Roulette's Law of Thirds

I just wrote an article about the infamous Roulette's Law of Thirds and it struck me that maybe there are more crazy things about random numbers I should be aware of.

The "Roulette Law of Thirds" states that if you spin a Roulette wheel 38 times (37 for European but lets just talk about American wheels) the following happens:

1/3 of the 38 numbers are duplicates, triplicates, quadruplicates, and more (about a dozen of them)

1/3 are missing - were replaced by the dupes (about a dozen "sleepers")

1/3 occur just once (about a dozen)

Go ahead and fill out a MS Excel spreadsheet with the =RandBetween(0,37) with 37 being Green 00 and copy it into 38 rows, or http://www.random.org/integers/ sort them (have to copy them to a notepad to get rid of the formulas and then copy them back to Excel)

You will see that for every 38 numbers generated about 1/3 are dupes, 1/3 are "sleepers" or "the sleeping dozen" and 1/3 show up only once.

Of course those numbers mean nothing when you generate the next number or the next 38 or billion but the "sleepers" and dupes are used to make hundreds of variations of Roulette systems that fail because they are based on this weird idiosyncrasy of random numbers.

But, like good humor, a super phony Roulette system, needs some truth to make it last for 200+ years. Other Roulette websites are full of folks who believe in the "Sleeping Dozen" and spend a lot of time building systems that always fail but they just can't seem to help themselves.

Is there some math behind this? Does the 1/3 "sleepers" work for a billion numbers generated for a billion slots? (I'm assuming the ratio holds - don't know why)

So, are there other things like this that occur with random numbers that can be the basis for hundreds more super phony Roulette systems? I can't think of any but that's why I'm writing this post.

Thanks for any input..........

Here is some more on that subject
Ludica - The Law of the Third
They have an Excel spreadsheet for download to look over.

Distribution for 37 spins 37 slot wheel.
Number of unique numbers

Distribution for 38 spins 38 slot wheel.
Number of unique numbers

Quote: MauiSunset

I just wrote an article.

Can I ask who you write for?

Maui,

For starters, there is no "law of the thirds".
Secondly, each spin of the roulette wheel is an independent event.

There's no reason whatsoever to even test such a system.

Please note: This supposed Rule of Thirds was developed by an Italian researcher in 1968. That means that if it worked the man would now be so rich that he would waste no time with writing articles but would be spending his well earned money on wine, women and song or else he would be off in Monte Carlo (the real one) winning untold sums at roulette and bankrupting the monarchy.

This paragraph is precious:
it's true that the percentage of the 100% of winning does not exist, but it's also true that 'The Law of the Third' is a undeniable truth which its sistemic application guarantees the probability of 67% to win the chosed chance within the first extractive fraction of the related cycle"

67 percent probability of winning at Roulette, providing of course that we are within some extractive fraction of a related cycle since apparently the wheel chooses to go in cycles that somehow differ from each other perhaps on the cosmic plane if we are seated under a pyramid.

Quote: odiousgambit

Can I ask who you write for?

I have a little website and YouTube videos that make fun of Roulette systems - you can do a search of my name and Roulette and find me if you wish.

Quote: Keyser

Maui,

For starters, there is no "law of the thirds".
Secondly, each spin of the roulette wheel is an independent event.

There's no reason whatsoever to even test such a system.

I know that, what I'm asking is if there are other quirks of random numbers that hoards of gamblers now or in the future can spend millions of man-hours and millions of dollars making fools of themselves - I'd love to write about it.

Quote: FleaStiff

Please note: This supposed Rule of Thirds was developed by an Italian researcher in 1968. That means that if it worked the man would now be so rich that he would waste no time with writing articles but would be spending his well earned money on wine, women and song or else he would be off in Monte Carlo (the real one) winning untold sums at roulette and bankrupting the monarchy.

This paragraph is precious:
it's true that the percentage of the 100% of winning does not exist, but it's also true that 'The Law of the Third' is a undeniable truth which its sistemic application guarantees the probability of 67% to win the chosed chance within the first extractive fraction of the related cycle"

67 percent probability of winning at Roulette, providing of course that we are within some extractive fraction of a related cycle since apparently the wheel chooses to go in cycles that somehow differ from each other perhaps on the cosmic plane if we are seated under a pyramid.

I kind of assumed that the Law of Thirds has been around for 200+ years - I'll do some research and see if I can find the first clown that started this all - kind of like a "Clown Zero".

Thanks much guys...........

Quote: MauiSunset

I know that, what I'm asking is if there are other quirks of random numbers that hoards of gamblers now or in the future can spend millions of man-hours and millions of dollars making fools of themselves - I'd love to write about it.

