Flopping a nut low is incredibly difficult; the odds are simply against it.  But most players don't understand this, and that's why they get into trouble when they raise with a bare A2xx in their hand.  I’m not going to attempt to explain the math behind probability; instead I will simply present the results assuming the reader has some foundation in the math behind it.  But before I do, let’s get one thing straight.  As I talk about the long odds of chasing the low, I’m only talking about chasing it with a bare A2 in your hand and no other draws (flush draws, straight draws, pair, two pair, 3-kind, etc.).

Counting the high and low cards in the deck

To calculate the overall probability on the flop, turn, or river, we need to know how many total board combinations exist at each of these stages, and the types of boards possible.  In our examples, we are interested in the flop separately from the turn and river.  We will calculate the turn and river odds separately, and merge them with the flop odds -- instead of presenting a completely separate set of odds for the flop, turn, and river which would inherently end up with the same results anyways.

To know the board combinations we need to know how many high cards and low cards exist in the deck.  There are 52 cards in the deck, 48 of which you haven't seen.  You're holding two high cards, an Ace and a Deuce (two low cards in this example).  That means there are 18 high cards left in the deck (four-9's, 10's, J's, Q's, K's minus the two high cards already in your hand).  However there are also three aces, and three deuces that are kind of orphans in the deck -- because they would counterfeit your low (but would add to your high).  Since we must account for these cards somewhere, we need to add these six cards to the list of high cards during our computations.  This leaves 24 non-counterfeiting low cards (four-3's, 4,'s, 5's, 6's, 7's, and 8's) left in the deck, and 24 high cards (the 18 already accounted for plus the three Aces and three Deuces). 

The flop can come in one of four combinations:  HHH, HHL, HLL, LLL.  The HHH flop kills our hand, unless we flop trips, quads, a straight, etc.  In the end, it would be nice to know if all of our numbers add up -- meaning if all of the HHH, HHL, HLL, and LLL flop combinations add up to the total number of flop combinations possible.

With 52 cards in the deck, of which 48 you haven't seen, the total number of board combinations are at the flop are:

Flopping 1-Low Card (Board=HHL):

The odds of flopping one low card are pretty straight forward.  All we need to do is divide some subset of board combinations by the total number of board combinations possible. 

Here, we're choosing two cards from the 24 big cards, and one card from the 24 low cards.

Since we only flopped one low card, we don't need to account do anything special to account for counterfeit cards.  Therefore, given the total 17296 total flop combinations, the odds of flopping a single low card are:

Flopping 2-Low Card (Board=HLL):

Flopping two low cards gets a little more complicated, but not as bad as you think.  We can use the same mathematical foundation presented above to calculate the odds.

Here, we're choosing one card from the 24 big cards, and two cards from the 24 low cards.

Of these 6624 possible combinations, some of them are counterfeits.  To factor out the counterfeits, the math will look quite different.  There are six distinct cards that do not counterfeit us, of which we want to select two.  There are always four ways to choose the two cards, and six distinct cards to choose from.  Therefore there are 4² ways to chose the non-counterfeiting cards:

Odds of flopping two low cards:

Flopping the nut low (Board=LLL):

You can see how the odds didn't change between flopping one low card and flopping two -- so long as counterfeiting didn't matter.  As strange as it may sound, this is because there exactly as many high cards in the deck as there are non-counterfeiting low cards.  But when you don't want to be counterfeited, the odds drop a bit.  The formula below is the same as presented above:  only the numbers inside are changing (# big cards vs. # low cards).  In the example below, we select from 0 big cards, and 3 low cards -- assuming counterfeits don't matter.

Of course, the number above isn't very useful because in order to flop the nut low, counterfeits do matter, and we must get rid of them.  There are still four ways to choose the cards, and six distinct cards to choose from.  But this time there are three cards to select, not two, and four ways to chose each of those cards: 

Odds of flopping the nut low:

That's right, there's only an 7.40% chance of flopping a nut low, as the odds are 13.5:1 against it.

In theory, we could have calculated this another way, and it would be helpful to cross-check our combinatorial math with a simpler method.  Since there are 24 cards that help us at first card of the flop (48 cards to choose), 20 non-counterfeiting cards left on the second flop card (47 cards to choose), and 16 non-counterfeiting cards remaining on the third flop card (46 cards to choose), the simpler method to calculate the probability of flopping the nut low would look like this:

(24/48) * (20/47) * (16/46) = 7.40%...the numbers add up!

Flopping 0-Low Card (Board=HHH)...making sure the numbers all add up:

Just to complete the discussion, let's make sure all of the numbers add up.  We've already determined that there are 17296 total flop combinations of three cards; 6624 HHL combinations; 6624 HLL combinations, and 2024 LLL combinations.  If we did all of the math correctly, then when we add all of the HHH combinations, it should all add up to 17296.

HHH board combinations:

  6624 HHL
+6624 HLL
+2024 LLL
+2024 HHH
=========
17296 Total

Thank goodness, the numbers all add up!

