Practical Poker Math

Reduce
13,936 / 3,360 : 3,360/ 3,360
4.1 : 1
A23X Single Suited >>> Nut Low or Ace High
Flush
There are 3,360 Flops that will make a nut low.
To flop an Ace-High Flush, the Flop must contain 3 cards
from the same suit as the suited Ace — Comb(11, 3):
(11 * 10 * 9) = 165
(1 * 2 * 3)
3,360 + 165 = 3,525 is the number of 3-card combinations
that will flop a Nut Low or an Ace-High Flush to this hand:
Total Possibilities = 17,296
– WILLs = 3,525
WILLNOTs = 13,771
Odds of Flopping a Nut Low or Ace High Flush
WILLNOTs : WILLs
13,771 : 3,525
Reduce
13,771 / 3,525 : 3,525 / 3,525
3.9 : 1
A2XX >>> Nut Low Draw
To flop a nut Low draw with this hand, the Flop must contain
2 unpaired cards of the ranks 3 through 8 with no card
that counterfeits either the Ace or the Deuce in the hole.
185
Before the Flop