Thread: guaranteed aa? View Single Post
#6
02-10-2007, 07:38 PM
 SpaceAce Senior Member Join Date: Dec 2003 Posts: 3,017
Re: guaranteed aa?

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but, why must there be an infinite amount of AA's dealt? Is it not POSSIBLE that you could be dealt 88 every single hand for 2 million, 100 million, infiite hands?

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No, that's what makes it infinity. I'm not a statistician, so I don't know how best to explain this, but I will try. You know that .1 is 10% and .01 is 1%, so .0-&gt;infinity (with an infinite number of deals, you end up with an infinite number of 0s) is 0. You will never get to the "1" after the decimal place because it comes behind an infinite number of 0s, and "infinite" means never ending. If the 0s never end, the 1 never shows up. I am sure someone else can phrase it better.

People tend to confuse any really big number with infinity, but infinity has its own properties that no other number, no matter how large, has. In an infinite test, every possible outcome happens an infinite number of times.

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I'm not familiar with kolmogrov's law, but based on wikipedia it seems as though the probability of AA occuring is "almost surely". An example given on wikipedia in the definition of almost surely says exactly what I'm thinking.

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I believe the "almost" part of "almost surely" only exists because you can never actually reach infinity. If you have a truly infinite number of flips, you WILL get all possible outcomes. The "almost surely" comes from the fact that if you stop at infinity-1 (obviously not possible since infinity-1 is still infinity, but you know what I mean), there is some non-zero probability that you never flipped a tail. True infinity doesn't leave any room for anything besides 0 or 1 and since tails is a possible outcome, it is 1 and will happen in an infinite number of flips. So will a series of 100 tails in a row, 1,000 tails in a row and 1,000,000 tails in a row IF you actually flip to infinity, which you cannot do, and therefore you are stuck with "almost".

&lt;Paging the math and stat supergeeks to come in here and set us straight&gt;

SpaceAce