The Experiment
The Paradox: Two Valid Arguments
Argument 1: The Dice Are Fair!
You're in the room. The dice are about to be rolled. Double-six kills everyone.
P(double-six) = 1/36 ≈ 2.8%
Therefore: P(survival) = 35/36 ≈ 97.2%
Relax! You'll almost certainly survive.
Argument 2: Count the Bodies!
When the experiment ends (double-six), who was shot?
The final batch is always 10× larger than all previous batches combined!
10n > 100 + 101 + ... + 10n-1
Over 90% of all participants are in the death batch.
Therefore: P(death) ≈ 90%
You're almost certainly doomed!
Which Argument Is Correct?
Both arguments are mathematically valid! The paradox arises from observer selection effects.
If you reason "I'm a random person in the room," then you're ~90% likely to be in the final batch.
The dice are fair, but you are not a random sample of dice rolls—you're a random sample of people.
Monte Carlo: Running 1000 Experiments
Understanding the Paradox
The Setup (John Leslie, 1996)
Imagine a room of infinite capacity. People enter in batches: first 10, then 100, then 1,000... Each time, two fair dice are rolled:
- Not double-six (35/36 chance): Everyone leaves safely. The next batch (10× larger) enters.
- Double-six (1/36 chance): Everyone currently in the room is shot. The experiment ends.
Why 90% Die Despite Fair Odds
| Round | Batch Size | Cumulative Survivors | If Killed Here |
|---|---|---|---|
| 1 | 10 | 0 | 100% death rate |
| 2 | 100 | 10 | 90.9% death rate |
| 3 | 1,000 | 110 | 90.1% death rate |
| 4 | 10,000 | 1,110 | 90.0% death rate |
| n | 10n | ~10n/9 | → 90% |
The key insight: the current batch is always about 9 times larger than all previous batches combined. So no matter when the experiment ends, roughly 90% of all participants were in the final (death) batch.
Connection to the Doomsday Argument
This paradox was developed by philosopher John Leslie to illustrate the Doomsday Argument.
If you're a "random" human, you're probably not among the first humans ever born. You're more likely near the middle of all humans who will ever exist. This anthropic reasoning suggests humanity's total population might be smaller than we hope.
The Shooting Room makes this abstract reasoning viscerally concrete: being "randomly selected" from a growing population puts you overwhelmingly in the final generation.
The Resolution
Both probability calculations are correct—they just answer different questions:
- 35/36 answers: "Given I'm in round N, what's the probability this specific roll kills me?"
- ~90% answers: "Given I'm a random participant in the experiment, what's the probability I'm in the death batch?"
The paradox reveals that observer selection can dramatically alter probabilities. You're not sampling dice rolls—you're sampling your own existence.