So in the US coin collector spectrum, there are famous coins such as the 1913 Nickel and '33 Double Eagle. What ancient coins fall into this category of "super rarities"?
Too many to name! Also, rarity alone is not a huge driver of value unless combined with other factors such as historical interest, eye appeal, etc.
Non-unique popular rarities: EID MAR denarius (shown above). Athenian Dekadrachm. Noah's Ark bronze Menorah bronze Poros Dekadrachm "Badge of Phanes"
Although whether or not some of these are true rarities depends on if you define rare as the number of known examples or by the deficit of examples relative to the number of collectors who want one.
Here’s an old thread you might find interesting, @CoinBlazer. https://www.cointalk.com/threads/100-greatest-ancient-coins-hjb-book-discussion.233595/
There are a couple parameters to take into account here. Harlan Berk's "100 Greatest Ancient Coins" book is a decent sampling which probably accomplishes what you're looking for but I'll offer a bit of differing context. I'm creating arbitrary terminology in this post but hopefully it is sufficiently illustrative. I've collected high end US coins and currently collect high end ancients so some parallels might be helpful. Like in US coins, there are "super rarity" types and individual "super coins". The former are the coins which are exceptionally rare and exceptionally in-demand and therefore exceptionally expensive, occupying the nosebleed range of $500K-2M. Ancient coins are, in general, less expensive than US coins but some can still be very expensive. In this tier I'd put the Agrigentum dekadrachm, Athens gold staters, Brutus aurei, gold medallions, Flamininus staters, Athens dekadrachms, and a couple other types. To me, these are the 1913 Liberty Nickels of the ancient world. I'd define the "super coins" range as exceptional examples of in-demand types which aren't overall that rare (relatively speaking: some are still just in the double digits of population). These tend to fall in the $100K-500K range and include coins like the Eid Mar denarii, Kimon/Euainetos dekadrachms, Colosseum sestertii, Naxos tetradrachms, Phanes trites/staters, Julius Caesar portrait aurei, and others. These are the "MS Chain Cents", half dismes, and "MS 1795 $10s" of the ancient world. The nicest examples will sell for significant premiums over average/below average coins but they are always expensive. The next tier represents the coins in broad demand that aren't quite as expensive but still desirable, like coins of Cleopatra (including "Aegypto Capta"), Hannibal, Noah's Ark, Alexander the Great, Constantine the Great, architectural depictions, etc. There are expensive and inexpensive versions of these types but they make up the "meat" of the "100 Greatest Ancients" book. They are the XF Chain Cents, AU 1795 $5s, and the MS64 High Relief St Gaudens of ancients. It's probably worth saying that, with ancients, you can get a ton of historical "bang for your buck". A set including Alexander the Great, Cleopatra, Brutus, and Julius Caesar can be assembled for a bit over $1K and will produce the desired jaw-drop from the average non-collector. Or, you can assemble the same set with different types for $2 million and probably receive the same response from that non-collector.
I like my budget version: Rimp AR Denarius AR Brutus EID MAR - Slavei duplicate ex FSR 103 Joe: I do not collect Modern US anymore, save for the occassional surgical-strike captures for the Grandkids, but yours is a GREAT write-up and analogy! Well-done and thanks for that! I collect historically, so your last paragraph NAILS it! It is fun to show someone a jaw-dropper, even if it is high-priced or budget!
This is a very articulate differentiation between collecting ancient vs. modern coins, at least to the extent that I understand/remember when I collected modern coins. I will add one overall thought about the differences: rarity is common among ancient coins. Thus, the major factor in an ancient coin's desirability (which is probably over 50% of its price) is the coin's historical context, not just its rarity or uniqueness. A unique ancient coin that has little or no historical significance will not be widely sought by collectors, and the main (and possibly only) factor in its price will be its condition. Conversely, an ancient coin that has a well-known historical significance, such as the Tiberius "tribute penny" denarius, will command unusually high prices despite its commonness and easy availability. This is the salient difference (in my opinion) from modern coins, which mostly have little or no historical significance per se.
Please remove the coin from its holder (it's only worth a dollar, if that--I'm not kidding) and photograph both sides and then post it in a separate thread called "Unidentified late Roman bronze." I'm sure you'll have your answer within a few hours.
You have an Ides of March? Just kidding, but I do hope you get the chance to own one someday. I'd certainly come to pay you a visit to hold that beauty for a few minutes.
If I ever win a sizeable lottery and have a few million dollars to spare, I'd definitely put an Athenian Decadrachm on my want list. Might take a while as there are only around 30 or so on the market, but yeah, this is what I'd want.