The Probability Problems That Make Your Brain Hurt - AfterMaths Summer Special 2 2026

Probability often feels as though it should be intuitive, right up until the mathematics tells us that our instincts are completely wrong.

In this AfterMaths Summer Special, Jon and Becky explore the strange mathematics of chance. From rainy-day board games and rolling two dice to coin-toss streaks, lottery numbers and casino myths, they investigate why humans are so determined to find patterns in genuinely random events.

Why is seven the most likely total when rolling two dice? How can just 23 people produce a better-than-even chance of two sharing a birthday? Are 1, 2, 3, 4, 5 and 6 genuinely bad lottery numbers? And after choosing between three mysterious doors, why should you abandon your original choice?

The episode concludes with the famously counterintuitive Monty Hall problem: three doors, two goats, one car and a very good mathematical reason to switch.

Expect hidden maths, questionable gambling strategies and several probability problems capable of making your brain hurt.

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Thanks for listening, and as ever, keep doing the maths.