Practical Poker Math

From the calculations above, we know that there are 3,200
Flops that will make a nut Low.
To flop an Ace-High Flush, the Flop must contain 3 cards
from either of 2 suits — Comb(11, 3) * 2:
(11 * 10 * 9) * 2 = 330
(1 * 2 * 3)
Also from the work above, we know that there are 134 Flops
that will make Aces Full.
There are 3,664 Flops that will make a nut Low, Ace High
Flush or Aces Full to this hand:
Nut Low = 3,200
Ace High Flush = 330
Aces Full = 134
3,664
Odds of Flopping a Nut Low, Ace High Flush
or Aces Full
WILLNOTs : WILLs
13,632 : 3,664
Reduce
13,632 / 3,664 : 3,664/ 3,664
3.7 : 1
AA23 >>> Counterfeited A or 2 or 3
To find the odds of a counterfeited A, 2 or 3 at least once on
the Flop, multiply the number of 2-card combinations possible
from the 48 unseen cards by the number of remaining
A’s, 2’s and 3’s — Comb(48, 2) * 8:
(48 * 47) * 8 = 9,024
(1 * 2)
179
Before the Flop