Dice in any game contribute suspense. Your strategy may appear flawless, but dice represent the fickle finger of Fate that tends to poke you in the eye just when victory is in sight. On the other hand, it can also point the way to safety just when you think all hope is lost. In a role-playing game, dice are the element of chance that is the great equalizer between the GM and the players. For the GM, dice are both a limitation and a liberation. The GM already bears the burden of describing a world and all the inhabitants the players encounter. When the dice are rolled, however, there is no such burden except to describe the results. Here is where the GM gets to participate like a player, where events in the world the GM created can be influenced by an external neutral force. For those GMs who rarely get the opportunity to be players, this is where they, too, can watch events unfold from a non-omniscient point of view.
In order for this dynamic to work, it is necessary for the dice to be rolled in the open. That is to say, the dice ought to be rolled in full view of the players and the GM. Certain kinds of rolls would still be made secretly by the GM, such as a percentage chance of a certain event or encounter happening or when a player character attempts a skill for which success is not readily discernible (e.g. searching for a secret door or detecting a trap), but rolls that represent a contest between characters or a character and the environment should be visible to all participants in the situation.
One problem this alleviates is distrust by the players. If a player can see the GM's roll, he or she knows that the GM is not fudging rolls for the players' benefit or detriment. Although some GMs are suspected of fudging rolls in favor of their NPCs or monsters, I suspect many more are actually guilty of fudging rolls in favor of the players because they do not wish to be too harsh. I suspect this because I was one of those GMs in my early days in the hobby. Mollycoddling players does them no good in the long run. You may think you are helping them, but in actuality you deprive them of the true taste of victory when they succeed if you withhold the bitterness of defeat when they fail. You are also obstructing their growth as gamers.
Any given dice-rolling tradition is probably as old as any other. Some GMs roll in the open; some roll in secret; some let the players roll, but never tell them the target number; some even roll for the players, too. Different groups have different needs. My needs, both as a GM and a player, require that I get to roll dice and let them fall where they may.
[Originally posted here in Fudgerylog.]