WardBlack's "Rolling Dozen" reprised..........

[TwoCatSam]

This is only food for thought.  No bloviation.  No smoke and mirrors.

Dang!  Lost half the crowd with the first sentence!!!

Ward came up with--what I think--is a truly original idea.  (Notice the caveat.)

You watch the numbers fall.  There will come a time in the trot where you have exactly 12 numbers which have not hit.  A dozen.  Or is it?

Some of the numbers that came may have came three or four times.  No matter.  Your 12 will appear.  Mathematically impossible not to.

Now here was Ward's logic:  If you have a minimum of 25 and a maximum of N spins, that means the "12" has slept for a minimum of 25
spins.  Maybe 40 or more spins. 

A dozen just doesn't sleep that long!!

Wow!!  I thought......he's right.  Well, not so fast.  I tested this 'till I needed cataract surgery and found it was not true.  What I found was
Ward had actually identified 12 sleepers.  After the 13th unhit number had hit and left 12.....seems they went for many spins without hitting.

Poor ol' dumb haid!!  Never occurred to me to bet the other 25!

So here's the food for thought:

1.  We know a dozen will rarely ever sleep for 25 spins.
2.  We know we will always get a dozen(?) that has, in fact, slept for 25 or more spins.
3.  What the heck?

Here's the big question:  Is twelve numbers who have not hit the same as a dozen that is identified by a dozen/column designation?  What about
two lines?  Four streets?  Lines and streets in far areas of the carpet?

Here's the really big question:

Is this Ward Black dozen really a dozen.  I mean it's 12, but it does not behave like a dozen.

I have spent countless hours studying on this problem.  It's gotten me through many a boring sermon.  I still have no answer.

My conclusions are that the Ward Black Dozen does not have a greater chance of hitting because it has slept for a minimum of 25 spins.  I
feel it has a lesser chance because Ward has identified twelve individual sleepers.

I'd love to have a discussion on this.

TwoCatSam

[buffalowizard]

Hi Sam. Interesting topic you raise. I have had similar findings. I used to look a lot into single street bets and wait until 3 or nine numbers had not hit. this was quick pain free and simple. Only it wasn't pain free because like you suggest after 10 or so spins and you thinking this is it, they would go on sleeping far longer and more frequently. So maybe there is a subtle difference

[TwoCatSam]

subtle difference

Wiz

Do you mean a difference between an identified dozen (2nd dozen) and a dozen singled out by the Ward Black idea?

To my mind there has to be, but it is a paradox.  Where's that Parrando fellow when you need him?

TCS

[ADulay]

   Just off the top of my head and with little or no serious thought about what I'm about to write, how about if you plot those "sleeping individual 12 numbers" on the wheel and target bet the SECTOR that those dozen numbers might be sitting in?

   If the 12 sleeping numbers are all over the wheel, then it's probably not worth wagering on AT THAT TIME but should the sleeping dozen start to congregate in any sized sector of note, would that not be a tageted area to play?

AD

[TwoCatSam]

AD

Thanks for your reply; I'm happy to answer.

Imagine you sit down/log on.  Take the first number that comes, say 17.  It is dead.  Every number after 17 is dead.  No matter how many times 17 hits, it's just plain dead.

You keep doing that and you will wind up with 12 numbers that are "alive".  No sectors involved.  No defined anything.  Just twelve individual numbers spread out around the wheel and across the carpet where ever they are. 

Now twelve is a dozen.  But a dozen rarely--very rarely--sleeps for 25 or more spins.

So what have we got?  I can't answer the question, but I think when it is answered it will lead to good things.


Sam

[TwoCatSam]

AD

I see your point about them congregating.  Never thought of that.

Imagine this:  While a sleeper is sleeping, it has less of a chance to hit than the other numbers.  No?  No.  Same chance, yet it sleeps.  Why?

What if these 12 were sleepers and had less of a chance--by sleeper standard---than the other 25?

This would be a wonderful computer study.  Well, I think it would....

