From what I've gathered, series 3 has more to do with Kazuya, the chairman's son. It seems like he sets up games and gambles for Kaiji to do. Essentially, the same as what the chairman does, except that Kazuya seems to have more direct involvement in it, like choosing sides on who he supports or something.
I could just be pulling shit from my ass, though.
As for the gambles, the only one I know of is the 17-step mahjong against Muraoka.