Im sorry if this is going to the wrong person, but TCG playing tips is the
closest heading I could have thought of.

In the article "The Folly of Single Cards", The Pokemon Lady wrote
__________________
number of card drawn Ratio of cards
wanted to Cards Left probability of achieving
the desired outcome  percentage likelihood desired card is drawn
08 1:53 0.018867924528 01.8867924528 % or 1.88 %
09  1:52  0.019230769231  01.9230769231 % or 1.92 %
10  1:51  0.019607843137  01.9607843137 % or 1.96 %
11  1:50  0.020000000000  02.0000000000 % or 2.00 %
12  1:49  0.020408163265  02.0408163265 % or 2.04%
13  1:48  0.020833333333  02.083333333 % or 2.08%

again the percentage likelihood, for event 8-13 (the placement of the 6
prize cards) are added together, and we discover that there is a 13.855587
%(or 13.86%) chance that IF the SINGLE card you desired was NOT drawn in
the first 7 cards, THEN it WILL be in the prizes.

Mathematics has shown that, if you only have 1 of any specific card, there
is a GREATER chance of your single card to be in the PRIZES than in your
opening hand of 7 cards.
_____________________


I agree with Pokemon Lady's view on having single cards in your deck,
because (stealing your topic) its not mathematically efficient, but in her
last statement there is an error.  She states the the chance for the
single card to be in your prizes is greater than in the opening hand is
wrong. 

In the writing in Italic, she is corrrect that 13.86 is the percent chance
of having the card in your prizes if its not in your hand.

now the next sentance is false.  The chance of having that card in your
prizes (regardless of having it in your hand).  The actual percentage is

.1386 X  (1-.1229) = .1216

(percentage in prize when not in your opening  hand) X
(the percentage its not in your opening hand)

In acuality the probabability of getting the 1 card in your starting hand
is negligibly larger (.13%) than if its in your prize.

The Pokemon Lady's error was that she did not take into account the chance
of the card being in the opening hand when she was calculating the total
chance that the card was in your prize.

Because I am a mathematics major, I could not let this error slip.

Everett
ens2@cec.wustl.edu