Gordon Wrubel: Liberty $20. gold pieces of 1873 were minted with both "Open 3" and "Closed 3". For the Philadelphia Mint issues, the Open 3 is common and the closed 3 is very scarce. But how can one tell the difference? Look at the larger ball on the lower curve of the 3. The diameter of the ball is about the same size as the opening and would just pass through it. On the Closed 3, the lower ball would not pass through the constricted opening. As you can see from the condition census data above, the Closed 3 is a rarity in Mint State.
David Akers (1975/88): Of the two main varieties of 1873, the Closed 3 variety is by far the rarest. In fact, it is one of the rarest P-Mint Double Eagles, roughly on a par with the 1862, 1868 and 1871 and just a little less rare than the 1859. Most known specimens are in the VF to AU grades and true mint state specimens are undeniably rare. I have never personally seen a choice or gem mint state specimen and no more than a couple of average Unc-60 quality.
The Saddle Ridge Hoard of gold coins, discovered in northern California in 2013, contained only one 1873-$20 Closed 3. After earning a grade of PCGS MS62, it became a Top Pop, tied with two others as the finest example of this date.