Coin flip probabilities and relevance

yudiski4

"The problem with probability is that there are some certainties about it ... The fallacy is the whole concept of infinity."

If you need to have certainties, and you outright reject the concept of infinity, then the study of probabilities is going to lead you to a stone wall.

chiro

Quote by yudiski4

Forget "waves", there are none. Try to look at it this way. In an infinite number of tosses the heads/tail ratio will come out to very, very close to 50%/50%. Agreed? And in that infinite number of tosses, there will have been, almost assuredly, a streak of 1000 straight heads. Also agreed? But the wave theorist says, "Woah, after those 1000 heads, assuming it was running close to 50/50 up to then, there would have to be a "tail wave" for it to end up 50%/50% at the end".

But the fallacy is: in infinity, there is no "end". The intuitive force that makes the "wave" seem inevitable is tied up in the human brain's inability to conceive of or think in terms of infinity.

You don't need to think of it necessarily in terms of infinity, but rather in terms of something "really large".

For many practical purposes the strong law tells us a lot about the kind of limiting probabilities for large enough sample sizes as it would for an infinitely large number of them.

To understand this its best to think of the derivative of 1/x. If x is big enough then any change thereafter is not going to have much of an effect if the observations up to that point reflect a mostly unbiased sample. If the sample is highly biased then we can't necessarily do this, but for most purposes "large enough" samples will provide a distribution that is good enough to represent the true distribution for "infinite" sample sizes.

TechnocratX

I know this thread is over 8 years old, but this reply is for the benefit of someone like me who stumbles across it. Plus I think I can explain it in a more simpler manner, especially for those with basic stats knowledge.

Quote by Verasace

Concerning coin flip probabilities.....

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.

Any thoughts, suggestions, comments

Ok, say you did the first 10,000 coin flips, and got 9000 heads. This gives you a 90/10 distribution. Now you're thinking you're at the top of a heads wave, and should expect a tail wave to take you back to a 50/50 distribution.

Then you carry on and do another 1,000,000 coin flips, but this time you get exactly 500,000 heads and 500,000 tails. So no increase in tails from a pressure wave. But, even without the tail pressure wave your graph has now moved to a 50.4/49.6 distribution.

What's happened is that you've simply increased the sample size and that has reduced the effect of the 9000 heads. Hopefully you can now see that the wave patterns tending towards the 50/50 distribution, are caused by the increase in samples and not an increase in heads or tails through a pressure wave.

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yudiski4	Coin flip probabilities and relevance "The problem with probability is that there are some certainties about it ... The fallacy is the whole concept of infinity." If you need to have certainties, and you outright reject the concept of infinity, then the study of probabilities is going to lead you to a stone wall.