SNAP 2017 Games & Tournaments — Previous Year Question

A, B and C played some card games. Each game had exactly one winner. No player won 2 games in succession. When a player was the dealer for a game he/she did not win the game. The dealer position proceeded from A to B to C, then this order was repeated until they stopped. The only player to win more than 2 games did not win the first game. Who was the only player to win more than 2 games?