# Difference between revisions of "Chance News 27"

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Halb rot und halb weiß<br> <div align=right> 19. Die schöne Müllerin<br>Franz Schubert, </div></blockquote> | Halb rot und halb weiß<br> <div align=right> 19. Die schöne Müllerin<br>Franz Schubert, </div></blockquote> | ||

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<blockquote>Consider the following two person game. Each player receives a random number uniformly distributed between 0 and 1. Each player can choose to discard his number and receive a new random number between 0 and 1. This choice is made without knowing the other players number or whether the other player chose to replace his number. After each player has had an opportunity to replace his number the numbers are compared and the player with the higher number wins. What strategy should a player follow to ensure he will win at least 50% of the time? </blockquote> | <blockquote>Consider the following two person game. Each player receives a random number uniformly distributed between 0 and 1. Each player can choose to discard his number and receive a new random number between 0 and 1. This choice is made without knowing the other players number or whether the other player chose to replace his number. After each player has had an opportunity to replace his number the numbers are compared and the player with the higher number wins. What strategy should a player follow to ensure he will win at least 50% of the time? </blockquote> | ||

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## Revision as of 13:58, 28 May 2007

## Contents

## Quotation

I could prove God statistically. Take the human body alone - the chances that all the functions of an individual would just happen is a statistical monstrosity.

George Gallup

This is from an ineresting article about the life of George Gallup: "The Human Yardstick", Williston Rich, Saturday Evening Post January 21,1939, p. 71. The article ends with:

His greatest delution is that he can forecast the stock market. his greatest fear, that a competitor will enter his field and be dishonest with the figures. His greatest devotion, to his family, his home and his church. He says "I could prove God statistically--.

Submitted by Laurie Snell

## Forsooth

The following Forsooths were in the May 2007 RSS News:

The Timesleader of 28 February tells us that taking regular dose of certain vitamins 'can actually increase the risk of mortality by five per cent'. Since the "risk of mortality' is already 100 percent this is very worrying.

AWF Edwards

Cambridge

Da springen drei Rosen, Halb rot und halb weiß

19. Die schöne Müllerin

Franz Schubert,

Submitted and sung by Laurie Snell

## How to own a random number

God created the integers; all else is the work of man, Leopold Kronecker

AACS is the copy protection technology used on HD-DVD and Blu-ray discs. The consortium that owns this technology are apparently trying to stop websites and newspapers publishing a specific 128-bit integer that, with suitable software, enables the decryption of video content on most existing HD-DVD and Blu-ray discs. As part of this effort, they have claimed ownership of the encryption key, which means that you cannot use, without written permission, that particular 30-digit integer (in base 10) and several million other unknown keys that they apparently are claiming ownership of. Not only that, but the numbers in question were chosen randomly so there is no simple way of knowing if your random choice conflicts with theirs, even if they were known publicly.

### Further reading

- How to own a random number, BoingBoing blog, 7 May 2007.
- You Can Own an Integer Too — Get Yours Here, Ed Felten, May 7, 2007 — this professor of Computer Science and Public Affairs at Princeton University suggests a way that you too can own your own random integer. He even suggests a use for your number:

Did we mention that a shiny new integer would make a perfect Mother’s Day gift?

Submitted by John Gavin.

## Two probability problems

IBM has a monthly "Ponder this challenge" which is often a probability problem. The April 2007 Challenge was the following random walk problem.

This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? You may consider the answer to be the limit as N goes to infinity of the fraction of integers between -N and N a frog starting at -N and randomly hopping as described misses on average. An answer correct to six decimal places is good enough.

You might also want to the Puzzle for February 2007 which provides another example of the occurence of the Golden Mean:

Consider the following two person game. Each player receives a random number uniformly distributed between 0 and 1. Each player can choose to discard his number and receive a new random number between 0 and 1. This choice is made without knowing the other players number or whether the other player chose to replace his number. After each player has had an opportunity to replace his number the numbers are compared and the player with the higher number wins. What strategy should a player follow to ensure he will win at least 50% of the time?