Coin flip probabilities and relevance

Verasace

JSCD.....

so did you even look at the graph?

It appears most of you didn't.

Again, look at the data, tell me your interpretation.

And again, I understand this postulation is contrary to established probability theory, but again, look at the data on the graph above, or run your own, a "probability wave" does exist as Halsoivy stated..

"What is TRUE (the "law of large numbers"- a more precise statement would be the "Central Limit Theorem") is that percentage will TEND toward "50/50" as the number of trials gets larger."

If a percentage is "tend"ing, then it CANNOT have an independent probabilty of 50/50, but the probabilty must "tend" toward 50/50

LOOK AT THE GRAPH!!!

What you will see is that along the way to tending towards 50/50 you will see wave scores similiar to:

-1,-2,-3,-4,-5,-6,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,3,4,5,6,5,4,3,2,1,0,1,0,-1,-2,-3,-4,-3,-2,-1,0...

jcsd

I despair, in your 'idea' it should either be impossible or there should be less probailty than the expected and observed probailty of getting a sequence of all heads.

Verasace

You still haven't look at the graph, have you?

A (long) sequence of all heads or tails is indeed possible, indeed probable, but then eventually the number of tails would outnumber heads eventually so that somewhere down the continuim of infinity a 50/50 balance MUST occur if the true probabilty is 50/50, regardless of where on that continuim you start.

Is that not correct?

As HalsofIvy pointed out in his? response, although future tosses may "favor" one outcome, eventually, you must return to 50/50. So if at the beginning of your sequence on the infinite continuim you get 10,000 consecutive heads, sooner or later you will get 10,000 more tails than heads to get back to 50/50 overall, for a string of consecutive heads cannot continue indefinitely.

jcsd

Firstly, a string of heads can contiune indefintely, as however many tosses there is always a non-zero chance of obtaining all heads (given by 2ⁿ). As I said it gets complex when you start considering an infinite number of tosses and there's no agreement on this, indeed there was an article in either Scientific American, Nature or a simlair journal (I forget) discussing probabilty after an infite number of trials and whether a probailty of zero corresponds to an event that can happen.

sol1

Coin Flips and Graphs

I just responded to what I subcribed too, so it is good to see that you actually did in create a thread.

This issue you are bringing forward is a problem with me as well?

That I don't undertand how we could not percieve a issue lets say like strings and consider the relevance of current advancement of thinking, and not seen the theory has answered some of these questions. Boltzman.

So the understanding unpredictablity has to bring forward the issue of how such probabilties might have be ascertained in considering strings, and its related issues as a value in gravitational consequuences. The energy value is directly related to what gravity will do?

Probabilty does not know the shape yet it does know that is must follow the issues of movement in terms of what gravity will do?

So for instance the idea of energy is fuzzy, yet on a graph it lets us know with certainty that it will have been defined in a peak. A a BEC condensate such imaging will let us know. Look at images of soliton and Bec configuration in three dimensional graphs and what is it we undertand? Greg Egan and his graphs, soliton configurations, will help you formulate. This is a guess and I would apologize for sending you down this road if the perspective is wrong.

I believe you are direct challenging current thinking and I will wait and see how they will respond to the real issues in light of the math that is being spoken too.

Good for you.

Sol

chroot

Man, the moderators really need to sweep this place up.

- Warren

jcsd

Think of it this way:

I decide to test the probailty and by an amzing (yet possible) fluke on my first 50 throws I get all heads, being a bad experimenter I decide to ignore these first 50 throws and carry on my experiment, now does the 'pressure' act on only those throws after the first 50 or act on all my throws including the first 50 that I decide not to include in my sample to bring the value to 0.5?

Both samples (the one with and the one without the first 50 throws) are equally valid yet I know that I will always get a different value for the ratio of H:T from the two samples.

jcsd

Ah yes, but your forgetting throatwarbler's fourth law of inductive quantum micro-managment[g)]

Verasace

Finally, some discussion.......

I propose that anywhere along the probability continuim you begin you will be subject to Probability Pressure (PP).

Imagine you are dropped into an ocean. You are then immediately on some point of a wave, perhaps a large wave, perhaps a barely perceptible wave, but a wave nonetheless.

You have no way of knowing if the 50 straight heads are at the crest, valley, going up or down, but sooner or later you will peak and head in the opposite direction. The middle of the wave is 50/50.

Now this wave is not perfectly linear, it has bubbles and ripples on the surface, but none the less, you will get to another crest and valley, as indicated in my graph, and your graph if you do one.

Is it perhaps this attempt to reach an equilibrium, and the bubbles and ripples that prevent a constant HTHTHTHTHTHTHT, for probability, like forms of energy is a waveform.

Once you can perceive probability as a waveform, the trend towards 50/50 despite long consecutive "favor" for either heads or tails is easy to understand.

I am not a mathmatician, formulas are admittedly not my strong point. Objective observation and interpretation outside of the box is my forte.

Again, LOOK at my graph to truly grasp what I am proposing.

jcsd

I do understand what you're saying but you're just wrong. As a said in my post before last you can have two equally valid samples which cannot both be 'acted upon by pressure' to return a ratio of 50:50.

chroot

Maybe the moderators need to do some sweeping here, too.

Thanks for holding down the fort jcsd. I got tired of arguing with him.

- Warren

Verasace

But I am not talking about samples, or portions of a wave, I'm talking about an infinte ocean, and eventually from the start point you will return to 50/50

Go ahead and sweep (censor) me, or just don't respond if you wish.

Just curious, who out there has looked at the graph? Only 4 others besides me since I posted it til now

jcsd

I've already explained the problems with infinite samples and how there is no agreemnet on exactly how to deal with the probailties they return.

For the time being I'll assume that an infinite sample will return an ratio of 1:1 for H:T, it's not a completely unresonable assumption as that is what the ratio should tend to when you increase the size of the sample. Going back to my example again where the first 50 trials are ignored, it's clear to you that whethr we include the first 50 trials or not will not affect the ratio even if they are all heads. Infact with the assumptions I've made so far you're right the first 50 trials won't affect the ratio, indeed the first n trials will not affect the ratio, therefore there is absolutely no need for this pressure as the trials before any given trial will not affect the final ratio of 1:1.

jcsd

Yes, your right the moderators should have a Stalin-like purge of these boards, it's getting a little tiresome having to argue about even the most basic well-accepted concepts of maths and physics.

Verasace

That is true for the FINAL ratio, but along the way to the end of the sample, if large enough, or infinity, you will may cross the 50/50 "zone" several times to end up at 50/50 at the end.

And the exchange of ideas is arguing, and arguing is bad so kick me off? The Flat Earth Society strikes again. Should I assume that "basic well-accepted concepts of maths and physics" are to never be challenged?

You still haven't answered my question from a few posts ago, did you look at my graph?

Njorl

It is not always easy to distinguish the earnest-but-ignorant from the true-believers. I don't know why, but this one set off all my alarms.

Njorl

jcsd

But you've not proved in any way that the 50/50 line must be crossed for any value of n.

I wasn't necssarily referring to you verasace, I think you have basically just misunderstood a vital element of probabilty.