Snakes and Ladders can be analyzed by converting it to a Markov Chain

University of Washington data scientist Jake Vanderplas found himself trapped in an interminable series of Snakes and Ladders (AKA Chutes and Ladders) with his four-year-old and found himself thinking of how he could write a Python program to simulate and solve the game. Read the rest

Turns out Star Trek redshirts are not likeliest to die

The Museum of Mathematics recently hosted James Grime's talk "Star Trek: The Math of Khan." He debunked a common stereotype about the show's security detail: redshirts are not the most likely crew to die. Read the rest

Nontransitive dice – how to win every time

[While I'm away for a week, I'm posting classic Boing Boing entries from the archives. Here's a gem from 2006.]

I'm reading a terrific book by William Poundstone called Fortune's Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street. On page 153 Poundstone writes about a 1968 dinner meeting between mathematician Edward Thorp and fund manager Warren Buffett. Poundstone mentions in passing that Buffett and Thorpe discussed their shared interest in nontransitive dice. "These are a mathematical curiosity, a type of 'trick' dice that confound most people's ideas about probability," writes Poundstone.

Curious, I googled "nontransitive dice" and found a nice description of them by Ivars Peterson at the Mathematical Association of America's website.

Peterson introduces the subject with this intriguing paragraph:

The game involves four specially numbered dice. You let your opponent pick any one of the four dice. You choose one of the remaining three dice. Each player tosses his or her die, and the higher number wins the throw. Amazingly, in a game involving 10 or more throws, you will nearly always have more wins.

The trick is to always let your opponent pick first, and then you pick the die to the left of his selection (if he picks the die with the four 4s, then circle round to the die with the three ones). It's just like playing Rock, Paper, Scissors -- only you get to see what the other guy picks in advance.

With these dice, you always have a 2/3 probability of winning -- what a great sucker's bet! Read the rest

SF writing competition: a world without the Normal Curve!

Charles writes, "It's hard to imagine how we would have gotten all of the whiz-bang technology we enjoy today without the discovery of probability and statistics. From vaccines to the Internet, we owe a lot to the probabilistic revolution, and every great revolution deserves a great story!

"The Fields Institute for Research in Mathematical Sciences has partnered up with the American Statistical Association in launching a speculative fiction competition that calls on writers to imagine a world where the Normal Curve had never been discovered. Stories will be following in the tradition of Gibson and Sterling's steampunk classic, The Difference Engine, in creating an imaginative alternate history that sparks the imagination. The winning story will receive a $2000 grand prize, with an additional $1500 in cash available for youth submissions."

What would the world be like if the Normal Curve had never been discovered? (Thanks, Charles!) Read the rest

The mathematics of tabloid news

Leila Schneps and Coralie Colmez have an interesting piece at The New York Times about DNA evidence in murder trials, the mathematics of probability, and the highly publicized case of Amanda Knox. What good is remembering the math you learned in junior high? If you're a judge, it could be the difference between a guilty verdict and an acquittal. Read the rest

A new system for studying the effects of climate change

I've talked here before about how difficult it is to attribute any individual climactic catastrophe to climate change, particularly in the short term. Patterns and trends can be said to link to a rise in global temperature, which is linked to a rise in greenhouse gas concentrations in the atmosphere. But a heatwave, or a tornado, or a flood? How can you say which would have happened without a rising global temperature, and which wouldn't?

Some German researchers are trying to make that process a little easier, using a computer model and a whole lot of probability power. They published a paper about this method recently, using their system to estimate an 80% likelihood that the 2010 Russian heatwave was the result of climate change. Wired's Brandon Keim explains how the system works:

The new method, described by Rahmstorf and Potsdam geophysicist Dim Coumou in an Oct. 25 Proceedings of the National Academy of Sciences study, relies on a computational approach called Monte Carlo modeling. Named for that city’s famous casinos, it’s a tool for investigating tricky, probabilistic processes involving both defined and random influences: Make a model, run it enough times, and trends emerge.

“If you roll dice only once, it doesn’t tell you anything about probabilities,” said Rahmstorf. “Roll them 100,000 times, and afterwards I can say, on average, how many times I’ll roll a six.”

Rahmstorf and Comou’s “dice” were a simulation made from a century of average July temperatures in Moscow. These provided a baseline temperature trend.

Read the rest

Odds are good you won't be hit by a satellite this weekend

A retired climate research satellite will plummet to Earth on Friday. There is a 1-in-3,200 chance of it hitting a person. BUT! Don't worry too much about that, says Scientific American reporter John Matson. A 1-in-3200 chance of a piece of the satellite hitting somebody, is not the same as a 1-in-3200 chance of it hitting you, specifically. He calculates the risk of that as 1-in-22 trillion. Read the rest