Chasing the nut low:

Once you've seen the flop, how far should you chase the nut low?  Is it a good idea to chase it?  That answer depends on how much money is in the pot, how many players are likely to stay until the river, and the probability that you could actually scoop the pot if you make the low.

As I said earlier, calling if you have a flush draw and/or straight draw, and/or a pair or two in addition to your low draw is a profitable thing to do.  Chasing your flush and/or straight gives you a great chance of scooping -- which is the whole point of a split pot game.  If you already have a pair or two, go ahead, chase to the river.  But if you have no pair and no other draw, chasing the nut low might not be a good idea.

Chasing on a 2-low flop:

After you've made that 2-low card flop, chasing the nut low isn't a bad idea; the odds of making it are clearly in your favor.  After the flop, there are 45 cards left in the deck at the turn, and 44 cards left in the deck at the river.  There are still only 16 cards in the deck that help you, so the math looks something like this on the turn and river:

Selecting the next low card (confirming there are 16 combinations):

Since there are 45 unseen cards at the turn, and 44 unseen cards at the river, the odds of hitting one of these are:

(16/45) = 35.56% +

(16/44) = 36.36%

=============  71.92% of making the low after the flop.

Therefore the overall odds of hitting a low once you've flopped two low cards are (roughly):

Even though there's roughly a 72% chance of making a low once you've flopped two low cards, the overall odds still stand at a modest 24%.  Regardless, with a 72% chance of hitting the low, chasing to the river should largely depend on how much money is already in the pot and how many players are likely to call to the river -- to give you the proper pot odds to make the play. Unless you're head's up, there's virtually no situation that do not generate sufficient pot odds to make this call.  With a 72% chance of hitting the low, you're a 3:4 favorite to hit.  Therefore you only need to get 4:3 on your money to make this call -- and with multiple players in the pot, the pot odds are already there.

Chasing the nut low on a 1-low flop:

Now that you've seen the odds of flopping a nut low, and obtaining a low when two low cards flop, let's look at the odds of chasing a runner-runner nut low.  With 20 cards left in the deck that help us, and 45 cards we haven't seen, the odds of flopping a single low card on the turn are:

(20/45) = 44.44% on the turn
(16/44) = 36.36%. on the river

Putting it all together, the odds of catching runner-runner low on the turn and the river are the product of these two  numbers:

(20/45) * (16/44) = 16.16%.

That's right, you only have a 16.16% chance of catching a runner-runner low once you’ve flopped a single low card.  That means it will happen less than one-in-six times you try.  Therefore, in order to make this chase profitable, you must be getting more than 6:1 on your money to chase it.  If you're head's up, there's no situation that can justify this chase.  With multiple players in the pot, the pot odds may be there, but most likely are not.

Overall, the odds of catching a runner-runner low on a 1-low flop are as follows:

Yes, that's only an overall 6.19% chance of making any low once only one low card has come.

Summary:

Chances are against flopping your nut low (almost 13.5:1 against).  But how far to chase the nut low depends on how many low cards flop, and how much money is in the pot, and how much money will be put on the pot on the flop and turn as well.  The odds of flopping a nut low are only 7.40%.  However, the odds of making a low once you've flopped two cards are an encouraging 72%. 

Chasing the nut low from a single card low flop is a horrible idea, unless you're going to be getting sufficient odds on your money to do it.  Even though you're a 6:1 underdog to make a runner-runner low, remember that Omaha Hi/Lo is a split pot game, and that means you need to be getting greater than 12:1 on your money for the chase.  Even though I criticized a raise with a bare A2xx from early position, if you're in late position with multiple players already in the pot, it’s probably a good idea.  Assuming everybody already in the pot will call the raise from your late position, you have helped give yourself the better pot odds to chase that runner-runner nut low -- even if only one low card comes on the flop.

If you have more low cards than a bare A2xx in your hand, these odds change substantially in your favor.  With a bare A2xx, raising from early position is probably a horrible idea; but there are situations where this can help you if you do it from late position.  There's only an 7.4% chance of lopping a nut low; a 24% chance of making it if you flop two low cards, and a little over a 6.2% chance if you only flop one.  Overall, that's 37.54% chance of making a nut low -- thus far less than a 50-50 chance of getting there.  Unless you have backup low cards in your hand, you're going to lose your money nearly 2/3 of the of the time.  If I'm holding a pair or two, then I welcome your chase -- as you'll be giving me all of your money most of the time.

Since only a true idiot would chase a runner-runner low draw, we can remove the 6.19% odds from our total to see the realistic odds of obtaining our nut low when we hold A2HH.  Once the 6.19% is subtracted from the 37.54% total, you have a meager 31.15% chance of making your low.  These are hardly the odds that would warrant mindlessly raising with a bare A2 in your hand -- but if you're like 1/2 the people who play on the internet...you'll do it anyways.  If you do, one fact can be established for certain:  you're more the idiot than the genius -- that's for sure.

References:

Low Board Probability by Brian Alspach: