Practical Poker Math

AA2X Single Suited to A
For the Flush possibilities it doesn’t matter whether the
Deuce or the fourth card is suited to one of the Aces. It only
matters that one of those cards is suited to one of the Aces.
In this example we will calculate the odds of having an AA2
with one of the Aces suited to either the Deuce or the fourth
card in the hole.
This includes the possibility that more than one of the hole
cards will be suited to either Ace.
The total number of 4-card combinations possible from a
52-card deck is 270,725.
There are 6 2-card combinations that can contain a pair of
Aces.
To find the number of 4-card combinations that can contain
AA2x single suited, multiply the number of possible pairs of
Aces (6), by the number of 2-card combinations that can
contain at least one Deuce and one of the 24 remaining cards
of the same suit as either Ace (4 * 24 = 96). The number of
4-card combinations that can contain one pair of Aces, one
or more Deuces and one card suited to either of the Aces is:
6 * 96 = 576
161
Starting Hands