@calvinhobbesliker:
@Dr.:
There’s another method:  Gather together multiple decks of cards (with the same card back, of course) and remove every card that isn’t an Ace, 2, 3, 4, 5, or 6.  Shuffle them together, and whenever you’d roll a die, draw one card and that’s your result.
This guarantees that throughout the game you’ll roll the same amount of one number that you’ll roll of any other.
How does it do that?
Simple.  Let’s say that you have a single deck of cards and you’ve taken out everything valued at 7 or higher (counting aces as ones).  This leaves you with 24 cards, four of each number (an ace of diamonds, an ace of spades, an ace of hearts, and an ace of clubs.  Then a two of diamonds, etc. and on up).
Now, let’s say that you roll 2,496 dice over the space of a game (each player has his or her own deck).  That means you’ve rolled exactly 416 ones, 416 twos, 416 threes, 416 fours, 416 fives, and 416 sixes.  Every possible die roll number has been rolled an equal number of times.  You did not roll a “6,” an automatic miss for every unit either attacking or defending, any more often than you rolled a “1,” an automatic hit for every unit either attacking or defending.
Completely random (assuming a competent shuffle), but no luck.