Sam

[buffalowizard]

subtle difference

Wiz

Do you mean a difference between an identified dozen (2nd dozen) and a dozen singled out by the Ward Black idea?

To my mind there has to be, but it is a paradox.  Where's that Parrondo fellow when you need him?

TCS

Yes that's what I mean. It's as if doZens or any form of number clusters behave differently if they are leftover or dead numbers. Perhaps it's a kick in the teeth for those who think betting cold numbers  or furthest back is the way to go.

[VLS]

Hello dear Sam,


Bayes already provided an answer to this question:

It's a little like the classic 'birthday problem' in probability which I mentioned in another thread recently.  A PARTICULAR dozen (ie; the 'standard' dozen, not just any 12 numbers) is indeed unlikely to sleep for 37 spins, but the probability of SOME 12 numbers sleeping that long is much higher, because there are a lot of ways you can choose 12 numbers from 37.

Topic: link:://rouletteforum.cc/roulette-and-gambling-framework/5/infrequent-events/230/msg1494#msg1494


Regards.

[TwoCatSam]

While playing the G.U.T. and using Track4, I always come to the 12 unhit numbers.  They are spelled out.  Seems when I get there, they just don't hit unless it's a crossing.   Not wanting to drift into that subject, but it reinforces my idea here.

[TwoCatSam]

Thank you Mr. Victor VLS.............


Geez, that was back in 2010.  I said some brilliant stuff back then  must go back and read it!!

JUST KIDDING!!

Sam

[VLS]

I actually wrote this too:



Hello dear Sam,

For properly analyzing this Wardblack’s rolling dozen event, start by considering it's not formed by a fixed set of pre-selected numbers (i.e. layout's columns/dozens), it's defined by ANY set of 12 numbers that sleep.

Ponder:

“Find an instance of numbers 1 to 12 that have slept for 37 spins.”

Is very different from:

“Find *ANY* set of numbers that have slept for 37 spins.”

There is only one set that complies with the first case, while there are a crapola of sets which will comply with the second.

Imagine as if it were a bingo game. Every set of  37 spins representing a full game.

Player A’s trategy is to buy only one bingo card per game.

Player B’s strategy is to buy-in all the possible cards.

No matter what the outcome is, Player B will have a valid card at the end of the game.

On the other hand, Player A will likely have to wait a lot of hands before the game accomodates the outcomes as seen exactly on his card.

Likewise, this Blackward’s dozen observation is simply a situation of “one among many" versus “many among many".

The expected outcome of sitting by the table expecting to witness a case of a pre-selected “1 to 12 dozen” to sleep is to have to wait a considerable amount of time, while “Mr. Blackward” has all the possible combinations on his hand, so by the end of the game it is certain one of his dozens would have slept -he has them all (every other non 1-to-12 combination).

Regards.

[VLS]

Funky order of appearance though


Thank YOU for keeping the discussion alive.


These days I don't really devote much time to creating new methods and pondering philosophical questions about the game.


--I'm focused on a certain Tool that is going strong -so far. (knock on wood)...

[TwoCatSam]

Thank you, my friend.

I have forgotten much!!

You are so right in your analysis.

Thank you two years later!

Sam

[GARNabby]

I think that this discussion has more to do with MM.

With a positive betting progression, it's nice to win a lot of series early, but you risk waiting a while before winning any; conversely, with a negative betting progression, it's nice to think that you could go a very-long time without losing a series, but you are (more exposed to the "vig" while) grinding out small profits relative to the average amount of the series being bet.

This must be taken into consideration together with how you intend to beat a casino-game (to best determine your MM.)

[Turner]

AD

  No?  No.  Same chance, yet it sleeps.  Why?

because....when 12 is sleeping....and is mabe on its 99th sleep....the next number our(33) isnt thinking "ive been out 3 times in 20 spins...where my old mate no.12?"
Each number is totally independant with no memeory or relation to the last or next number.

With that in mind...there is no reason at all why all numbers will sleep for long times.

No one is counting only us humans looking for patterns.