The following information is from my eBook on Type One Liberty Head Double Eagles at http://doubleeaglebook.com/
It is likely that 120,000 1866-S double eagles were made with the Type One reverse (the figure of “12,000” as stated in the first edition of this book was a typographical error) in February, prior to instructions that were received from Philadelphia to change to the new Type Two reverse. The 1866-S No Motto was formerly an unheralded issue but its fame (and price levels) grew after the first edition of this book was published in 2002. Today, it is recognized as one of the rarer Type One issues. It is in demand both among specialists and more general collectors who appreciate its status as a Transitional issue. In fact, it is the only regular issue Liberty Head double eagle which is a dual issue; the 1907 is found with both the Liberty Head and the St. Gaudens design types.
STRIKE: The obverse always shows a weaker strike than the reverse and may appear to be at least a full grade lower in terms of sharpness. The curls around the face and below the ear are often weak but there is sometimes some separation of the hair located below IBE in LIBERTY. The first two or three stars at the left obverse are usually flat at their centers while the others tend to be sharper. Some examples have weakness at the obverse border from approximately 10:00 to 2:00. The reverse is nearly always weak on the horizontal lines in the shield and on the banner below the arrow heads. The mintmark is small and it can be lightly impressed.
SURFACES: I can’t think of many Type One double eagles which are more difficult to find with choice surfaces than the 1866-S No Motto. Virtually all known examples are very heavily abraded. These marks are usually deep and they are often poorly situated in locations such as on the cheek of Liberty or in the field directly in front of the face. Any piece which is not copiously marked is rare and is worth a strong premium over a typical 1866-S No Motto double eagle.
LUSTER: The luster on the typical example is considerably below average. This is the result of a number of factors. Most pieces are worn to the point that little—if any—mint luster remains. Those which are not well worn are extensively abraded and these marks tend to affect the luster. In addition, many have been cleaned at one time. Any 1866-S With Motto double eagle with better than average luster is extremely scarce and desirable.
COLORATION: The natural coloration is a medium to deep orange-gold or green-gold. There were, at one time, a decent number of pieces known with natural color but these have become extremely hard to find as most have been cleaned or lightened to obtain a higher grade.
EYE APPEAL: The typical 1866-S With Motto has inferior eye appeal. Most are weakly struck on the obverse, show poor luster, and have heavily abraded surfaces. This is among the most difficult Type One double eagles to locate with good eye appeal.
INTERESTING VARIETIES: All 1866-S With Motto double eagles have a small mintmark. There are no significant varieties known.
HOARDS: No hoards of 1866-S With Motto double eagles have been reported. The Saddle Ridge Hoard of 2014 included the single finest known, an example graded MS62 by PCGS.
BUYING TIPS: For many collectors, the purchase of this issue will be among the largest expenditures in their Type One set. Because of this, the collector should be patient and wait for a coin which has acceptable eye appeal. It will be nearly impossible to find a “pretty” coin but with patience and persistence, you should at least be able to find one with better than average eye appeal.
AUCTION RECORD: The current auction record for this date is $246,750, set by Heritage 8/14: 5712. This coin was graded MS62 by NGC.
FINEST KNOWN: The finest known is a PCGS MS62 which was found in 2014 as part of the Saddle Ridge Hoard. It was advertised for sale at a sum of $1,000,000 but it did not find a new home at this enthusiastic level. Other Uncirculated pieces include the NGC MS62 mentioned above; an NGC MS61 which sold for $188,000 as Stacks Bowers 8/14: 13257 and a PCGS MS61 which is likely ex Heritage 4/06: 4217 (as PCGS AU58) for a then-record price of $172,500.
TOTAL KNOWN: 175-225
Very Fine: 90-100
Extremely Fine: 60-90
About Uncirculated: 21-31
POPULATION FIGURES: As of the beginning of 2015, the population figures for Uncirculated examples is the same at both services: two in MS60, one in MS61, and one in MS62 for a combined total of eight. These figures are slightly inflated due to resubmissions. CAC has approved a lone Uncirculated example, graded MS61.
PERFORMANCE SINCE 2002: In the current market, a choice Extremely Fine example of this date (equivalent to EF45) is worth in the $25,000-30,000 range. In 2002, when the first edition of this book was published, a comparable example would have sold in the $6,000-8,000 range. In the current market, a nice About Uncirculated example (equivalent to AU55) is worth $65,000-75,000. In 2002, a similar coin would have sold for $25,000-30,000.
COMMENTS: Prices for this issue really took off around 2003; most likely as a result of the publication of the first edition of this book. They peaked around 2008-09 then dropped after the financial crisis affected the economy and the coin market. Since then, prices seem to have drifted back upwards, especially for problem-free examples. It is interesting to look at auction appearances over the last ten years to see the surprising frequency of appearance for this issue.
Including no grades and problem coins, there were 16 auction appearances in 2014, 10 in 2013, seven in 2012, 11 in 2011, three in 2010, and 10 in 2009 for a total of 57 in just the last six years alone.
The Saddle Ridge Hoard of gold coins, discovered in northern California in 2013, contained only a single example of the 1866-S No Motto $20, but it was a doozy. At PCGS MS62, it became immediately the best example known of this scarce issue.
David Akers (1975/88):
The Double Eagle collector who would like a high grade (AU or better) example of this date is likely to be disappointed. Actually this issue is very rare in any condition, second among S-Mint issues only to the 1861-S Paquet, and 28th in the entire 204 coin series. In rarity according to average grade, the 1866-S No Motto is tied for first with the 1870-CC and 1871-CC. When available, which is not really very often, the 1866-S No Motto is typically VF and heavily bagmarked. A strictly graded EF is very rare and, above that level, the 1866-S No Motto is excessively rare and, for all practical purposes, unavailable.