The Dice Roller's Dilemma

Technically, when you roll a dice each number has an equal opportunity to land face up. However, we all know this is not the case. We all know that the damn things apply Murphy's Law, and we damn know that the smug little bastard to your left gets all the good rolls. So, naturally, we try to cheat chance, fool fate and do whatever seems reasonable to appease the Random Number God.

Two prevailing theories have led to the dice roller's dilemma:

1. A die that has consistently got good rolls is a 'good' die. Roll this die.
2. A die that has consistently got good rolls has used up its 'luck'. Don't roll this die.

Isn't that sweet?

Mind you, this applies to any random number generator, including gambling and the lottery. Almost every person who buys a ticket chooses numbers that pop up often, following theory one, or rare numbers following theory two.

Which theory, if any, works? That's the thing with random. You never know.