Making nut low the hard way

This is a question:

In Omaha HiLo, I start with 3 low and 1 high card. The flop is 2 high and 1 low, giving me the nut low draw. What are the odds of my making nut low? How do I compute them? My thinking was as follows:

There are 32 low and 20 high cards to start with. After the flop, there are 28 low and 17 high cards in the deck. I don't want the low on board or the two low that make my nut low draw to hit the board. This leaves 19 low to help and 26 cards to hurt. 19/45 x 18/44 is 342/1980. This is 17.2% Is this my chance of making nut low?

Go to the 'Essays' link under 'Directory' here and look for the one entitled something like 'A Few Good Omaha Percentages' by Sklansky. The answer to your question is 16.2%, via copy and paste:


3. What about a back door low?


If you have Q-Q-A-2 and the flop is K-Q-8 you need two perfect cards. The chances are (20/45)(16/44) = 16.2 percent.


4. With the same flop, suppose your hand is A-2-3-K.


Here you start off with 25 good cards. If fourth street is good you now have either 16 or 21 depending on whether it was A,2,3 versus 4,5,6,7. The exact formula is (9/45)(16/44) + (16/45)(9/44) + (16/45)(12/44) = 24.2 percent. Once again, an extra low card helps a lot.

Oops, I reread your question and noticed you said you had 3 low and 1 high card, so the answer would be 24.2% (from question and answer 4.) not 16.2%.