Oh what the hell, I'll take a stab at it.....
Episode #1:
During the zodiac challenge, Recruit Debb was very bossy and annoying to her fellow recruits. As a result she was voted off in a 15-1 vote. Although she voted for Kimmi b/c of her X-rated bedtime stories, Debb decided to use the takedown rule on Recruit Jeff because she didn't want to face the prospect of sitting next to the annoying Kimmi on the long plane ride home. Plus, Jeff was sick so it seemed like a mercy decision.
Episode #2:
Fearing his long term ability to win, the Scerri's kids alliance votes out Recruit Kel, gaining support from several Kucha's with a fabricated story about Kel smuggling contraband into the bathroom with him where he proceeded to stay for 10-12 minutes. Kel gets his revenge and nabs Jerri as his takedown target.
Episode #3:
A mercy vote by the recruits sends MadDog Marilyn packing after shewas unable to compete in any of the challenges. MadDog brings Tina with her claiming that she was "conjoined to Tina" and therefore had no choice.
Episode #4:
Citing the fact that he was mad that the producers actually expected him "to actually do stuff and work hard and things like that" Recruit Mitchell asked to be dismissed. He was, which meant that the takedown rule would not apply at this episode's Dismissal Hill. At the Hill, the tribe is finally able to rid themselves of the annoying Kimmi.
Episode #5:
After his continued laziness cost them yet another Mission reward, Nick is the easy choice for Dismissal Hill. For his takedown he grabs Amber cause, "I ain't never had me no white woman."
Episode #6:
During mission training Recruit Mike accidentally falls on a live grenade, which blows up killing him instantly. Once again there will be no takedown at Dismissal Hill. Sensing an opportunity, Recruits Liz, Rodger and Alicia band together to vote off the one remaining member from Jerri's kids alliance, the Colbster.
Episode #7:
The final four features Keith, Rodger, Liz and Alicia. Keith is the target, but somehow secures amnesty when he leads the recruits on a successful mission. Rodger and Liz band together to vote off Alicia. Alicia, pissed that Liz turned on her uses the takedown rule to bring her with.
Episode #8:
In the final episode, Keith and Rodger complete in the Gauntlet, a series of 7 grueling competitions. The winner of each leg gets a dogtag and then at the end of the show the last six recruits dismissed are brought back to vote. They vote by giving up their dogtag to the recruit they vote for...in the end, the recruit with the most dogtags wins the money.
The jury for the final vote will consist of Nick, Amber, Colby, the executor or Mike's estate, Liz and Alicia.
Keith, knowing that Rodger is much more likeable than he could ever dream of being, figures he needs to win all 7 competitions in order to claim the money.
The first competion is an all night run: keith wins
Comp #2 is an obstacle course: Keith wins
Comp #3 is a pull-up contest, Rodger quits after 3: Keith wins
Comp #4 is a weapons exercise: Rodger finally wins one
Comp #5 is an all-nihgt cooking competition: Keith wins
Comp #6 is Chinese Checker: keith wins
Comp #7 is Indian leg wrestling: Keith wins
Final tally = 6 dog tags for Keith and 1 for Rodger
At the final vote, Keith only needs one vote to be the winner:
Liz = votes for Rodger
Alicia= votes for Rodger
Nick = votes for Rodger
Amber = Votes for Rdoger
Mike's estate = votes for Rodger
And now the Colbster.....colby shocks everyone and votes for his old bnk buddy, Keith
So there you have it, Keith wins.
Go ahead and try to poke holes in my theory, it is based on the most informative of spoilers and logical reasoning.