Let?s be blunt about early U.S. quarters. The simple fact is that they are very tough in almost any grade.
Early quarters saw low mintages. The first two, the 1796 and 1804, both had mintages lower than 7,000 pieces. The only reason the 1796 is available is because someone at the time hoarded them. That did not happen with the 1804 and it shows in the numbers available today.
In 1804 the Mint suspended the production of silver dollars and gold eagles to make more of lower denominations. The impact on quarter production was almost immediate. The 1805?s mintage topped 100,000. The 1806 had a mintage of 206,124, which was more than all the other quarters combined.
Even with its larger mintage there was no reason to expect any substantial saving of the 1806 since quarter collecting was not exactly widespread at the time because of sporadic mintages and production. Even if a collector was able to find all of the quarters produced by 1806, there would only be four coins in the collection.
It is also important to remember that back in 1806 a quarter was a significant amount of money. To regularly collect such a large denomination would have been a big investment.
Under the circumstances, finding a Mint State example of the 1806 today is a long shot. It is $220 in G-4, but that jumps to $6,300 in MS-60 and $56,000 in MS-65. The 1806 is basically the least expensive date of the type. The fact that there are so few dates (1805 to 1807) creates a strong type demand, making Mint State examples even tougher.
It is also hard to find nice examples of the 1806. At the time strikes were routinely light. This shows on the details of the portrait, the eagle, the border and stars. In addition many show adjustment marks that were made at the Mint.
Despite the production problems of the day, grading service totals tell us that there is a relatively healthy supply of the 1806 quarter. The Numismatic Guaranty Corporation reports that 38 examples of the 1806 have been seen in Mint State, and a few have actually reached MS-65 or better. At the Professional Coin Grading Service, the 1806 has been seen a total of 35 times with an additional 19 in AU-58. Of the total Mint State examples, there have been a couple called MS-65. These totals are well above the other dates from the period.
In fairness, the lower Mint State grade coins could have the typical problems such as light strikes, but the fact remains that the 1806 stands out as the one quarter of the type that is attainable in Mint State, assuming you have the budget for it. It certainly can?t be called readily available, but it does appear with some frequency. For a quarter of the period, that is unusual.