The Monty Hall Problem: Probability, intuition, and Math.

LET'S MAKE A DEALThe old game show, Let’s Make a Deal, featured a segment in which contestants could choose the prize behind one of three doors. “Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, ‘Do you want to pick door No. 2?’ Is it to your advantage to take the switch?”

This case provided an interesting case of conflict between our intuitive beliefs and math. This problem was so simple yet confusing, even math professors and other experts got it wrong. Below is an article about the whole story and below that is a link to play an online version of the game in which you can choose a door and then decide whether to switch. The site tallies your overall effectiveness at winning the prize.

The unexpected power of baby math: Adults still think about numbers like kids

“A new study has found new evidence that educated adults retain traces of their innate sense of numbers from childhood — and that it’s more powerful than many scientists think. The findings could contribute to the development of methods to more effectively educate or treat children with learning disabilities and people with brain injuries.”

The problem of really big numbers

“If you were around during the last technology boom and bust cycle of the early 2000s you were likely exposed to the concept of really big numbers. Countless business plans for all manner of ill-conceived ideas began with “If just 0.00001% of all internet users visit our site…” and used that as the core foundation of their revenue model. While it all seemed logical at the time, the logic of really big numbers had two fundamental failings.”

4th Down Bot. Live analysis of every N.F.L. fourth-down decision

4th Down Bot copyThis is a clever program that does an analysis of every 4th down play in every professional football game. It determines based on mathematical expected value whether teams should go for it, punt, or kick a field goal. It breaks down the math behind its decision making. What’s interesting is how often the mathematical decisions are not the ones followed by the people on the field. Who is right in a case like this? What happens when the “common sense” approach is different from the mathematically “true” approach?

How Oregon Coach Chip Kelly Can Spark ‘Moneyball’ Revolution In NFL

“Those fourth down calls epitomize Kelly’s aggressiveness but what the average football fan doesn’t realize is that Chip’s play-calls (the fourth down tries, fake punts, two-point conversions, etc.) are almost always the correct mathematical decision. Like Paul DePodesta and Billy Beane did in baseball, Kelly’s genius comes from exploiting arithmetic that other coaches are too naïve to acknowledge.”

A Natural Log: Our Innate Sense of Numbers is Logarithmic, Not Linear

“We humans seem to be born with a number line in our head. But a May 30 study in Science suggests it may look less like an evenly segmented ruler and more like a logarithmic slide rule on which the distance between two numbers represents their ratio (when ­di­vided) rather than their difference (when subtracted).”

Do athletes really get “hot hands” when they’ve hit a few shots in a row?

Interesting research into whether making one basketball shot makes you any more likely to hit your next one. The first two links summarize the fallacy and the third one questions it. Interesting way of using math to help us know and understand something too large to keep track of or understand simply by our memory.

How does math help us understand the world around us? How do we reconcile mathematical knowledge that contradicts our intuitive knowledge?