Paradoxes - Puzzles and Hidden Patterns
Five short lessons on the Monty Hall problem, Newcomb's paradox, Catch-22 black swan events and Benford's law.
Some answers feel wrong even when they are right, and some traps are built so that no exit exists. These shorts cover a game show puzzle, a predicting wizard, a bureaucratic loop, rare catastrophic events and a pattern hidden in real-world numbers.
The Monty Hall Problem
Published 2026-07-22 · Watch the short
You pick one of three doors, with a car behind one and goats behind the other two. The host, who knows what is behind every door, opens a different door and shows a goat. Should you switch? Most people say it makes no difference, but switching raises your odds from one in three to two in three.
| Choice | Chance of winning |
|---|---|
| Stay with your first door | 1 in 3 |
| Switch to the other door | 2 in 3 |
The host never picks randomly, so the two-in-three chance held by the other doors lands on the one that remains. In 1990 Marilyn vos Savant explained this in her column and received roughly 10,000 letters, most saying she was wrong. The short adds that mathematician Paul Erdős initially refused to accept it until a computer simulation supported it.
Newcomb’s Paradox
Published 2026-09-25 · Watch the short
Physicist William Newcomb proposed the problem in 1960, and philosopher Robert Nozick later made it famous. Box A is transparent and holds $1,000. Box B is opaque and holds either $1,000,000 or nothing. A predictor who has never been wrong filled the boxes in advance, putting the million in Box B only if it predicted you would take Box B alone.
- Taking both boxes looks sensible, since the contents are already fixed and you gain the guaranteed $1,000.
- Taking only Box B looks sensible, since everyone the predictor judged correctly who took one box ended up with a million.
The short reports that a 2020 survey of professional philosophers was still nearly split. It adds that the deeper question is whether choosing freely was ever part of the equation.
Catch-22
Published 2026-07-15 · Watch the short
A Catch-22 comes from Joseph Heller’s 1961 novel of the same name. A pilot can be excused from dangerous missions if he is insane, but asking to be excused proves he is sane, so he can never get out. Everyday versions include needing experience to get a job that is the only source of experience.
The short’s advice is that a real Catch-22 is not a puzzle with a missing move. It is a structure designed so that no solution exists, so it is worth asking whether the trap was ever meant to have a way out.
Nassim Taleb and Black Swans
Published 2026-07-25 · Watch the short
In 2007 statistician Nassim Taleb published The Black Swan, arguing that the events that reshape history are rare, catastrophic and only obvious in hindsight. The short gives the 2008 collapse of Lehman Brothers and the March 2020 pandemic shutdowns as examples, and warns of a severe solar storm hitting the power grid, citing a 1989 Quebec outage and a 2014 Lloyd’s of London study.
Important
The solar storm figures, including how many people could lose power and for how long, are the video’s claims. They are worth checking against primary sources and are not presented here as verified.
Benford’s Law
Published 2026-08-25 · Watch the short
In many real-world data sets, such as populations, river lengths and stock prices, the first digit is not spread evenly. The digit 1 leads about 30 percent of the time, 2 appears less often, and so on downward. This is called Benford’s law. Forensic accountants sometimes use it to spot fraud, since invented numbers tend to spread digits more evenly than natural data does.
Conclusion
Each puzzle shows that intuition and reality can disagree. Updating on new information, noticing structures with no exit, respecting rare risks and spotting hidden patterns all begin with distrusting what simply feels right.
FAQ
- 1 in 3
- 1 in 2
- 2 in 3
- 3 in 3
(3) Staying keeps your original one in three, while switching wins two times out of three.
The short says Marilyn vos Savant’s correct explanation was accepted immediately by readers.
False. She received roughly 10,000 letters and most of them said she was wrong.
- After you choose
- Before you walk in
- While you are choosing
- Never
(2) The prediction already happened, so the boxes are already filled and nothing you do can change what is inside.
The short says a 2020 survey found professional philosophers still nearly split on Newcomb’s paradox.
True. This is the video’s report of the survey.
- They are frequent and predictable
- They are rare, catastrophic and obvious only after the fact
- They only affect banks
- They are always natural disasters
(2) The short gives the 2008 Lehman Brothers collapse and the 2020 shutdowns as examples.
| Concept | Description |
|---|---|
| A. Monty Hall problem | 1. First digits are not spread evenly in real data |
| B. Catch-22 | 2. A rule that protects itself so there is no exit |
| C. Benford’s law | 3. Switching doors raises the odds of winning |
A - 3, B - 2, C - 1.
Vocabulary
References
- Travis Mayo. Switching doors doubles your odds. YouTube Shorts, 2026-07-22.
- Travis Mayo. Pick the right box!. YouTube Shorts, 2026-09-25.
- Also posted: 2026-07-15.
- Travis Mayo. Stuck because every solution creates another problem?. YouTube Shorts, 2026-07-15.
- Travis Mayo. Nassim Taleb explains why experts miss the biggest risks. YouTube Shorts, 2026-07-25.
- Travis Mayo. August 24, 2026 (Benford’s law). YouTube Shorts, 2026-08-25.
- Also posted: 2026-06-30.