The name for the point where a probability changes

1/16 is true at the time prior to the rolls, 1/4 is true at the time after roll 3.I once made a computerprogam that averaged the last 1000 random numbers picked by the computer. The result was a value that fluctuated like a wave. It would tend to go up and up, or down and down, same as your computer more likely to repeat the last 3. But whether this says something about the nature of randomness in general, or the nature of the computer random function is beyond me.regards,
Mohammad Nor Syamsu

It was your post that made me see my error.After you make a choice the probability of any one of all the remaining doors having the correct door for the prize is (n-1)/n where n is the total number of doors ...... and when all the {non-prize\non-choice} doors are opened (eliminated) the chance that the other door is the prize door is 100% of that (n-1)/n ...thus 2/3rds for the standard game and 99.9% for your version.I have corrected my post with the calculation, as I see the error in the early morning light.

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we are limited in our ability to understand
by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}

I think this is more of a problem with the way standard computers generate random numbers. That is, they're not really random at all.Maybe if you repeated the tests with a true random number generator you'd get different results.

I have corrected my calculation, as I found my error myself, thanks.No, the reference makes no reference to "realization" at all, which has to be pretty curious for a college level course on probability don't you think?I was not able to find any source that really talked about it. hmmm. must be all my fault there eh?and you are playing word games. what happens happens regardless of the probability of it ... probabilities don't really "exist" - they are just intellectual constructs to make guesses when not all the facts are known.and something that does not exist cannot affect the course of events.

I guess the problem here is that you can argue what sort of world we live in. We have a few choises:A - A basically deterministic world where at least physical things like gambling are just a chain of causes and effects.In this case, probability is just an useful tool to us, but is just a model with no deeper insight in how things really are.B - A world where events on our scale are completely random and it's impossible to know what will happen until it happens.In this case, probability is still an useful tool to us, and a way to accurately describe the truth of our reality.C - A world where events are deterministic but humans have a non-deterministic mind with at least some random elements.In this case, probability is still an useful tool to us, but it is completely missleading as a way to describe the world around us.

meaningless?logical fallacies are errors of construction and show that the resulting conclusion has no real, rational or valid basis from the the precepts given.apples are fruits
gay people are called fruits
therefore all gay people are applessimilar logical fallacies to your construction.the "special" thing about "realization" is that you know the result in that one case that has happened but not what it would be for any other result ... better? worse? does it matter?only if you think it is "special" eh?enjoy.

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we are limited in our ability to understand
by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}

what you are dealing with is that after eliminating all the other possibilities but the 1 in 8 where you have 3 heads in a row you then have a 50:50 chance of heads or tails and overall you have a 1 in 16 chance of having the exact pattern HHHT and a 1 in 16 chance of having the exact pattern HHHH. The full number of possibilities is:HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT The first is within the margins of error for a 50:50 chance.The second is actually finding the odds of HT or TH patterns within the overall pattern, and this means that the number of iterations is reduced (slightly) — it’s result is also not surprising in a run of only (100-1) two toss samples (97.2/99 = 98%)Your last option is based on the probabilities of larger sub-patterns within the total samples, in this case HHT or TTH and betting more on the outcome (you don’t say whether you extended this to also finding HHHT and TTTH patterns and HHHHT and TTTTH patterns and ....), and thus your total samples are reduced to the ones where you have HH or TT together before making a larger investment ... and what you are really finding is that HHT happens more often than HHHT (this is obvious when you see that there is an HHT within each HHHT but not the other way around, and you break even on the HHHT events [one HHH and one HHT] but make money on all the other HHT events).Enjoy.

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we are limited in our ability to understand
by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}

... in stead of arguing like you do, you have to argue like: something that does not exist can't be decided on, something that doesn't exist can't be "realized", probabalities can't be decided on / realized.That is the construct you are either to accept or reject, realization on probabilities, NOT probabilities effecting, affecting or whatever. You are arguing a strawman of your own making. I already pointed this out to you 5 times.Let's try to turn this around. There are no such things as causes, there isn't any realization taking place on causes, therefore they have no power of realization on reality, so they don't exist, and something that does not exist can't have any realization over what happens. Round and round the merry-go-round...As before if you just do an internet-search, google, on realization and probability, you will get many incomprehensible technical papers in your search result. So I think it is the correct word by looking at it's usage there.It's certainly very curious that the collecourse doesn't have reference to realization in the collegepaper, but I think that may be explained by deeply ingrained prejudice towards "cause and effect". I presume they have no name at all for a point where a probability changes, their talk of probabilities lacking coherency at the point where probabilities change because of the lack of a proper name for it.regards,
Mohammad Nor Syamsu

As mentioned many times before, I take the common knowledge view. There is a past, causes are there, they relate to the present through their effects. There is a future, probabilities exists there, they relate to the present by their outcome.There are no causes in the future that effect the present. There are no chances in the past that get realised to the present.You can deny it here, but you live by this knowledge in your daily life, because you use the common language in daily life, the common knowledge.regards,
Mohammad Nor Syamsu

lolyou tell me that you do not need to construct a logical argument for your position (logical fallacies are irrelevant) and then proceed to tell me how to argue?wait while I take that one to the bank ....knowledge of probabilities cannot change past events
knowledge of probabilities cannot change what is happening at this instant.the only thing that we can change is what our personal choices are, and that is valid whether we do calculations or not. and to a large degree the choices we make are based on the knowledge and choices we have made in the past ("we are limited ...").there is no magic moment of realization that defines {{result A}} from {{result B}} because we do not really know what {{result notA}} would entail.all we can know is that {{result A}} happened.and that deeply ingrained prejudice could be to a better understanding of probability and what it really means.

I tried to avoid that issue by randomizing using the internal timer as a seed number before each toss. The differences in elapsed time betwen each randomization event help it to be a little more random than a complex pseudo random number. There may still be an underlying pattern but it is infinitely more complex and I don't think it would really make much difference to the outcome.Good point though.PY

The fact that the random bet came in almost exactly at no net gain or loss is a reasonable indicator that the computer is generating a good approximation of a true random number.The pattern was extended infinitely. Each time a head or tail was tossed, a counter was increased to keep track of how many same side results were observed in a row. It was reset when an opposite side result was observed.If HHHHH was observed then the counter would stand at 5. As the chances of 6 in a row are 2 to the power of 6 (2^6) to one against then that was the size of the bet placed against that outcome.My problem with this is that although the concept works and invariably makes a profit, I am not really sure how the probability issue fits.
If the bet were made prior to the first toss then the chances of 6 in a row would be pretty slim but the bet is actually adjusted after the event of the previous toss (as you pointed out) so the actual odds are not quite so easy to calculate based on my earlier assumption.However I still see the huge odds against large numbers of heads in a row must have an effect on the overall outcome of the experiment even if it doesn't effect the outcome of a single toss.I would like to see somebody try this experiment on a roullette table betting on black and red. I see no way that it could fail to make money unless the wheel was fixed.PY

Agreed. Same with the result of the always the opposite choice (98% is close enough for me in a sample of 100), and I would expect both to stay near even money in the longer haul ... say 1000 runs. Actually, it was only extended to the maximum run seen in the 100 samples ... right? (someone check my math this time eh?)It is doubtful that this pattern would emerge in a sample size of only 100 runs, as you are dealing with a 1 in 2¹⁰ probability, so it is likely that you will see a profit in a small number of runs.If you had some other winnings before you hit this streak you would not be as badly off (but not by much with only $1 winnings per win round), but if you play it enough times you will eventually have a big enough loss to offset any winnings.What I don’t see is how you could generate as much profit as you claimed (unless you are betting more than double): the maximum times you can win is determined by the flips (which is also measured by the second method) so at most you cannot win more than $100 in 100 samples.Certainly betting double means that your net return is less the longer the run goes (and against a higher probability that you will end up with the broke streak this is a bad idea).Lets try tripling: You can also figure what you would need to bet to win $1 for every round played, and your bets would be and you would be up against it after a 9 round run. (The bet sequence is 2ⁿ-1).ps -- what you are playing is a variation on the old gambler routine of doubling up the bets that lose, and it can take a large resource of cash to carry through. You also need to do all the calcs in your head, as they will take a dim view of "counting" and other known "systems" ... and the roulette wheel is loaded with (I believe 2) blank slots that are neither red nor black nor any number — they are house winnings.Whether both of these are sufficient to stop you from winning I do not know (I don't gamble as a rule)

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we are limited in our ability to understand
by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}

I think those are the choices. I have a tendency to lean towards C. Here's why. It comes down to randomness. At the macroscopic scale, it seems the only element of randomness introduced is the result of the mind. Most, if not all, probabilities seem to be formulated under the tacit assumption that it is the mind that introduces the randomness, and most questions regarding probability can be formulated in terms of the mind.I shuffle a deck of cards. I then pick a card from the top of the deck. What are the chances of it being the Ace of Spades? Most people would say 1/52, assuming the deck has 52 cards. I would disagree. The chances are either 1 or 0, it either is or isn't the Ace of Spades. This can be clearly seen by another scenerio, in which someone shuffles the cards, looks at the top card, then sets the deck down. Someone else comes along and picks up the top card. Well, it's not going to chance from when the last person looked at it, so the chances of it being the Ace of Spades is either one of zero.I think the correct way to formulate the question would be: what are the chances that the mind, working through the body, has shuffled the deck in such a way that the top card is the Ace of Spades? The same can be said about the box behind the doors. The question shouldn't be, "what are the chances of the box being behind door number three?" It should be, "What are the chances that the person (mind) who was putting the boxes behind the doors chose to put it behind door number three?"Then the question is: is the mind a generator of randomness or deterministic? Just like Melchoir said, it comes down to whether there is randomness in this world. If there is, then probabilites are an accurate depiction of reality, if not, then they are only useful tools to aid humans with inadequate knowledge.Which one is it though? At our scale, it seems things are deterministic, barring the mind. At the quantum scale, treating particles are probability waves seems to accurately describe the world....I have to go, I'm not sure this was going anywhere anyway. Does what I am saying make sense to anybody out there?

yes. I'd say that fits with my thoughts on the subject.probability of an event does not really tell us what the real actual final result will be, only the event actually occurring does that.this ultimately makes probability irrelevant as anything other than an intelligent (but often wrong) guess.

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we are limited in our ability to understand
by our ability to understand RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}