Is this like using the same number in a lottery, and getting to believe that as more and more regular consecutive draws do not pick the number, that there is an increased chance that the next time it will happen?
with 2 instead of the high number of lottery uniformly independent different draw events, that is.
The probability that N consecutive draws be the same can be logically computed. so can the probability of any N+1 consecutive draws sequence instances.
Then I think the human, having witnessed that particular sequence, and having also some notion that the repeated draws should be independent, makes that the next draw should have higher probability to be the complement of the known past repeated event.
N draws of 0, mean at N+1, if each draw were independent and unbiased (uniform), then N+1 draws being all 0, is smaller than N first be 0 and the last be 1. As one would expect frequency sampling (statistics is recording in memory or knowing the N first draws) to converge to the probabilities, eventually. I am saying that this may be the reasoning. I should read that paper.
but probability calculation does not follow. each repeated draw being independent, the probability of any sequence of 0s and 1s is always the same for all possible sequences of same length N. Pi of each event probability. p0^N. p0=p1.
all possible sequences of finite length are equi-probable, even those that look biased. I guess it is better to look at probability of sequences, and the repetition of such sequences, and then considering all of them.
So knowing one instance has all 0, has no effect on the next repeat probability or the augmented sequence with all 0. The op could compile same length as mentioned biased sequences that he or she has witnessed but from many different players. and then I wonder if the length of same coin flip consecutive sequences would be all over the place. If biased, then the same hypothesis would apply to all those randomly chosen players. If unbiased than we have more chance that way to get closer to statistics as probabilities. Replace the length with many players.
It might be a memory problem, either size of sequence length. or time to wait for sufficient length. Temperament, like patience levels, or others traits, might make one person wait longer before finding a given length of same coin flip looking bias. Memory size, persitence, and maybe even attention. Many players statisitcs should average that out. and allow more sequences to be seen in shorter amount of time.
Is this like using the same number in a lottery, and getting to believe that as more and more regular consecutive draws do not pick the number, that there is an increased chance that the next time it will happen?
with 2 instead of the high number of lottery uniformly independent different draw events, that is.
The probability that N consecutive draws be the same can be logically computed. so can the probability of any N+1 consecutive draws sequence instances.
Then I think the human, having witnessed that particular sequence, and having also some notion that the repeated draws should be independent, makes that the next draw should have higher probability to be the complement of the known past repeated event.
N draws of 0, mean at N+1, if each draw were independent and unbiased (uniform), then N+1 draws being all 0, is smaller than N first be 0 and the last be 1. As one would expect frequency sampling (statistics is recording in memory or knowing the N first draws) to converge to the probabilities, eventually. I am saying that this may be the reasoning. I should read that paper.
but probability calculation does not follow. each repeated draw being independent, the probability of any sequence of 0s and 1s is always the same for all possible sequences of same length N. Pi of each event probability. p0^N. p0=p1.
all possible sequences of finite length are equi-probable, even those that look biased. I guess it is better to look at probability of sequences, and the repetition of such sequences, and then considering all of them.
So knowing one instance has all 0, has no effect on the next repeat probability or the augmented sequence with all 0. The op could compile same length as mentioned biased sequences that he or she has witnessed but from many different players. and then I wonder if the length of same coin flip consecutive sequences would be all over the place. If biased, then the same hypothesis would apply to all those randomly chosen players. If unbiased than we have more chance that way to get closer to statistics as probabilities. Replace the length with many players.
It might be a memory problem, either size of sequence length. or time to wait for sufficient length. Temperament, like patience levels, or others traits, might make one person wait longer before finding a given length of same coin flip looking bias. Memory size, persitence, and maybe even attention. Many players statisitcs should average that out. and allow more sequences to be seen in shorter amount of time.