That Celtic harp is a sure giveaway you are dealing with an Irish coin. It is a Hibernia half penny. Hibernia is the Latin name for the island of Ireland.
The catalogs list only copper half pennys for 1766 and 1769. Check the date on you piece. There were numerous tokens and patterns, which are not coins per se, with the same George III and Hibernia design. Some tokens might even be made of silver. Generally the tokens and patterns are worth quite a bit more than regular half pennies. It takes an expert to tell the two apart. Patterns and tokens are often very well preserved because they were not used in circulation.
Here are some typical catalog values for George III pieces dated 1766 to 1782:
worn: $15 US dollars approximate catalog value
average circulated: $30
well preserved: $200
fully uncirculated: $300
Coins dated 1766 and 1769 were made with both a short bust and a long bust. The short bust coins are worth about twice that of long bust coins when well preserved and fully uncirculated. For an example of the 'short bust' type, see this page on IrishCoinage.com.
Coins dated 1773 are very rare and the catalogs do not report their value.
Only 5 coins dated 1774 are known, and they sell for thousands of dollars when they are once in a while seen at auction.
For coins dated 1776 in worn and average circulated condition, triple the values above.
Coins dated 1775, 1781 and 1782 are less scarce in higher grades; they catalog for $100 in well preserved condition,
For a coin to qualify as fully uncirculated, it must be in a holder. If it has been stored in contact with other coins, it is not uncirculated. A coin that is just barely uncirculated will lose a significant amount of value compared to an absolutely, fully uncirculated specimen. Figure a catalog value around halfway between the 'well preserved' and 'fully uncirculated' values for coins much prettier than well preserved specimens, but with evidence of rub against other coins.
These are catalog values. Actual values will differ, as explained on our Terminology page.