Practical Poker Math

of combinations that will make the starting hand,
the odds are easily calculated as demonstrated below.
2. Probabilities — The probability of any starting
hand can easily be determined by multiplying the
probability of the first card by the probability of
the second.
As demonstrated in Chapter 1 — Basic Calculations — and
throughout this book, any odds are easily converted into
probabilities and vice versa.
Pocket Pairs
For each rank — cards 2 through A, there are 6 possible pair
combinations — Comb(4, 2):
(4 * 3) = 6
(1 * 2)
With 13 ranks of 6 possible pair combinations there are 78
pair combinations possible from a standard 52-card deck.
The odds and probability that any given player will receive
the Pairs listed below as his hole cards are:
53
Starting Hands
Hand Probability Odds
Any Pair 5.9% 16 : 1
Any Specific Pair (AA) .452% 220 : 1
Pair of Jacks or Better 1.8% 54.25 : 1
22 through TT 4.10% 23.6 : 1