Is it disadvantageous to win the first individual immunity challenge?

No player in Australian Survivor history has won the first individual immunity challenge and gone on to win the game. Is winning the first one disadvantageous? Does it raise the player’s threat level too much?

Nah, probably not. Here’s why.

The first individual immunity challenge

Firstly, let’s look at the first individual immunity challenges for the nine seasons of Australian Survivor.

Two players have finished second but no one has won. Is this weird?

Probabilistically speaking

Let’s simulate this by assuming equal probability of winning for each player i.e. the chance of winning the season is 1/(number of players). If there are 10 players in the first challenge, there is a 1/10 chance the player who wins the first challenge also wins the season. I’ll randomly draw a winner for each season.

library(tidyverse)
library(survivoR)

filter_post_merge <- function(df) {

  if("tribe_status" %in% colnames(df)) {
    out <- df |>
      filter(tribe_status == "Merged")
  } else if("challenge_id" %in% colnames(df)){
    out <- df |>
      left_join(
        survivoR::challenge_results |>
          distinct(version_season, challenge_id, tribe_status),
        join_by(version_season, challenge_id)
      ) |>
      filter(tribe_status == "Merged")
  }

  out

}

filter_au <- function(df, .season = 1:99) {

  df |>
    filter(
      version == "AU",
      season %in% .season
    )

}

p <- survivoR::challenge_results |> 
  filter_post_merge() |> 
  filter_au() |>
  filter(
    challenge_type %in% c("Immunity", "Immunity and Reward"),
    outcome_type == "Individual"
  ) |> 
  group_by(version, version_season) |> 
  slice_min(challenge_id) |> 
  summarise(n_players = n_distinct(castaway)) |> 
  mutate(p = 1/n_players) |> 
  pull(p)

n <- 4000
mat <- matrix(runif(length(p)*n), ncol = length(p))
y <- apply(mat, 1, function(x) sum(x < p))

table(y)/n

After 4000 simulations, the above chart shows the probability distribution of how many players won the first individual immunity challenge also won the season out of the 9 Australian Survivor seasons. There is about a 47% chance that out of 9 seasons, there would be 0 cases of this happening. So, pretty much 50/50 whether we see this happen 0 times or 1 or more times.

Therefore, can’t say it’s a disadvantage; it’s well within the realm of possibility.

But, there have only been nine seasons which is a small sample. What about the US?

Right. What about the US?

Same thing here, but simulating across all 47 seasons.

p <- survivoR::challenge_results |> 
  filter_post_merge() |> 
  filter_us() |>
  filter(
    challenge_type %in% c("Immunity", "Immunity and Reward"),
    outcome_type == "Individual"
  ) |> 
  group_by(version, version_season) |> 
  slice_min(challenge_id) |> 
  summarise(n_players = n_distinct(castaway)) |> 
  mutate(p = 1/n_players) |> 
  pull(p)

n <- 4000
mat <- matrix(runif(length(p)*n), ncol = length(p))
y <- apply(mat, 1, function(x) sum(x < p))
table(y)/n

Based on this, we would expect about 4-5 players (mean is 4.36) out of 47 seasons who have won the first individual immunity challenge to also win the season. 5 players have done so in the US.

It is true that challenge threats are targeted post-merge because “they’re just going to win every challenge” and as soon as they lose “we have to vote them out now because we won’t have another chance”. So if anything, it should be lower, but it’s right in the middle.

Final thoughts

Definitely not a disadvantage to win the first immunity challenge. And it’s probably really nice to hold it for the first vote after merge.

The fact that no one who has won the first individual immunity challenge and also won the game in Australian Survivor isn’t unusual, but we’ll reassess in the next 10 years.

If you want more info or the data, follow the links.

• {survivoR} package
• The Sanctuary
• Google sheets data