21. Apprentice/Market Square
While it might not be too surprising that this combo works, it sure is a lot of fun to play. Open Silver/Silver, and then pick up market squares on 3 or 4 and apprentices on 5+. Prioritize trashing estates and silvers over coppers, and activate market square’s discard as early as possible. Once you collide an apprentice with a gold, start trashing golds with your apprentices to draw your deck, still discarding market squares. After you have around 6 or 7 apprentices, the first 3 or 4 will draw your deck, and the remaining ones can pick up extra golds. To illustrate, suppose your deck and discard pile are empty. Trash a gold with an apprentice, discarding 3 market squares, and then draw the 3 golds and 3 market squares. Each apprentice is effectively “gain 2 golds, putting them into your hand”. It turns out this does drain the gold pile, so don’t plan on having one huge megaturn where you buy all the provinces. It usually takes 2 turns at the end of the game to get enough green to win. This hits 4 provinces in 12-13 turns, and all 8 in 14-15 turns. While it doesn’t keep its estates, it often has enough late pile control to make up for it; just make sure you have enough market squares to get to the number of buys you need.
From here, I’m just going to pick out a few of the remaining combos that I like or think are interesting.