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I would call it counterstamp instead of overstrike.
Correct. An "overstrike" is when an entire new coin design is stamped onto a pre-existing coin, rather than a blank planchet; the original undertype or host coin is mostly obliterated in this act; it's condition before the overstriking is academic, as it would be almost impossible to determine in most instances. A "counterstamp" or "countermark" or sometimes "counterstrike" like this example only obliterates a small section of the former design.
That's my usage, anyway, and it's in line with Doty's "Encyclopedic Dictionary of Numismatics" and the CCF Glossary. I notice, however, that Krause considers "overstrike" and "counterstamp" to be synonymous; they say "counterstamp is with machine-powered dies, countermark is with a hand-punch". So if you wish to stick to Krause-approved word usage, then this coin is countermarked, not overstruck.
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Of course, depending on the source of the counterstamp, some would only see a damaged coin. One man's trash...
In this particular case, these coins were officially counterstamped by the Brazilian government, to revalue them, in 1835.
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The way that I grade them is to look at wear on the coin as though the counter stamp wasn't there. In the case of this coin I would grade it at F-12.
I would disagree, especially if an entire new coin was being made and the existence of the counterstamp was the primary cause of interest in the coin itself. Take the NSW Holey Dollars, as an extreme example - there are coins that exist in that series where the host coin is so badly worn it's unidentifiable as to date and mintmark, yet the countermark is sharp and clear. Obviously, a heavily worn dollar was used as the "blank" for such a coin, which then saw relatively little circulation as a Holey Dollar. In grading such a coin, it's the condition of the detail in the counterstamp that's most critical in determining grade and value.
I would be curious to know if the TPGs had an official policy on this matter - I looked them both up but didn't see the issue raised on their Grading Standards webpages. Given their penchant for "market grading" - giving a coin a grade that reflects its market value, rather than reflecting its actual state of preservation - I suspect that they would be inconsistent and not have an overall policy. For valuable specimens such as the Holey Dollar, they would use the condition of the counterstamp for 90% or more of the final grade. But for cheap stuff like Brazilian and Costa Rican counterstampers, the host coin would be the key component, since it's the overall eye appeal of the coin that adds value.
The fairest thing would be a clear split-grade, host/counterstamp, but such a thing would probably be too hard for the investors to get their head around.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis