The name for the point where a probability changes

Hi SyamsuSorry to jump into your conversation with RAZD but it appears to me that you are both talking at cross purposes.
You seem to be talking about probability of stuff happening in real life while RAZD is referring to the Quantum Mechanical explanation for probability functions. It can be a little tricky to see how that can be applied in real life without specific examples.
QM doesn't necessarily imply that there are multiple universes, each determined by a single outcome of a probability function. It has been proposed that that is the case but it is not the premise of QM to speculate on that.Have you ever heard of "Schrodinger's cat"? It is a neat example of probability functions. If you haven't, then here is how it goes.First we have a sealable box which once sealed is impervious to any and all methods by which we can directly observe what is happening inside. In short we have no way to tell what is happening in there.
Into this box we place a single atom of a radioactive isotope with a half life of some really large number (say 1 billion years). We also add a very sensitive mearuring device which will detect that the isotope has decayed. To this measuring device we connect a vial of deadly poison such that is will release its contents when the isotope decays.
Now we place a cat into the box and seal it.After a few minutes we ask "Is the cat alive or dead?" Since the isotope caould decay at any time with equal probability then the cat could be alive or dead also with the same probability. QM states that for this situation a probability wave exists in which the cat is both alive and dead simultaineously, the wave being the only objective reality as long as the box remains sealed.
As soon as we open the box, the probility wave collapses and resolves into one of the two possible outcomes. The cat jumps out or the cat is dead. Could be either. (Please don't try this at home. Unless you hate your cat.)PY

If you were to do that then that would be the same as opening the box. The act of observing the outcome in any way collapses the probability wave.PY

That is just route cause analysis. We do it all the time when accidents happen in order to try to prevent future occurences of those same things.
Even figuring out the cause of something after the fact is often close to imposible so what chance do we ever have of really understanding the chance of a future event occurring based on present and past knowledge. There is just no way that we can ever know all of the factors involved so how can the probability of something happening ever be more than an aproximation of the real event.As far as your question about the fundamental importance of fully understanding probability, I would say that we can never fully understand how future events will unfold or even be able to make any more than an educated guess about how they will do so. Any more would require omniscience, a factor that humans are sadly lacking.Probability is and will reamain (as RAZD has stated repeatedly) a mathematical concept put in place by less than perfect humans to approximatly predict future events with varying degrees of precision.
The actual probability of something happening has only a very loose relationship to our model so the point at which it changes is at best pointless to consider, and at worst non-existent.PY

Here is another one that has always baffled me.
It is based on the simple coin toss.
I think everyone would agree that for each time you toss a coin there is a 50:50 chance of it coming up heads or tails.But then what is the chance of getting 2 heads in a row? 1 in 4
3 heads in a row? 1 in 8
4 heads in a row? 1 in 16etc.Does this effect the chance of the fourth toss coming up heads after 3 previous heads? On the one hand it must as the odds of 4 in a row are only 1 chance in 16 while on the other hand the odds are still equal. Which is correct?I put it to you all that they are both equally correct and yet incorrect at the same time.This has bugged me for some time now so when this thread started up i decided to do some experiments in the subject regarding the success of bets based on the two different interpretations.I set up a computer program to generate a sequence of 2000 coin tosses. I also set up three players that each bet in different ways on the outcome of each toss.The first bets randomly
The second always bets on the opposite of the last toss.
the third bets inteligently based on the odds of the total number of same-side tosses in the most recent sequence. (if the last two tosses have both been heads then he figures that the odds of another head are 2^3 or 8 to 1 so he bets a sum of money equal to those odds on tails)The results of several hundred runs of this were very interesting.all three players start with 1000
Player 1 ends up with an average of 1001 after 100 rounds of 2000 tosses.
Player 2 ends up with an average of 972 after 100 rounds of 2000 tosses.
Player 3 ends up with an average of 4927 after 100 rounds of 2000 tosses.I am still not 100% sure that this proves my theory but it sure as hell cheats the odds as far as betting on coin tosses goes. Using this method player 3 wins consistently every single time!Comments?PY

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

I think you have the wrong end of the stick. I ran 100 blocks of 2000 flips. Each block started out with a total stake of 1000. By monitoring the running total after each bet for each flip I noted that the money-in-pocket never dropped more than about 20 or 30 points below the 1000 but gradually and steadily rose through the length of the test run.
During each block of 2000 flips, the money-in-pocket increased to a value of around 5000 by the end of the block.
In real betting terms though, it would take a heck of a long time to place 2000 bets. Still a $4000 profit for a day's work isn't too bad.Potentially the odds could have reached 2^2000:1I see your point about the possibility of going broke though. About 20 losses in a row would completely destroy your bank roll. I had it set up so that the program would stop if that happened. It didn't ever happen during the 100 sets. If you just treat the "0" and "00" as not winning and keep increasing the odds of the bet then it shouldn't make any difference whether the sequence isRRRR0RB or
RRRRRRBThe bet is still the same size.I will have to try a simultion of a roullette wheel to see how this works.PY

Yeah you did enable your email. I just checked.I will send you the program this evening when I get home. I don't have the program here.
It is written in a Microsoft Excel format with a VBA macro doing the calculations.Py