Re: [Phys-l] probability problem

[John Denker <jsd@av8n.com>]

On 06/29/2010 08:41 AM, Carl Mungan conjectured:

> [perhaps 3 out of
> (52-7.5) since the computer had to go through on average 6.5 cards to
> find an ace?].

I don't think 6.5 is the right number.

My calculations indicate that the expected amount you need 
to skip before finding the first ace in a shuffled deck
is 9.6 cards.

The number 6.5 struck me as very implausible, since it is
the number you would get if the aces were as far apart 
from each other as possible, located every 13 cards like
clockwork, and then you _cut_ the deck randomly rather
than really shuffling it.  Shuffling causes the aces to
be somewhat more likely to be bunched up, increasing
the expected number of skips if you start in a random
place.

If you ignore the bunching you're off by a factor of 
9.6/6.5 == 1.47

=============

Tangential remark:  People make the same mistake all the
time in connection with Poisson statistics.  It is easy
to show that in the Poisson case, if you ignore the
bunching you're off by a factor of 2 exactly.