your hand and had managed to code everything in a way which fits neatly together.
A lot of it probably gets lost in the translation. On saying that, I am not running away from it. I think the best thing I can do is start up ONE thread and treat it like a blog. I can just slowly put things on there which I think people may find interesting.