I suppose you could also do this with just two players. Before the first game, snap a picture of the setup or do something to record the starting layout of the patches. Then, after completion of the first game, set it up exactly the same way and reverse the starting player and play another full game. Whoever's combined score of the two games is highest is the overall winner.
Tried this tonight. I was concerned that it might be a bit boring or repetitive because it was two games with the exact same layout, but once the first different move was made it completely changed the rest of the game. Clearly, the person who won the first game is going to want to mix things up early in the second game in an attempt to not suffer the same fate as their opponent did in the first game. So the two games were very different. The second player seemed to have the early advantage in both games, and won both games, but by much different margins. I would highly recommend this format if you want to minimize the luck factor.