Not the Grail, just a regular one - Bablokos!!! - page 80
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... Say, we have 20 eagle hits, so... it is probably logical to think that in every situation where we have 20 eagle hits, to expect at a certain cleavage the appearance of tails, so...
This is where you have a mistake. THE FACT THAT THERE ARE 20 EAGLES IN A ROW IS NOT ABLE TO INFLUENCE THE OUTCOME OF THE NEXT SHOTS (!!!). And the statistics confirm this very fact. (Or do you have other data...?).
(after 20 eagles the series will continue exactly as if you had just started casting).
You're catching on... fox.
How many series of 20 eagles would be in a sample of 10,000,000 throws? Well, on average?
And a series of 21 eagles? Fewer?
Of course the coin doesn't care what you throw before it, but I personally would start betting on tails after the fifth eagle in a row.
Have a look here, I think you'll find it interesting )
... Of course, the coin doesn't care what you put in front of it, but I personally would start betting on tails after the fifth heads in a row.
This is where you have a mistake. THE FACT THAT THERE ARE 20 EAGLES IN A ROW IS NOT ABLE TO INFLUENCE THE OUTCOME OF THE NEXT SHOTS (!!!). And the statistics confirm this very fact. (Or do you have other data...?).
(After 20 eagles the series will continue in exactly the same way as if you had just started the rolls).
Add to this the INSERTIONS of the original row. on one row of course it does not matter, read at least the previous post in its entirety. I specifically explained it....
I didn't write to you about one row. A about obtaining from the initial series of rows that in a particular point (on each count) will have the same (in a general sense the conditions for the series, each its own).
BUT these series are not linear, i.e. series values although pulled from the original series, but have their own rules of formation.
After 20 eagles, the series will continue exactly as if you had just started casting
What some people don't realise is that the probability of heads or tails depends on the physical shape of the coin. That is, if the coin is perfect, the odds are 50/50, regardless of previous results. If it is deformed, one side will roll more often than the other, again regardless of previous results.
Exactly the same at roulette. The probability is determined by the ratio of looses. If the roulette wheel is European, red as well as black occupy 18 pockets out of 37. Therefore the probability of both Red and Black for European Roulette is 18/37, regardless of previous results. And the probability of Zero is 1/37, because Zero is one pocket out of 37. Because the number and quality of pockets at the roulette wheel does not change depending on previous results, the probabilities remain constants.
But there are games where the previous result is withdrawn physically (without returning to the 'basket'). Therefore, the probability of results not yet falling out increases. For example, if a number is drawn in a sports lotto, the probability of other numbers in that draw increases because the same number cannot be drawn twice in one draw. This fact is taken into account in combinatorics.
I.e. probability is a physical quantity and is a constant. A constant cannot be dynamic by definition (pardon the triviality). To change the probability for a sequence generator with a return "to the basket", you have to physically distort the random sequence generator. That's what some arcade players do, i.e. they physically replace the electronics with a curve and make money on it.
... And exactly as well as I do, starting with the first...
again-twenty-five... but not with the same!
a series of six eagles is, on average, less frequent than a series of five, despite the independence of the result of one shot from the other. A paradox? Of course it is. Nevertheless, with each new eagle the probability of getting tails is not, not so - the number of tails after the fifth eagle will be more than the number of tails after the fourth.
Add to this - the EXTENSION of the original row. on the same row of course it does not matter, you read at least fully the previous post. I explained it on purpose ....
I did not write you about one series. It is about obtaining rows from the original series, which will have the same (in a general sense, the conditions for the series, each of them) at a particular point (at each counting).
BUT these series are not linear, i.e. series values although pulled from the original series, but have their own rules of generation.
I understand all this, Vlads. But, unfortunately, the coin does not know anything about it.
Please clarify, do you intend exactly to REVERSE VARIABILITY, or use some STATISTICAL property of the sequence for the benefit...?
Now that is a SERIOUS claim.
It also needs to be proven with real data.
Do you have instructions on how to get them, or can we just poke around in Excel...?