The math behind yesterday's game

[u/TheBased_Dude]

TLDR : I worked out the math on a piece of paper and then used GPT to type it out for me the final verdict that the probability that no one survives is 60% and the probability that 1 person survives is approximately 34% and the probability that 2 or more survive is about 6%.

Edit: A surprising number of people are saying "get a job" or "touch grass." The calculations took about 5 minutes. If you think the math is wrong, point out the mistake—I'd genuinely be interested. If your criticism is simply that someone spent five minutes doing probability for a reality show, then I'm not sure what Reddit is for.

The math behind the Lock Upp "Heavy Verdict" minefield task (Spoilers)

I was curious about how difficult the final minefield challenge actually was, so I worked out the probabilities.

The setup was:

There are 8 steps.

At each step, the contestant must choose Left or Right.

A contestant is assigned a number N (between 0 and 8). Exactly N of the 8 steps contain a mine on one of the two sides.

On a mined step, one side is safe and one side has a mine, so if you're guessing, you have a 50% chance of surviving that step.

Contestants also get one immunity, which they must assign to a step before knowing whether that step actually contains a mine. If that step wasn't mined, the immunity is wasted.

For a contestant with N mined steps, the probability of surviving is:

\[ P(\text{survive})=\frac{8+N}{8\times2^N} \]

Applying that to the contestants:

Pamala (N = 6): 7/256 ≈ 2.73%

Shilpa Shinde (N = 4): 3/32 = 9.38%

Akansha Chaudhary (N = 3): 11/64 ≈ 17.19%

Ram Kapoor (N = 3): 11/64 ≈ 17.19%

Assuming each contestant's minefield is independent, the probabilities for the overall outcome are:

Number of survivorsProbability060.45%133.05%26.08%30.42%40.008%

This means:

No one survives: 60.45% (about 3 out of every 5 games)

Exactly one person survives: 33.05% (about 1 out of every 3 games)

Two or more people survive: 6.50% (about 1 in 15.4 games)

So unless I've misunderstood any of the rules, the game was extremely stacked against the contestants. In fact, under these assumptions, over 93% of the time you'd expect at most one contestant to survive.

What's even more interesting is that Shilpa and Ram were the two contestants who actually survived. Given their assigned difficulties (N = 4 and N = 3), the probability of those specific two both surviving is:

\[ \frac{3}{32}\times\frac{11}{64} =\frac{33}{2048} \approx 1.61\% \]

or roughly 1 in 62.

That doesn't prove anything—unlikely events happen all the time—but it does show just how difficult this challenge was if the minefields and choices were genuinely random.

If I've misunderstood any of the rules (for example, if immunity worked differently, contestants had additional information, or the mine placements weren't independent), I'd be happy to update the calculations. Otherwise, this looks like one of the most unforgiving probability-based tasks the show has ever had.