*[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!
Link
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*[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!
Link
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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!*)
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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!*)
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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. Parameters for random variability came from the extent to which each individual July was warmer or cooler than usual.

After running the simulation 100,000 times, “we could see how many times we got an extreme temperature like the one in 2010,” said Rahmstorf. After that, the researchers ran a simulation that didn’t include the warming trend, then compared the results.

“For every five new records observed in the last few years, one would happen without climate change. An additional four happen with climate change,” said Rahmstorf. “There’s an 80 percent probability” that climate change produced the Russian heat wave.

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. Parameters for random variability came from the extent to which each individual July was warmer or cooler than usual.

After running the simulation 100,000 times, “we could see how many times we got an extreme temperature like the one in 2010,” said Rahmstorf. After that, the researchers ran a simulation that didn’t include the warming trend, then compared the results.

“For every five new records observed in the last few years, one would happen without climate change. An additional four happen with climate change,” said Rahmstorf. “There’s an 80 percent probability” that climate change produced the Russian heat wave.