Some musings on the math inspired by JAW OF THE THIRDS by Dane

[TwoCatSam]

Hello

Let's think of an event.  Not a number of spins, but an event.   It is an EVENT.  An EVENT may be one or two spins and either one, two, or three different outcomes. Got it?

We look at the carpet and think A and Not A.  A is the column/dozen we bet on and Not A is everything else.  So there is no dozen 1, 2, or 3 and likewise with the columns.

Now let's play an EVENT.  We place a bet on A.  (Makes no difference what column or dozen it is; it is A)  Let's look at the three outcomes:

1.  We win the first spin.  We hit A.  The event is over in one spin.
2.  We hit Not A.  The event is not over and we must spin again.
3.  We hit A and win one unit for the event.
4.  We hit Not A twice in this event and lose two units.

Now it would appear there may be four outcomes, but there are only three:  Win two units, win one unit or lose two units.

Now let's play 1,000 events.  EVENTS, not spins.

Here's how the breakdown looks:

333 times we will win two units.
555 times we will win one unit.
444 times we will lose two units.

So we have 666 units won + 555 units won and 888 units lost.  Calc that out and it's a whopping 333 units profit for this thousand event trial.

NOW I KNOW THIS IS WRONG!!  But I can't find the flaw in the math.

Someone help..

Samster

[Colbster]

The flaw is that 333+555+444 doesn't equal 1000.  You will win 1/3 of the time (333 x +2).  Of the remaining 2/3 of the time, you will win 1/3 (222 x +1).  You will lose 2/3 of 2/3 (444 x -2).

666+222-888 = 0

Sorry!

[TwoCatSam]

Don't be sorry!!

I asked where I was going wrong.  I'll study it and see it for myself.

Thanks, Colbster.

Sam

[psimoes]

It got me thinking too. But YES vs NO is for ECs. When you think of betting one dozen, the other two have iqual chances of hitting like the one youŕe thinking so it could be more like YES vs PROBABLY vs NO, NOT REALLY.


Suppose you bet on Dz1 for the first spin and Dz2 hits. For the next spin Dz2 has less chance of hitting a second time in a row (like in same dozen hitting four times in a row is a rare event; hitting three times less rare than four; hitting two times less rare than three; hitting one time only, the least rare).
Now for that second spin, we concentrate on Dz1 and Dz3. If you go for Dz1 you are giving it a second opportunity to appear. Dozens are abstract, Ok, but a bankroll is for real. The returns you expect directly correlate to how much you bet on what. It could be as simple as that.

[GLC]

Psimoes,  I want to point out one concept that gets overlooked when talking about rarity of events.  If you spin dozen 2, how does that make it less likely that dozen 2 will hit on the next spin.  It always has the same chance of hitting every spin.  Now if you say the odds of dozen 2 hitting on the next four spins in a row, that's uncommon.  But if it's already hit 3 times in a row, it has the same odds of hitting that 4th time in a row as not.  This is why waiting for a trigger of say dozen 2 hitting 3 times in a row and then betting against it hitting the 4th time in a row based on the reasoning that 4 hits in a row is fairly rare is a fallacy because the 3 hits in a row are past history.  It's that same as if a blind man walked up to the table and said he wanted to bet on Black but he didn't know that Black had just hit 18 times in a row.  And it doesn't matter because once Black has hit 18 times in a row, it has the same chance of hitting again on the 19th spin as Red does.

At one time I was sucked in by the idea that if I wait until something has occurred a certain number of times and then start betting it, I was giving myself an advantage.  I was wrong.  Even if I wait until there are 20 Blacks in a row, the next spin could just as easily be a Black as a Red.

So what we're saying is that every time we get 20 Blacks in a row, which won't be very often, the chance of it going to 21 in a row is the same as it ending with 20.  If that event happened 10 times in one evening, you should win either 5 times and lose 5 times or win 4 times and lose 6 times (one time to the zero).

I know that I'm stating the obvious but I'm doing it for the newbie's sakes.  By the way, we like to ignore the obvious, otherwise things would be pretty quiet on this and other roulette forums.

GLC

[psimoes]

GLC, at this point, I have to say it has to be a paradox. The deeper we dig into chaos everything is false and everything is true. There is nothing axiomatic about it, thus we need to change the paradigm in order to, you know, at least have a glimpse of what it's all about. I lack the vocabulary needed. It's about frame of mind, as you say there. It's why I like to question what may seem obvious, from time to time. It's boring to read, I know. But I say we must clean our mind (I'm not sayin this Kuato-style btw) from what we've been told. And start from scratch. Reset. I know what a fallacy is, I just don't label something as such so easily.

I'll quote a brief paper on probability that's around in the net:

"What about that graph above?

In the graph of the probability of seeing the same colour over multiple spins of the wheel, it shows that the probability of the result being the same colour halves from one spin to the next.

However, this is only if you're looking at the set of trials/spins from the start.

If the last spin was red, the chances of the next spin being red are still 48.6% -- they do not drop to 23.7%. On the other hand, if you hadn't spun the wheel to see the first red result and wanted to know the probability of seeing red over the next 2 spins (and not just on the next 1 spin), the probability would be 23.7%."

(end of quote)

This almost reminds: If a tree falls in a forest..."

