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Welcome to FT!
The availability of award seats can vary widely from airline to airline, and from flight to flight. Airlines typically will not offer a lot of award seats at a "low" redemption rate for flights that they expect to be able to sell a lot of seats on for cash.
Some frequent-flyer programs have more than one "tier" for award-seat redemptions. In those programs, you may be able to get award seats on any flight you want, but will have to pay a lot more miles.
Different programs also vary widely in fees, rules, and how many miles are needed for the exact same flight. For example, a "SAAver" award seat on AA from Central or Western NY to Chicago in Economy would cost 12,500 AA miles one way. The very same seat on that AA flight would cost only 4,500 British Airways Avios.
Tell us a little more about your intended redemptions (from where, to where, in what class of service, at what time of year), and we might be able to give you better advice.