Practical Poker Math

Total Possibilities = 17,296
– WILLs = 9,840
WILLNOTs = 7,456
Odds of Flopping a Nut Low Draw
WILLNOTs : WILLs
7,456 : 9,840
Reduce
7,456 / 9,840 : 9,840 / 9,840
.76 : 1
AA2X >>> Nut Low or Aces Full
To flop a nut Low with this hand, the board must contain 3
unpaired cards ranked 3 through 8. There are 6 ranks and
thus Comb(24, 2) 2-card combinations minus the 36 possible
pairs among these ranks:
(24 * 23) = 276
(1 * 2)
276 – 36 = 240 is the number of 2-card combinations that
will flop the nut Low draw. This is multiplied by all of the
remaining cards ranked 3 through 8 that are not represented
by the first 2 cards of the Flop (16), to produce the number of
3-card combinations that will make a nut Low to this hand:
240 * 16 = 3,840
To flop Aces Full, the board must contain an Ace and any
pair. With this hand there are 66 unseen pairs ranked 3
through K, plus 1 pair of Aces and 3 pairs of Deuces = 70
possible pairs that might appear on the board. This is multiplied
by the number of unseen Aces (2), to produce the
number of possible 3-card flops that will make Aces Full or
better to this hand:
181
Before the Flop