Based on your past post and the dealer's $1750 price tag I'm guessing you're referring to your 1912-H half penny.
Here are some comparable coins at auction:
Numis Bid Sale 20, PCGS MS65RD, est $1950 - $2350, sold for $1488
Numis Bid Sale 25, PCGS MS64RD, est $600 - $725, sold for $900
Australian Coin Auctions Sale 314, lot 1558, full red nearly Gem Unc, est $1000, sold for $900
Numis Bid Sale 25, PCGS MS64RD, est $600 - $725, sold for $900
Numis Bid Sale 27, PCGS MS64RD, est $900 - $1100, sold for $715
Noble Numismatics Sale 102, lot 1666, Full original mint red, uncirculated/choice uncirculated, est $750, sold for $600
Noble Numismatics Sale 104, lot 1593, Full blazing golden mint bloom, est $600, sold for $600
Noble Numismatics Sale 104, lot 1594, Full original mint red, light toning on obverse, choice uncirculated, est $600, sold for $600
Numis Bid Sale 34, lot 62, PCGS MS64RD, est $675 - $850, sold for $413
Noble Numismatics Sale 104, lot 1595, Subdued full mint red, uncirculated, est $500, sold for $400
Noble Numismatics Sale 105, lot 1542, Nearly full original red, uncirculated, est $400, sold for $400
Numis Bid Sale 22, PCGS MS64BN, est $410 - $490, sold for $324
Numis Bid Sale 37, lot 36, PCGS MS64RB, est $230 - $290, sold for $300
Australian Coin Auctions Sale 317, lot 1457, mainly red Unc, est $350, sold for $300
Australian Coin Auctions Sale 314, lot 1559, in PCGS holder graded MS63RB, est $400, did not sell
and some price history charts:
MS64RD

MS64+RD

MS65RD

Why would you believe one over the other? Take from the above as you will but note that an auction house has a vested in overrating your coin (so you consign with them) while a dealer has a vested interested in underrating your coin (so they can profit more).
Considering the large variances in the pricing between the grades, it's entirely possible (and likely) that the range of estimates you receive are based on slightly differing grading opinions - even half a grade point which is within the margin of error for the best third party grading services would explain the large variance. To avoid this, get the coin certified by PCGS.
Also note that the coin is on a down trend so expect dealers to buy with a high margin to account for depreciation while holding the coin.