Gordon Wrubel: San Francisco minted 1873 Twenty Liberty coins come with both Open and Closed 3s. But, unlike her Philadelphia sisters, the Closed 3 is the more common occurrence. The ratio of Closed to Open is about three to one. If you are looking at a raw coin and do not have the comparison photos above for reference, it is easy to determine whether the coin has an Open or Closed 3. The ball at the end of the lower loop of the 3 is about the same size as the opening of the 3 and may just pass through. On the Closed three the ball will not pass through the opening. As you can determine from the Condition Census above, this coin is rare graded higher than MS 62.
David Akers (1975/88): There are two main varieties of this issue just as there are two varieties of the 1873 Philadelphia Mint issue. Both varieties are scarce but the Open 3 variety is the more rare of the two. As a date (i.e. not considering the two varieties as separate issues), the 1873-S is similar in overall rarity to the 1869-S, 1870-S 1871-S and 1872-S. However, the 1873-S is not as rare in full mint state as the four S-Mints immediately preceeding it. Nevertheless, in strictly uncirculated condition, the 1873-S is scarce and in choice or gem Unc. it is definitely rare.