We were playing in a private dining room, they were hosting me, and there were probably about 12 people at the table. We were playing 2 at time, and the winner would keep playing and the next person around the table after the loser would play. So you couldn't take advantage of the trick you mentioned, since the sum was from the new player. I guess the way to cheat would be to delay showing your hand versus the other guy, then sum up based on what you knew you would show (I think this is what they thought I must be doing), but the idea was both players should show pretty simultaneously.
Yes, I was able to do it more often than I thought I could. The funny thing was, most of the guys were much better than me at ping pong, but of course that didn't translate to their ability to get the ball into a cup, so I could see several of the better players were frustrated that they couldn't do it as they repeatedly attempted it. So I got some minor revenge for all beatings they gave me at the ping pong table :-) But, honestly, it's a privilege to play guys like that, and you're really happy to have the chance to get beaten by them.