Any given Dice Room can only give this effect once. When Isaac crosses the die, a certain effect will occur that randomizes a certain aspect of the run, dependent on how many pips were on the die face shown.
The amount of pips shown will be between one to six, chosen randomly.
In addition to whatever else the room holds, there will always be a symbol of one of the sides of a six-sided die in the 5x5 center of the room.