Condition: The condition of the coin plays a significant role in determining its worth. Coins in higher grades, such as Mint State (MS) or Proof, are more valuable than circulated coins that show signs of wear and tear.
Variety: There are two main varieties of the 1951 50-cent piece: the regular issue and the "D" mint mark variety. The "D" mint mark indicates that the coin was minted at the Denver Mint. The "D" mint mark variety is generally more valuable than the regular issue.
Rarity: The rarity of the coin also affects its value. The 1951 50-cent piece is not particularly rare, but certain rare die varieties or errors can increase its value significantly.
In general, a 1951 50-cent piece in circulated condition can be worth a few dollars, while a coin in Mint State or Proof condition can be worth several hundred dollars or more, especially for the "D" mint mark variety or certain rare die varieties.
As with any coin, the best way to accurately determine its value is to have it appraised by a professional numismatist or coin dealer who specializes in U.S. coinage.