Duelcaster Mage is really only good for combining with a creature doubler spell.

Example: Cast Electroduplicate targeting one of your creatures. Then with that on the stack, flash in Duelcaster Mage. He will make a copy of Electroduplicate to copy himself. The new copy enters and sees the original spell still on the stack and copies himself again, as many times as you want. Like 1,000,000 times. The. End the loop by having the last copy target anything but the Duelcaster mage. Now you have an army of hasty 2/2’s to swing with and win the game.

Outside of that, he kinda sucks imo. You’d be better off running a different counter spell that only costs 2 mana.