Here's a general range of values for an 1887 US $3 gold piece:
1. Well-worn or circulated condition: An 1887 US $3 gold piece in well-worn or circulated condition can have a value between $350 to $500.
2. Fine to Very Fine condition: If the coin is in fine to very fine condition, with some wear and tear but still retaining some original details, its value can range from $500 to $800.
3. Extremely Fine to About Uncirculated condition: An 1887 US $3 gold piece in extremely fine to about uncirculated condition, showing minimal signs of wear and preserving most of its original luster and details, can be valued between $800 and $1,200.
4. Uncirculated condition: A truly uncirculated 1887 US $3 gold piece, with no visible signs of wear and retaining its original mint luster, can command a much higher value. Depending on its specific grade and rarity, an uncirculated 1887 $3 gold coin can be worth several thousand dollars or more.
It's important to note that these values are approximate and can fluctuate based on market conditions, demand, and the specific characteristics of the coin. If you have an 1887 US $3 gold piece and are interested in its current market value, it is recommended to consult with a professional numismatist or coin dealer for an accurate appraisal.