You fly on some airline, you register with their frequent flyer program (although each airline comes up with their own goofy name for the program, such as "Dividend Reward Value Sky Miles Plus"), you earn miles, and when you earn enough, you cash them in on a free flight. So they're worth something to you, but what? If you cash in 25,000 miles on a flight that would have set you back $500, that doesn't mean that each mile was worth 2 cents, although that is a popular figure for estimates of a frequent flyer mile's average value. Getting a seat on that plane is much more difficult using miles than just forking over the cash, so they're really not equivalent.
My wife and I recently had an opportunity to learn that it's worth less than half that to US Airways. While waiting for a flight home on an overbooked flight, she took them up on their offer for a voucher for a round-trip ticket in the continental US if she waited a few hours for another flight. When I tried to use this voucher for a family vacation, I found that it had the same restrictions that using frequent flyer miles does: each flight has a limited number of seats that the airline gives to people who aren't paying cash, and those seats go very quickly—especially when your local airport is not very big, and neither are its planes—so the voucher is as difficult to use as the miles.
It becomes an eighth grade math problem.
The US Airways woman on the phone (another annoying part about using US Airways miles is that you have to book over the phone) offered me another option: the voucher could be used for a $200 credit on any flight that wasn't completely full.
Now it becomes an eighth-grade math problem. If using this voucher for a round-trip flight gets you the same choice of seats and flights as 25,000 frequent flyer miles, but US Airways will also give you $200 credit toward any flight for the same voucher, how much is a frequent flyer mile really worth? Eight tenths of a cent.
I gave up trying to book a family trip to the Grand Canyon with the voucher and my collection of frequent flyer miles, which on paper were enough to do the trick. It was just too difficult. And, shortly after, when I was shopping for a new Mastercard, I skipped all the ones that give you frequent flyer miles with purchases, now that I knew how little they were worth.