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Verasace

In my graduate undergrad & grad stat classes I learned the probability of getting heads or tails is 50/50.

But I have something to toss out into the ring for comment....

According to my limited research, the 50/50 probability appears to be a mean probability, and that the actual probability is relevant upon previous coin flips in order to obtain an mean 50/50 probability.

For example, if out of 10,000 coin flips, I get 9000 heads, then for the next 10,000 flips, the distribution of heads vs. tails would not be 50/50, but would be weighed in favor of more tails in order to get back to the 50/50 mean.

I call such a change in normal tendency as "probability pressure" (PP)on the "probability wave" (PW). I realize the term probability wave is already established in reference to light, but it seems to apply here.

If one graphs the results of 10,000 coin tosses (or 100,000 as I have), giving heads a value of +1 and tails a value -1, one can easily visualize the PW and should be able to recognize the strength of the PP, either positive or negative, seems to increase the greater the distance from the mean “score” of 0 the wave extends.

Considering the range from the crest of one wave to the next, and the distance between the crests, one may theorize that at the peak of each wave the odds are not truly 50/50, but are skewed.

One may also see that there appears to be a limiting factor on the actual height, or frequency, of the wave, as the possible range for 10,000 tosses could theoretically be a score of 10,000 (100%) either positive or negative, but I have not observed a variance of more than about 3%.

A question I have yet to solve is developing a formula to determine the true probability of a coin toss when relevancy is considered. It appears that the higher, or lower, the score from the mean probability, the greater the skew from 50/50, perhaps on some type of ratio.

Any thoughts, suggestions, comments