Practical Poker Math

Low Draw with Backup Low Card in the Hole >>>
Low with 2 Cards to Come
With a Low draw and a backup low card in the hole, 12 of
the unseen 45 cards will make a Low. A Low can also be
made by counterfeiting any 1 of the 3 low cards in the hole.
12 + 9 = 21 cards among the 45 that will make the Low.
21 * 24 = 504 is the number of 2-card combinations, one
card of which will make the low.
Comb(21, 2) is the number of 2-card combinations that
contain 2 cards either of which will make a Low, including
pairs. To make this Low, none of those 2-card combinations
may counterfeit more than one rank of the cards in
the hole.
27 2-card combinations each of which contain a card that
counterfeits a different rank in the hole, must be subtracted
from Comb(21, 2) to find the number of 2-card combinations
that will contain 2 low cards and still successfully make
a Low to this hand:
(21 * 20) = 210
(1 * 2)
210 – 27 = 183
504 + 183 = 687 possible 2-card combinations WILL make
the low:
Total Possibilities = 990
– WILLs = 687
WILLNOTs = 303
205
After the Flop