[Rick Seaney is the CEO and cofounder of FareCompare, and columnist for Investopedia. The views expressed by columnists are those of the author and do not necessarily reflect the views of Investopedia.]

You know the old rule of thumb: If it sounds too good to be true, it probably is. That’s the case for airfares, too, though some come close to the ‘impossibly good’ standard! Like this recent fare I found on my site: Boston to Amsterdam for $325 in October.

But what about transatlantic fares for say, $51? Or tickets that are free? Do they exist? Sometimes. Is there a catch? Usually. In other words, time to sort out the real deals from impossible fares. Most fall under two major categories.

Free Tickets

These may pop up on Facebook or Twitter, appear in inboxes, even show up at your home as a snail mail postcard. The offer usually mentions that you have won free tickets from a large airline – Southwest or Delta, maybe.

In almost every case, the airline has nothing to do with this; instead, it’s a prize for attending a time share talk or joining a travel club of some sort, complete with dues. Those who get these ‘free’ tickets may be told that only the base fare is free and the recipient must pay taxes and fees.

Example: The full fare for an American Airlines round-trip flight from Los Angeles to New York in July is $524, while the base fare is $460. The free ticket would cost the recipient $64. It’s a lot harder, though, to put a price on the time you’d spend sitting through a sales presentation you have zero interest in.

Mistake Fares

These are rarer than they used to be, but mistake fares still occur. These error fares, as they’re sometimes called, are due to simple or complicated mistakes ranging from a human finger hitting the wrong number when pricing a fare or a vendor error of some kind. In 2012, El Al deals from the U.S. to Tel Aviv that normally cost as much as $1,900 were mistakenly sold for as low as $350. In 2013, Delta offered Boston to Honolulu flights for $68. That $51 first-class transatlantic fare showed up in 2015 on certain flights to Denmark. 

So – did the airlines honor their mistakes? Sometimes they did, sometimes they didn’t. It seemed to depend on how much bad publicity they might encounter. Then in 2015, the U.S. Department of Transportation announced new rules for ‘mistaken fares,’ which basically gave airlines the right to cancel these fares without penalty, as long as they reimbursed passengers for the cost of the ticket, as well as any trip-related expenses including “non-refundable hotel reservations, destination tour packages or activities, cancellation fees for non-refundable connecting air travel and visa or other international travel fees.” If this could be you, hang on to all receipts.

Are Mistake Fares Ever Honored?

We’ve heard anecdotal evidence that impossibly cheap fares may still be honored from time to time, but it’s rare. And some carriers – Delta, for one – now have language in their contract of carriage legal documents that specifically gives it the right to "cancel the ticket purchase and refund all amounts paid by the purchaser." The purchaser also has the option to have the ticket reissued "for the correct fare."

Bottom line: The odds are not good that your mistake fare will be accepted. If you have one, don’t relax until you’re in the plane and it’s taking off.

How to Find Super-Cheap Fares

Suggestion: Sign up for airfare alerts; my site has this, but so do many others. You indicate where you want to go, then sit back and wait for legitimate deals to come to you.

The Cheapest Days to Fly in 2018 and When Is a Deal Not a Deal? will also help you find good prices.