Ah, the great numismatic unicorn, the 1971 "Ike" dollar with no mint mark that's also made of silver. What makes it rare is quite simple: it's not supposed to exist. It's the numismatic equivalent of a platypus, a creature so bizarre it seems like a mistake, but a valuable one at that.
Here's the skinny. In 1971, the U.S. Mint was very particular about its ingredients. The Philadelphia Mint, which used no mint mark, was given the recipe for the standard, circulating Eisenhower dollar, made of a copper-nickel clad blend. Meanwhile, the San Francisco Mint was the exclusive chef for the fancy collector's editions, striking them on special 40% silver planchets and proudly stamping them with an "S" mint mark. There was supposed to be a strict separation of church and state, or in this case, copper and silver.
So, a 1971 silver dollar with no mint mark is a ghost in the machine. Its rarity comes from the fact that for one to exist, a 40% silver planchet, destined for San Francisco, would have had to escape, go on a cross-country journey, and sneak into a coining press at the Philadelphia Mint. This would be a mint error of epic proportions, a true happy accident.
In short, the vast majority of the 47 million no-mint-mark 1971 dollars are just the common clad variety. Finding one that's actually silver is incredibly rare because it was a mistake, an accidental crossover that defied the mint's very specific plans. It's a coin that, by all official accounts, should have never been born.