I can't speak to 'hoards of gamblers', but Ken (mrjjj) has posted quite a variety of systems that he wins with. If you go to posts he started you will find them. They focus on 'sleeping streets', numbers that have hit 3 times recently, numbers that haven't, etc...

Quote: guido111

Here is some more on that subject
Ludica - The Law of the Third
They have an Excel spreadsheet for download to look over.

Distribution for 37 spins 37 slot wheel.
Number of unique numbers

       group         middle     freq  freq/100
----------------------------------------------
13.50 <= x < 14.50    14.00        2     0.00%
14.50 <= x < 15.50    15.00        8     0.00%
15.50 <= x < 16.50    16.00       75     0.01%
16.50 <= x < 17.50    17.00      546     0.05%
17.50 <= x < 18.50    18.00     2928     0.29%
18.50 <= x < 19.50    19.00    11871     1.19%
19.50 <= x < 20.50    20.00    36258     3.63%
20.50 <= x < 21.50    21.00    83709     8.37%
21.50 <= x < 22.50    22.00   147735    14.77%
22.50 <= x < 23.50    23.00   199500    19.95%
23.50 <= x < 24.50    24.00   204807    20.48%
24.50 <= x < 25.50    25.00   159242    15.92%
25.50 <= x < 26.50    26.00    94069     9.41%
26.50 <= x < 27.50    27.00    41714     4.17%
27.50 <= x < 28.50    28.00    13654     1.37%
28.50 <= x < 29.50    29.00     3244     0.32%
29.50 <= x < 30.50    30.00      547     0.05%
30.50 <= x < 31.50    31.00       86     0.01%
31.50 <= x < 32.50    32.00        5     0.00%

----------------------------------------------
                     grouped data
items:                  1000000   

minimum value:               14.00
first quartile:              22.00
median:                      24.00
third quartile:              25.00
maximum value:               32.00

mean value:                  23.57
midrange:                    23.00

range:                       18.00
interquartile range:          3.00
mean abs deviation:           1.53

sample variance (n):          3.61
sample variance (n-1):        3.61
sample std dev (n):           1.90
sample std dev (n-1):         1.90

----------------------------------------------
                  cumulative
----------------------------------------------
13.50 <= x < 14.50    14.00        2     0.00%
14.50 <= x < 15.50    15.00       10     0.00%
15.50 <= x < 16.50    16.00       85     0.01%
16.50 <= x < 17.50    17.00      631     0.06%
17.50 <= x < 18.50    18.00     3559     0.36%
18.50 <= x < 19.50    19.00    15430     1.54%
19.50 <= x < 20.50    20.00    51688     5.17%
20.50 <= x < 21.50    21.00   135397    13.54%
21.50 <= x < 22.50    22.00   283132    28.31%
22.50 <= x < 23.50    23.00   482632    48.26%
23.50 <= x < 24.50    24.00   687439    68.74%
24.50 <= x < 25.50    25.00   846681    84.67%
25.50 <= x < 26.50    26.00   940750    94.08%
26.50 <= x < 27.50    27.00   982464    98.25%
27.50 <= x < 28.50    28.00   996118    99.61%
28.50 <= x < 29.50    29.00   999362    99.94%
29.50 <= x < 30.50    30.00   999909    99.99%
30.50 <= x < 31.50    31.00   999995   100.00%
31.50 <= x < 32.50    32.00  1000000   100.00%

                    

Distribution for 38 spins 38 slot wheel.
Number of unique numbers

       group         middle     freq  freq/100
----------------------------------------------
14.50 <= x < 15.50    15.00        4     0.00%
15.50 <= x < 16.50    16.00       17     0.00%
16.50 <= x < 17.50    17.00      175     0.02%
17.50 <= x < 18.50    18.00     1166     0.12%
18.50 <= x < 19.50    19.00     5613     0.56%
19.50 <= x < 20.50    20.00    19566     1.96%
20.50 <= x < 21.50    21.00    51920     5.19%
21.50 <= x < 22.50    22.00   107810    10.78%
22.50 <= x < 23.50    23.00   169362    16.94%
23.50 <= x < 24.50    24.00   204896    20.49%
24.50 <= x < 25.50    25.00   189740    18.97%
25.50 <= x < 26.50    26.00   135346    13.53%
26.50 <= x < 27.50    27.00    72917     7.29%
27.50 <= x < 28.50    28.00    30183     3.02%
28.50 <= x < 29.50    29.00     8936     0.89%
29.50 <= x < 30.50    30.00     2001     0.20%
30.50 <= x < 31.50    31.00      315     0.03%
31.50 <= x < 32.50    32.00       31     0.00%
32.50 <= x < 33.50    33.00        2     0.00%

