domingo, 27 de maio de 2012

Dice

Imagine a world without random numbers. In the 1940s, the generation of statistically random number was important because was important to physicists simulating thermonuclear explosions, and today, many computer networks employ random numbers to select unbiased samples of potential voters.
Dice, originally made  from anklebones of roofed animals, were one of the earliest means for producing random numbers. In ancients civilizations, the gods were believed to control the outcome of dice tosses; thus, dice were relied upon to make crucial decisions, ranging from the selection of rulers to the division of property in an inheritance. even today, the metaphor of God controlling dice  is common, as evidence by astrophysicist Stephen Hawking's quote, "Not only God play dice, but He sometimes confuses us by throwing them where they can't be seen."
the oldest known dice were excavated together with a 5,000 year backgammon set from the legendary Burnt City in southeastern Iran. The city represents four stages of civilization that were destroyed by fires before being abandoned in 2100 B.C. At this same site, archeologists also discovered the earliest known artificial eye, which once stared out hypnotically from the face of an ancient female priestess or soothsayer.
For centuries, dice rolls have been used to teach probability. For a single roll of an n-sided die with a different number for each face, the probability of rolling any value is 1/n. The probability of ruling a particular sequence of i numbers is 1/n^i. For example, the chances of rolling a 1 followed by 4 on a traditional die is 1/6^2 = 1/36. Using two traditional dice, the probability of throwing any given sum is the number of ways to throw that sum divided by the total number of combinations, which is a sum divided by the total number of combinations, which is why a sum of 7 is much more likely than a sum of 2.

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