Practical Poker Math

5. Odds in Omaha Hi-Lo
There are 20 cards ranked 8 or lower that do not match any
of the hole cards. The number of 2-card combinations —
Comb(20, 2):
(20 * 19) = 190
(1 * 2)
From the ranks 4 through 8, there are 30 possible pairs that
must be subtracted from the total to indicate the number of
2-card combinations that will make the draw:
190 – 30 = 160
While the third card may counterfeit one of the hole cards
and still produce a nut Low, it must not be a card above the
rank of 8 and it must not pair one of the other 2 board cards.
Thus there are 46 – 20 (number of cards 9 through K) — 6
(number of cards that will pair either of the board cards) =
20 possibilities for the third card. The number of 3-card
Flops that WILL make a nut Low to this hand:
160 * 20 = 3,200
With a total of 17,296 possible 3-card Flops, the odds of
flopping a nut Low or a Set of Aces:
Total Possibilities = 17,296
– WILLs = 3,200
WILLNOTs = 14,096
Odds of Flopping Nut Low or AAA
WILLNOTs : WILLs
14,096 : 3,200
Reduce
14,096 / 3,200 : 3,200 / 3,200
4.4 : 1
176