----------------------------------------------
                     grouped data
items:                  1000000   

minimum value:               15.00
first quartile:              23.00
median:                      24.00
third quartile:              25.00
maximum value:               33.00

mean value:                  24.20
midrange:                    24.00

range:                       18.00
interquartile range:          2.00
mean abs deviation:           1.54

sample variance (n):          3.72
sample variance (n-1):        3.72
sample std dev (n):           1.93
sample std dev (n-1):         1.93

----------------------------------------------
                  cumulative
----------------------------------------------
14.50 <= x < 15.50    15.00        4     0.00%
15.50 <= x < 16.50    16.00       21     0.00%
16.50 <= x < 17.50    17.00      196     0.02%
17.50 <= x < 18.50    18.00     1362     0.14%
18.50 <= x < 19.50    19.00     6975     0.70%
19.50 <= x < 20.50    20.00    26541     2.65%
20.50 <= x < 21.50    21.00    78461     7.85%
21.50 <= x < 22.50    22.00   186271    18.63%
22.50 <= x < 23.50    23.00   355633    35.56%
23.50 <= x < 24.50    24.00   560529    56.05%
24.50 <= x < 25.50    25.00   750269    75.03%
25.50 <= x < 26.50    26.00   885615    88.56%
26.50 <= x < 27.50    27.00   958532    95.85%
27.50 <= x < 28.50    28.00   988715    98.87%
28.50 <= x < 29.50    29.00   997651    99.77%
29.50 <= x < 30.50    30.00   999652    99.97%
30.50 <= x < 31.50    31.00   999967   100.00%
31.50 <= x < 32.50    32.00   999998   100.00%
32.50 <= x < 33.50    33.00  1000000   100.00%
             

Thank you very much - I'll spend some time studying this. I appreciate the link.

Quote: SOOPOO

I can't speak to 'hoards of gamblers', but Ken (mrjjj) has posted quite a variety of systems that he wins with. If you go to posts he started you will find them. They focus on 'sleeping streets', numbers that have hit 3 times recently, numbers that haven't, etc...

Oh I'm well aware of Mr J - he has deleted and modified many of my posts on the websites he administrates; I don't waste my time there anymore; they are true believers and beyond salvation.

The Law of the Third has many disciples - someone has to make the casinos rich...............

Quote: MauiSunset

"Clown Zero".

I don't care that you wrote this, I'm totally stealing it. Next time I see a group of idiots doing something stupid, I'm going to ask them which one is Clown Zero.

Basically - and this will help you understand the "rationale" behind many systems - if an effect will occur on average once in a given span of many trials (15 is a fairly decent over/under for "many"), it has only a slightly higher chance of happening once than of not happening, and these chances converge on about 36.8% (=1/e), so not far off from a third. This leaves slightly more than one in four "dupes."

Consider that something with a one in n chance of happening, in n trials, will fail to happen with probability ((n-1)/n)^n, as is common sense. It's also not hard to see that it will happen only once, on a certain trial with probability (1/n)*((n-1)/n)^(n-1). So if it can happen at any trial, so long as it only happens once, this becomes ((n-1)/n)^(n-1), so the ratio of the probabilities of it happening exactly once and not at all is (n-1)/n, which is reasonably close to 1 for something like a roulette wheel or a 52-card deck.

A billion pulls of the lever, if there are a billion equally likely outcomes, will see 36.8% "sleeper" outcomes for the same reason.

Does anyone else think that MauiSunset and Ken might be identical twins who were separated at birth ??

That's a horrible thing to say. S/he's fallen into some lunacy, but lunacy that superficially makes a modicum of sense, not Ken's kind of lunacy that falls dead at the first whiff of reason, adherence to which drove him to argue against reason itself.

I had a very strong suspicion it was 1/e, but hadn't bothered to do the Maths to confirm. Thanks, I needn't bother now.

Quote: 24Bingo

That's a horrible thing to say. S/he's fallen into some lunacy, but lunacy that superficially makes a modicum of sense, not Ken's kind of lunacy that falls dead at the first whiff of reason, adherence to which drove him to argue against reason itself.

Actions speak louder than words. Both want to convince you that Roulette can be beaten. At this point in time Ken's case is stronger.

no one's case is stronger until I see them beaming proudly at a roulette wheel and the former casino owner slinking off in tears.