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"How much is the 87-S?"
"That's thirty-seven dollars."
"Thirty-seven? Greysheet is twenty-nine."
"OK. Go buy it from them."
Red Book, Blue Book, Greysheet, Trends, Teletrade... what a coin is "worth" depends on why you want to know. What anything is "worth" depends on the context of the question.
The idea that you can look at an authoritative listing and know what an item is "worth" is one of the many negative affects of public schooling. People who are insulated from markets are prevented from learning how markets work. Price guides, whether the Red Book or Greysheet, or the NYSE listings in the business section of your newspaper, only record the past. Whether the past is indicative of the future is arguable.
If you see a coin you want and the price guides show it at some other price, then you can learn a lot by actively shopping for the coin, actually looking for sellers at the price you think is more correct. You may find that some coins (small US Gold or certain Hard Times Tokens, for instance) are unavailable except at an arbitrarily large mark-up over the published prices. For ancient coins, this is especially true because each coin is more clearly unique. (In theory, every coin is unique.)
It is only the commodity nature of US Type coins that makes the spectrum of price guides possible. You might also find that other coins can be had for impressively less than the published guides claim. Over time, prices change. Since the supply of US Type coins is constant, it is the demand that changes most. Coins that were hot last year go unsold this year. Ancient coins are more subject to changing supplies as new hoard material affects the price.
There are only two ways to sell anything: greed and fear. Sometimes they come together in a moment of agoric beauty. You see a nice coin but it is priced way above Greysheet. If you pass this one up, can you buy another? If you buy this one, will you discover that you could have bought another for less? Decisions, decisions...
The only question to which you have an objective answer is this: Do you want the money in your pocket more than you want the coin? What somebody on another continent claims that their friends somewhere else paid for the coin yesterday is irrelevant.
To determine which seller has the best price for you right now (whether "now" is measurable in seconds or months) depends on knowing the markets, i.e, knowing the material, the buyers and sellers. Knowing the price guides is part of this. Red Book, Greysheet, Trends, etc., are only editorial approximations based on the reported transactions.
Whether a buyer or a seller can be said to drive a transaction depends on psychology, not economics. Two dealers with the same material will have different experiences. Two collectors seeking the same material will have different experiences. You can buy under Greysheet and sell over Redbook if you have charisma. People who are basically unlikeable can have great agoric charisma. The bottom line is: "it all depends..."