Last One Standing - Colegiul National C. Negruzzi (Iași - Roumanie)

In the game show ’Last One Standing’, n contestants are arranged in a circle, each numbered from 1 to n. The host eliminates contestant number 1, and then counts every second contestant clockwise, who is then asked to leave the circle. This process repeats until only one contestant remains.
If you are a contestant on this game show, what seat should you sit in to be the last one standing?
Further possible questions are:
• If instead every kth contestant is eliminated, what is the optimal seat?
• Further, suppose the mth contestant picked is the winner. What is the optimal seat in this game?
• Suppose the host now alternates, eliminating every second player, then every third player, and then repeating. What should your strategy be now?