This document is in Courier font because it is a fixed width font and the formulae will not appear correctly otherwise.
The probability of a card in your opening hand:
Comb(M,k)
* Comb(N-M,n-k) / Comb(N,n) = Pr
where
M = number of wanted card in deck
k
= number wanted in opening hand
N
= number of cards in deck
n
= number of cards drawn (usually seven)
'Comb'
is the Combinations function. It gives you the number of combinations
of j objects taken i at a time. The formula for this is:
j!
Comb(j,i) = ---------
i! (j-i)!
The
'!' is the factorial sign and can only be applied to a whole number.
It is defined as:
1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
I
think you should see the pattern here. The only exception is that 0!
(zero factorial) is equal to 1.
To
find the chances of having two cards in your hand, let's add two more variables.
X
= number of card B in deck
y
= number of card B wanted in hand
The
Probility (Pr) is:
Comb(M,k) * Comb(X,y) * Comb(N-M-X,n-k-y) / Comb(N,n) = Pr
Repeat
for three cards, four cards, even up to complete hand construction.
