Key takeaways
Yes, winning back-to-back individual immunity challenges decreases your chances of surviving the next Tribal Councils. At the final 8, where a player has just won back-to-back immunities, they have:
- 75% chance of surviving the next Tribal Council (vs 86%)
- 65% chance of surviving the 2nd (vs 71%)
- 44% chance of surviving the 3rd (vs 57%)
The narrative tends to be “they’re just going to win all the challenges, we have to vote them out now!”. By becoming a challenge threat, you make yourself a winning threat as well.
Survivor is about alliances and manipulation. If there is a unifying point, like this person is a challenge beast we have to vote them out, I guess that’s as good of a reason as any to get people onboard.
So, what are the odds of surviving the next Tribal Councils? This is the position that Savannah is in at the time of writing, and this post will mostly refer to her.
Considerations
I’m going to use all 48 seasons of Survivor but the challenge thing is that the game changes a lot e.g. when they merge, how many players there are at merge, when a player wins back-to-back immunity challenges, how many are left, how many winners for each challenge there are, if the player loses one but wins the next one, two players that have won back-to-back immunity challenges, etc.
I could go into each and explain their impact on the analysis, but for now I’m just going to wave my hand and say they exist.
All of these things change the probability of being voted out next, so it’s not a straightforward calculation. In a similar way to other analyses, I’ll look at what the probability is of making it through the next Tribal Council unprotected is based on equal probability, and see what effect winning back-to-back challenges has on adjusting that probability.
This effect will be different for different parts of the game, but this will allow us to measure the average effect to use as a guide.
Model
I’ll use my standard model:
![\[\begin{array}{rl}\beta & \sim \text{normal}(0, 1.5) \\\lambda & = \text{log}\left(\frac{p}{1-p}\right) + \beta\\\kappa & = \frac{1}{1+e^{-\lambda}} \\y & \sim \text{bernoulli}(\kappa)\end{equation}\]](http://gradientdescending.com/wp-content/ql-cache/quicklatex.com-ce88df6c83baccb5d959cc616d5ad6be_l3.png "Rendered by QuickLaTeX.com")
Where
is the chance of being voted out based on equal chance
is the log odds of base probability plus an effect parameter 
.
If is above 0 then there is a positive effect, in this case higher chance of being voted out.
I’m going to fit the model for the 1st tribal unprotected after winning back-to-back individual immunity challenges, the 2nd, and the 3rd, to see if there is a change.
Results
Let’s look at the results.
It’s pretty interesting. According to the model, the first tribal after winning back-to-back individual immunity challenges definitely increases the chances of that player being voted out. Although the 2nd and 3rd, not so much, the posterior covers 0 pretty comfortably, and the 2nd tribal it’s slightly in the negative.
Based on this I’d say that the first tribal is what matters but the 2nd and third don’t really change the odds.
What does this mean in real terms? I’ll convert it to probabilities in a sec but to do so, I need to make a decision – a what stage of the game did someone win the back-to-back challenges?
Since I’m writing it just after Savannah won 2 in a row in Season 49, let’s do this for her case, at the final 8, and assume she does NOT win the next 3 challenges. I’m also going to flip it to the probability of surviving the next tribal council, rather than the probability of being voted out. Here are the probabilities.
Or Savannah has a:
- 75% chance of surviving the next Tribal Council (vs 86%)
- 65% chance of surviving the 2nd (vs 71%)
- 44% chance of surviving the 3rd (vs 57%)
Definitely lower than the baseline, assuming equal chance. And you can see how the solid line pretty much follows the dotted line after the first tribal. So it really is the first tribal council that matters the most.
Final thoughts
The narrative tends to be, “we have to vote them out now because we may not get another chance”. Winning a string of challenges elevates your threat profile. But I can’t really see someone winning Survivor based on challenges alone, maybe it would be good to keep the threats around and ensure true threats don’t win immunity.
One of my favourite winners is Rachel from S47. She won two back-to-back immunity challenges from the final 8, protected herself with an idol at final 6, and won the final two immunity challenges. That’s a strong finish.
Links
🔥survivorstatsdb / 🧑💻Github
Code
challenge-streak.R
