The 1851-O Half Dollar is one of those dates that is not really common, but it is also not that scarce, unless one considers the Mint State versions. Compared to several of the O-mint dates in the 1840s and 1850s, the 1851-O is right on par. The overall strike characteristics of this date are above-average for a New Orleans Mint product, though the stars may show varying degrees of weakness.
At the Mint State level, most 1851-O Half Dollars fall into the MS62 to MS64 grades. At the Gem level, this date becomes very rare. The top grade for this date at PCGS is MS66.