The Challenge: Fresh Meat II Wes's Coalition

With Wes's coalition in such a dominate position, the 7 teams in it have to start moving beyond the threat of Kenny's alliance (3 teams) and strategizing  for the end game. In particular two things: avoiding the elimination round and being one of the final four teams that gets to compete for the cash prize. As long as Kenny's alliance remains, Wes's coalition will keep choosing them to go into the elimination challenge. Wes's coalition could be left with 7 teams or it could lose a couple elimination challenges and be left with 5 teams when Kenny's alliance is down to one team. At that point Wes's coalition will have to turn on itself.

Wes's first priority is to keep the teams in the coalition together so those on the outside do not defect to Kenny's alliance. At the same time, the teams in Wes's coalition want to form a union of 4 or 5 teams. This union would then try to control the game. If the union wins a reward challenge, it will select one of the non-union teams into the elimination challenge and vote another non-union team into the elimination challenge. The most important thing is to be one of the teams in the union. It also helps if the teams in your union are good at reward challenges but bad at the final round (which would be an unlikely combination). Besides, if a team in your union is likely to be good in the final round you can turn on them when there are 5 teams left and vote them into the elimination challenge.

So that's the balancing act. Form a strong union while at the same time keep the teams non-union teams from defecting. If you are a non-union team you would have to win at least one and possibly four elimination challenges just to survive to the final round. What is the probability of a non-union team making it to the final round?

Let's start with the easier case of a union team making it to the final round. To simplify things, let's say there are 4 union teams, they win all the reward challenges and control the voting thus making it so only non-union teams go into the elimination challenges, and that each team in an elimination challenge has a 50% chance of winning it. When there are 5 teams left one of the union teams will have to go into the elimination challenge against the non-union team. Under such a scenario, the union team has a 87.5% chance of making it to the final round: 3/4*1+1/4*1/2 = 87.5% (Chance of not being selected for the elimination round * chance of making it too the final round if not selected to the elimination challenge + chance of being selected for the elimination challenge * chance of winning the elimination challenge)

Now the case of a non-union team making it to the final round. Some assumptions: each of the non-union teams are equally likely to be selected to the elimination challenge and each of the teams in an elimination challenge is equally likely win. Let's say there are 8 teams left. 7 teams in Wes's coalition and a remaining team in Kenny's alliance. Let's say the union is 4 teams and the non-union is 3 teams. Kenny's alliance team is always voted into the elimination challenge as long as it remains and one of the non-union teams is randomly selected into the challenge. Under such assumptions a non-union team has a 14.6% chance of making it to the final round.

87.5% > 14.6%  It is much better to be in the union than not in the union. In real dollar terms--I believe the teams in the final round will be competing for $300,000--being in the union is worth about $55,000 more in expected earnings.