When Should I Draw?

[CCass]

Assume that you are one of 12 participants in a blind draw. Each of the 12 participants paid $100, and there is 1 winning ticket worth $1,200. Mathematically, what is the best position to draw from? Is there any advantage to any of the positions?

Now assume that there are 12 tickets and only one winner, but you can see the other draws as they happen, and if the "winner" is drawn, you don't have to "buy" your chance, and can therefore save your $100. What is the best position to draw from in this scenario?

I have attempted to compute answers to both of these scenarios, but I fear my math skills are lacking, so I have turned to the experts to either concur with my findings, or expose my shortcomings.