Hold on I think I have picked up the meaning of this game?
Are you not picking 1 team to win per week? Or is it a single team to win the whole competion so too speak?
Survivor is a variation of pickem where instead of picking the winners of ALL the games for that week, you only pick one team that you think will win their game for that week.
Example
Week 1. I pick the Patriots to beat the Dolphins. If the Patriots WIN, I move on to Week 2. If the Patriots tie or lose, I get 1 strike. If the Pool is a single elimination pool, I am eliminated. If the pool is double or triple elimination, I move on to week 2, but have 1 strike.
I can not pick the Patriots again (for the entire season). Once a team is picked, its considered "Used" and can no longer be picked again... that is part of the strategy.
Week 2. I pick the Cowboys to beat the Giants. Same thing as I explained in week 1. If the Cowboys win, I move onto
week 3. If they tie or lose, I get another strike. If the Pool is Double elimination, I am eliminated from the Pool. If its Triple elimination, I move onto week 3.
I can not pick the Cowboys again (for the entire season). Once a team is picked, its considered "Used" and can no longer be picked again... that is part of the strategy.
You play until there is only one player left (Sole Survivor) OR to the end of the season (in which anyone that is still alive is considered co-winners).
You can only play as many weeks as you have teams in the league. The NFL has 32 teams, so you can easily go a full 17 weeks. Other leagues might have longer seasons, but they don't have enough TEAMS to go long. Survivor is designed to be HARD, so its RARE that Surivor leagues even get into double digit weeks, specially with soccer where TIES are common and tend to bite survivor picks in the butt lol
Anyway... hope that helps you understand a bit better.