But it's rather simple. The probability of an even chance being 50% is only a static concept, an idea. Now a string of even chances no matter if red or black is that idea put into practice. It's something that is actually happening. Advance.
It's all in the context, but we can't deny the importance of past history. As long as there is memory and some record of those events we will have to acknowledge that some fact occurred. For one what happened had to happen. We don't need to be able to explain why it happened. Science can't and it's bugged since ever that it can't predict when such phenomena start and end. Yet it accepts the idea of a trend which by its own definition is something that won't last forever. More than 20 reds occurred at some time and ended because the opposing chance wanted to have a word with that trend. 
Science, or better, Western Knowledge is empirical thus is deeply rooted in Past History of events. We know for instance that after Winter there will be Spring then Summer then Fall because it's been going like that for a while. However there's a kind of vanity that makes it refute anything it can't prove, as fallacy. Science is always in progress, which is proof enough of its imperfection. In the early 20th Century some respected Doctor professed in a conference at the Royal Academy that science had reached its peak. In that age of prodigies such as electricity and steam, he said, there was absolutely nothing more to discover or to invent. What a brilliant mind! We know everything!

Sam mentioned Yin & Yang and it was about time. You know what is the oldest book ever written? It's called The I Ching. The Book of Change. I've spent a good part of my life consulting that book. Buy the edition translated by Richard Wilhelm with a preface by Gustav Jung. Just the preface is obligatory read. Without it you may well find the I Ching a bunch of gibberish.There he explains the differences between intuitive wisdom of eastern civilization and rationale thinking. Each one has an even chance in dealing with Chaos.

For me, using method and intuition is key to better gambling.

I didn't say anything meaningful really, did I? Sorry!...

[psimoes]

yeah I forgot to explain about the dozen 2 not repeating, lol. let's see: we use Ecs for better understanding.
We look at R B R B R B and count 6 single events, then look at R R R R R R and count it as 1 single event. We deduce then that the repeating event is rarer, when in reality it's an equal number of events. My fault. there's some reasoning to it but not in this specific context. Still "a priori" the fundament may be true because we must start from "somewhen". We have to be really picky, down to the most insignificant grain of sand if we want to decode Randomness. First we think of probabilities in terms of static ideas. We consider three dozens as abstractions in some dimension in time where time itself doesn't even exist. Once we're given the idea of a process, that is three spins, then our "ideal" dozens will show up all three. It's perfect. All the talk about a dozen repeating, that's for later. For now Dz2 will not repeat because the concept of repetition is still secondary. Shows up once, won't show up twice. And it should be like that because a repetition is just a reflection of a corruption in the process, influenced by some external factor. I believe this ideal state shows up time and time again as we can verify in the history of outcomes. Something like a Dozen Messiah? Well, either these thoughts deal with quantum mechanics or with medieval thinking. Or just maybe plain idiotic. Your interpretation... Cheers!

[Colbster]

There is no future advantage by playing against the dozen that has just hit as George explained.  That said, the future spin will quickly become part of the past and part of the huge number of spins that conform to the odds in the long term.  No, there is no advantage but it will very likely appear as you would anticipate.

[psimoes]

Colbster, you seem to do the number-crunching right. What are your thoughts on the Jaw formula?

[TwoCatSam]

Here's the rub............

You rarely see five ECs in a row, i.e., RRRRR.  I know math will predict how often this should happen, just not when.

So you look at four ECs in a row and say, "Man, it rarely goes five in a row.  I'll bet against it."

So you have a conundrum.  It has the same chance of hitting, but it rarely does.  What's a boy to do??

Samster

[Colbster]

Colbster, you seem to do the number-crunching right. What are your thoughts on the Jaw formula?

It is flawed on the premise that we expect positive results from following a past spin in any way other than for making bet selection easier.  After one third has hit, each of the thirds still has equal odds of occurring.  We don't have 55% as promised, but rather just 33%.  We have 55% odds that, over the next two spins, we will get a hit on the third that we have chosen.  We can't utilize a paper loss to give ourselves an edge here.  We could just as easily arbitrarily pick any of the thirds and bet 2 spins and have the same odds.

[psimoes]

There's a sense of DOOM each time we talk about Prob theory, isn't it? It's good at observing past events but still gives no guarantee about the future based on same past events. It's not really of much help, is it?

I just downloaded Grabb's RC. It can be of some use in combination with BRaG.

[TwoCatSam]

We have 55% odds that, over the next two spins, we will get a hit on the third that we have chosen., opined Colbster.

Well, that sounds like a good thing.

Sam

[psimoes]

Here's the rub............

You rarely see five ECs in a row, i.e., RRRRR.  I know math will predict how often this should happen, just not when.

So you look at four ECs in a row and say, "Man, it rarely goes five in a row.  I'll bet against it."

So you have a conundrum.  It has the same chance of hitting, but it rarely does.  What's a boy to do??

Samster

Last night I went to the B&M and played two games based on past history and educated guessing of future events. I won both, so I made the right decisions.

[psimoes]

Can't get over this being anything more than a math exercise:

If the last spin was red, the chances of the next spin being red are still 48.6% -- they do not drop to 23.7%. On the other hand, if you hadn't spun the wheel to see the first red result and wanted to know the probability of seeing red over the next 2 spins (and not just on the next 1 spin), the probability would be 23.7%.

I have some opinions on the above, but for the sake of simplicity let's go on.

Let's forget for a moment the probabilities for ANY dozen to hit on EACH spin.
Let's admit the first dozen to hit in a series of THREE spins has less probability of hitting on the second spin and even lesser on the third.
Because the odds are against that dozen to hit two and three times in a row (if anyone doubts, imagine you arrive at a table and bet for THREE spins on Dz2 to hit. How much does anyone expect to win?).

Basing on the above "assumption" I propose two experiments:

1A. Note last dozen that hits. Bet for the other two dozens to hit on the next spin.
2A. Wait 2 spins (this is important) and restart.

So, every three spins bet on two dozens different than last.

1B. Note which dozen(s) hit on the previous two spins. Bet for the least recent dozen to hit on the next spin.
2B. Wait 2 spins (this is important) and restart.