would love to get the answer to this math question

[simon]

A roulette wheel with 36 numbers and no zeroes is spun 200 times.  We are not concerned with house edge, bets or payouts, only to know if after 200 spins of the wheel, can we expect to see more of one particular sequence of events vs another particular sequence of events.

The wheel is divided between two groups of numbers.  Group A has 20 numbers and Group B has the other 16 numbers.  After every spin of the wheel, the outcome decisions of "A" or "B" are recorded one after the other.

After 200 spins, two particular sequence of events will be counted:

Sequence 1 is:  (....A-B-A...) which means, a single B contained within one or more A's.

Sequence 2 is:  (....A-B...B-A...) which means, two or more B's contained within one or more A's.

To put it another way, every time we see a single B in the pattern we will call this a B "chop", and every time we see 2 or more B's in a row in the pattern, we will call this a B "run."

My questions:

1)  After 200 spins, can we expect to see more B "chops" than B "runs"?

2)  After any amount of spins, can we expect to see more B "chops" than B "runs" and if so, how many spins are required for their to be a majority of B chops over B runs by a margin of at least 20%?

Reasons we might expect to see more B chops than B runs within x amount of trials:

1)  It has been stated that we can expect half as many runs (consecutive decisions of the same outcome) of 2 as runs of 1, and 1/2 as many runs of 3 as runs of 2, and half as many runs of 4 as runs of 3, etc... So that in for example 247 trials the ideal distribution of runs is 64 runs of 1, 32 runs of 2, 16 runs of 3, 8 runs of 4, 4 runs of 5, 2 runs of 6, and 1 run of 7, and the total of any run within x amount of trials will be equal to the total of all runs greater (which is why it is useless to "wait" for a long run of one particular chance in order to bet the opposite, because in the long run the total of all runs that will occur that are longer than the run you are betting against, will be equal to the total number of runs that you thought were safe to bet against, and the house edge will prevail.)

Therefore, we should expect to see half as many runs (two or more B's in a row within the pattern) as chops (one B within the pattern.)

2)  Since there are less numbers in Group B than Group A, B is less likely to repeat, and more likely to be followed by A.

Reasons we should not expect to see more B chops than B runs within x amount of spins:

The above two statements are either not valid, or not valid as concerns this particular trial.

[gizmotron]

Just one question about these runs. Why should each 200 - 247 set of spins produce similar results. Each time you sit down for eight hours of play you see something completely different. I mean you will still see runs and chop but they won't be happening at the same times for each session. In a case like this, recognizing the differing types is more important than the timing. Don't you have a plan for the different types of conditions that you see? I would be more concerned about the duration of the dominating conditions. Some times trend patterns reveal to you similar sized forms of domination types. There's no math to help you here. Each session will mostly be different. If you want a baseline then test millions of spins to get the averages.

[Herb]

In the random game of roulette there are no trends, and there are no patterns.  There are only disconnected links.  There's nothing there that you can exploit.

[gizmotron]

In the random game of roulette there are no trends, and there are no patterns.  There are only disconnected links.  There's nothing there that you can exploit.

Hey Herb, if you begin to bet on black after five blacks in a row and the blacks continue to hit for ten more spins have you used a reason for betting black or not?

[Herb]

No

[gizmotron]

No

So that advertisement on TV for pattern recognition software for the stock market is a phony concept too?

Guess what Herb, Visual ballistics and dealer signature don't exist either. In fact the roulette wheel is really a flying saucer from outer space, and the aliens always win. Gads Herb. How can you be so closed minded? It's almost astonishing. It's like defending a flat world.

[Coxx16]

Just as I suspected.....its the damn aliens! LOL

[Tangram]

Gizmo,

This doesn't mean I completely agree with Herb about the disconnected links, but stock market movements are not disconnected, because many of the patterns are based on psychology which isn't present in the numbers from a roulette wheel. History does matter in the stock market. 

[gizmotron]

Gizmo,

This doesn't mean I completely agree with Herb about the disconnected links, but stock market movements are not disconnected, because many of the patterns are based on psychology which isn't present in the numbers from a roulette wheel. History does matter in the stock market. 

Pattern recognition is a cognitive process that occurs in the mind of the observer. It is not a psychic linkage to the mechanical process for achieving a random outcome. The mechanical process is a true form of "disconnected links." The cognitive process is however not. The perception of linkage comes down to two and perhaps several conclusions. One, the "gamblers fallacy" where something must be due because something else happened, and at least that "clustering analysis" can be used for a premise to establish an imagined  bet selection process that can be tested while using it for degrees of effectiveness.

I would rather react to data than pretend that nothing is the only significant reality that can exist. I gave up on discovering that randomness was really just meaningless events. It's far more than that in my imagination.

It comes down to using what works when it is working. That works for everyone too. Nothing works very well while nothing exists. It's impossible to base bet selections on nothing though. I'm a bet selection, MM expert. I take that into casinos and win with it all the time. I could not bet based on nothing. Nothing is a vacuum of the imagination. My house does not need what sucks to clean it.

[simon]

I thought that in x number of spins, this....

we can expect half as many runs (consecutive decisions of the same outcome) of 2 as runs of 1, and 1/2 as many runs of 3 as runs of 2, and half as many runs of 4 as runs of 3, etc...

...was true (but maybe it's not-- really I don't know exactly what law of probability it is, but I have seen it here and there. )  And if it WAS true, then the system I have in mind would work, especially I would think if I am betting a larger group of numbers (group A) against a smaller group of numbers (group A to follow B, instead of a repeat of B.)

The system I have in mind would only sustain ONE loss for every run of the B group, no matter how long or short (greater than 2 in a row) the run was.  Therefore there should be more wins on single hits of a specific chance, than runs.  But that is only true if it is true that there should be half as many chops as runs of two, etc.

[gizmotron]

Your system will have differing levels of it working and differing degrees of it not working. So you might want to use a method to figure when best to use it. I have discovered that just walking into a casino and walking right up to the table does not trigger that it's a best time to use many of my systems. Sometimes pinching a c**ktail waitress triggers wins.

I'm always fascinated by rule based systems. There is no consideration for situational awareness.

[Tangram]

we can expect half as many runs (consecutive decisions of the same outcome) of 2 as runs of 1, and 1/2 as many runs of 3 as runs of 2, and half as many runs of 4 as runs of 3, etc... 

Simon,

This is only valid for the even chances (that's why successively longer streaks occur half as often). For your system, if you're talking about the "B" group streaks, then the chance of a series of 2 is (16/36)², the chance of a series of 3 is (16/36)³, etc. So the multiplying factor is not half, as in the ECs, but 16/36. ie a series of 2 will occur 16/36 times as often as a single, a series of 3 will occur 16/36 times as often as a series of 2, etc.

[Herb]

Gizmotron wrote -"Guess what Herb, Visual ballistics and dealer signature don't exist either. In fact the roulette wheel is really a flying saucer from outer space, and the aliens always win. Gads Herb. How can you be so closed minded? It's almost astonishing. It's like defending a flat world."

Sorry Gizmotron, I was just stating the facts.

[gizmotron]

Sorry Gizmotron, I was just stating the facts.

Herb, we are all entitled to our own opinions but we are not all entitled to our own set of facts. You have not made a scientific effort to refute clustering analysis and how I claim it applies to Roulette randomness too.

[Herb]

Gizmotron,

Clustering analysis???

Do you make this stuff up as you go?

[Herb]

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