Can a magician bias the result of a fair die? Some time ago, Persi Diaconis was discussing probability and made the point that the level of information a person possessed about an event played a role in his accessing probabilities. To illustrate this point, he did a very nice demonstration showing how a magician can toss a fair coin in such a way that he will always get heads. 
(See 2:10 in a video of Diaconis  http://www.youtube.com/watch?v=ZdA7TeoZD_g)
I am curious if this is possible using a fair die?
TIA,
Matt
 A: This is more of a physics question, isn't it? Assuming you can control a specific way of rolling well enough, you could get any number you want by simply adjusting the starting position of the die in your hand.
The trivial case would be making a die roll over only once. Almost anyone can do this and thus control the result based on the position of the die before the roll.
A: The video linked discusses probability of the outcome of a coin-flip as a consequence of the observers knowledge of the world. The magic trick is an illustration.
On the subject of surprising results in the realizations of coin flips.
The $P(TTH)$ occurring first in a run of coin-flips is twice the $P(THT)$ than after it. The $P(THH)$ occurring first in a run of coin-flips is three times the $P(HTT)$ than after it.
There's a more at Mathworld on Coin flips.
Diaconis' more famous work about card shuffling uses group theory and Martingales to study how the entropy of separation distances increases with shuffling. How many times must a deck of cards be shuffled until it is close to random?
A: It's absolutely possible. Beyond the trivial example of rolling a die so that it falls out of hand rolling over exactly once, skilled rollers can throw along one rotational axis so that 2 of the 6 faces are eliminated (or simply less likely).
An informative example is casino craps: the person rolling must bounce the dice off the back wall for the throw to be considered legal. This rule was instituted because of actual problems of people biasing their throws; the technique is known as "dice sliding".
A: I think your question revolves around how you define stuff. 
When I think of a fair die or fair coin I think of an abstract entity that produces a sequence of random results that satisfies its advertised probability distribution.
So a fair die (or count or tack) by definition cannot be biased. 
Perhaps another way to look at it is that your question is stated in a way that is bound to lead to a paradox.
