Rock Paper Scissors

[Poker Punk 9]

I won some money of this guy playing rock paper scissors. It was a weird situation so I was wondering what you guys think. The deal went like this first to 3 wins the bet. But, he starts with a 2 win lead. But, I was getting paid 10-1.

I didn't have much time to think about it but I was figuring that I'm going to win 1/9 times(if we assume we are equally skilled in rock paper scissors) and I was getting paid 10 to 1. Is my logical flawed in this scenario? Was this a good gamble on my part?