Re: hal still doesn't understand basic Bernoulli Trial (was: Re: Xiaou? [taptap] Is this thing on?)

"WannabeSomeone" <WannabeSomeone@xxxxxxxxxxxxxxxxxxxxxx> wrote in
news:esUZf.4674$pZ3.633282@xxxxxxxxxxxxxxxxxxxxx:


"Robert Low" <mtx014@xxxxxxxxxxxxxx> wrote in message
news:1144493305.388047.141970@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

This is not because you
will get more tails to compensate, but because if you get 700
heads and 300 tails in the first thousand, then toss it a million
more times, the 200 extra heads in the first lot gets swamped
by the other tosses.

You guys might have misread what I said. What I meant was that if you
get a whole lot more heads in the first 700 tosses , you can expect
more tails than heads in the final 300 tosses.


Sorry, wannabe, the expectation for the final 300 tosses is 50/50 - no
matter what happened in the first 700 tosses. Coins have no memory!

In fact, **in the real world** if I saw a great preponderance of heads in
the first 700 tosses, I would question whether it was a fair coin (or
whether some other skulduggery was afoot). IOW if a got way more heads
in the first 700 tosses I'd expect to still see **a lot more heads** in
the following 300, not some compensatory mechanism. But that's because I
would be questioning the *given* (i.e., a fair coin) not because I think
fair coins "struggle" in order to get back onside to 50/50-dom.


No way you can get 700 heads in 1000 tosses if you have a fair coin.

So a more reasonable way to interpret what I said is that if you have
in the first 700 tosses, instead of getting 350/350, you get 370 heads
and 330 tails, you can expect more tails than heads in the final 300
tosses. Otherwise it will be getting more and more difficult to
balance itself out because the imbalance will keep adding up.


Coins have no memory. They also do not do anything to "balance things
out". Take any (apparently "random") sequence of 10 tosses, let's say
for the hell of it: H-H-T-T-H-T-H-T-T-H. The following sequence has
EXACTLY the same chance of occurring: H-H-H-H-H-H-H-H-H-H.

What are the chances of a bridge hand being dealt where each of the 4
players gets a complete suit: clubs, hearts, spades, and diamonds?
Astronomically unlikely you say? Well, I've got news for you - the a
priori chance of ANY particular distribution of cards is *exactly the
same* as my "four complete suits" case. Therefore bridge is impossible
since the chance of any set of hands occuring is so nearly zero as to be
not worth considering :-)

Regards,

PS Call it nemo's paradox: Any complicated event (which includes almost
all real events) has a vanishingly small a prori probability of occuring.

.

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