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Old Nov 17, 2005, 1:30am   #21
axhed
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axhed
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oooookay....


deal out 221000 hands of poker and count the number of times you get AA back to back....

is the answer closer to 0 or is it closer to 1000?

you will probably get AA 900-1100 times....
you will most assuredly get AA -> AA less than twice.

forget about semantics and look at the big picture
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Old Nov 17, 2005, 11:09am   #22
Stew
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What you just said is correct. The difference is not semantics at all, but very important. At what point you choose to calculate the odds can alter them dramatically.
The chance of being dealt AA then AA in any string of hands is (1/221)*(1/221). Everyone agrees.
You have just been dealt AA. It has happened, therefore the probability is 1. What is the chance you will now be dealt 77? It is 1/221. What is the chance you will now be dealt AA? 1/221: the same as always.

Being dealt AA then AA is very unlikely, but by only starting counting on those occassions when you have been dealt AA (itself unlikely), you shorten those odds. (This is a favourite of 'psycics' who use optional starting and stopping points in experiments to 'defy' chance).

We are agreeing, we just started counting in different places.
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