Dice in Dungeons of Olde have a Die Rank (DR) equal to their number of sides. Thus, d6's have DR 6. The Dungeons of Olde rules require dice with an odd number of sides, and sometimes even call for unusually large dice; for rules to handle these situations, refer to Odd Dice Ranks.
Die rolls are described in the following format: NdR, where N is the number of dice thrown, and R is the die rank, or number of sides on the die. Exploding dice are indicated with an ! immediately after the die rank. Thus, a declaration of 2d6 means two six-sided dice, while 2d8! indicates two exploding eight-sided dice.
Sometimes, an Adjustment will be made to a die roll. In such cases, the number to be added to or subtracted from the roll will be included in the die declaration immediately following the number of sides. As such, 2d4+1 directs you to roll two 4-sided dice, and add 1 to the total, while 1d12!-1 declares that you roll one exploding 12-sided die, and subtract 1 from the result.
Rolling Dice vs. Throwing Dice
In these rules, a throw of the dice is the single, specific act of shaking a die (or dice) and dropping it (or them) onto the table to randomly generate a single value. A die roll, on the other hand, refers to the potentially multi-step process of using dice produce a final value, including any modifications, additions from any exploding dice, and adjustments. Thus, a single die roll may include one or more throws of the dice, along with a bit of math to factor in modifications and adjustments.
For example, a die roll calling for 2d4!+1 (two four-sided dice, exploding, plus one point) begins with a throw of two d4's, which turn up a "2" and a "4", for a subtotal of 6. Since these are exploding dice, however, the die showing the "4" is picked up and thrown again, this time showing another "4,"" and exploding again. The value of 4 is added to the running total, bringing it to 10, and that die is thrown again, this time turning up a "1,"" which brings the running total to 11. Since we've finished throwing dice, we find the final result of the roll by adding in the adjustment of +1, for a final total of 12.
The distinction between die rolls and die throws is generally clear from context throughout the rules, so don't worry too much about it. But we did want to be clear that Dungeons of Olde does deliberately use these words to mean slightly different things.
Many rolls in Dungeons of Olde are made with exploding dice. When throwing an exploding die, if the maximum value for a die is shown, its value is counted in the total for the roll, then the die is thrown again, and that value is also added to the total. The process is repeated until the die shows a result other than the maximum value.
For example, an exploding d8 is thrown and shows an "8", the maximum possible value. That 8 is counted as part of the total for the roll, and the die is thrown again, this time showing a "4". Since 4 is not the maximum value on a d8, the roll is now finished. The 4 on the second throw is added to the previous total of 8, for a final total of 12.
Odd Dice Ranks
The standard array of polyhedral dice used in gaming includes the d4, d6, d8, d10, d12, d20, and d100. You probably already own these dice, but if not, they are easily acquired online or at your friendly local game store (FLGS). Dungeons of Olde, however, calls for extra-weird dice, like d5s and d9s. You can track those weird dice down online and order them, but that can be expensiv. Alternately, you can use "normal" polyhedral dice to roll the odd die ranks, as follows:
d2 and d3
For a d2, roll a 6-sided die, counting results of "1," "2," and "3" as a 1, and "4," "5," and "6" as a 2. A d2! explodes on any result that counts as 2. For a d3, roll a 6-sided die, counting results of "1" and "2" as 1, "3" and "4" as a 2, and "5" and "6" as a 3. A d3! explodes on any result that counts as a 3.
d5, d7, d9, d11 and d19
Roll the next larger die, and count the maximum result as if it were the median (middle) result. For example, for a d7, roll an 8-sided die, and count any roll of "8" as if it were the median value of 4.
An odd-ranked die explodes when value named in the die rank is thrown. That is, a d5 explodes when a "5" is thrown. Thus, on a d5!, results of "1," "2," "3," and "4" are counted at their face value, and a "6" is counted as a 3. A result of "5" explodes—add 5 to the total and roll the die again.
A d19 won't come up often, or possibly ever, but if it does, you can handle it just like the more common odd-ranked dice: roll a d20, and treat a result of "20" as a 10. A d19! explodes on a result of "19."
Dice between d12 and d19
On those rare occasions that you need to roll dice with a rank greater than d12, refer to the following table (assuming you haven't ordered d14s, d16s and d18s!):
In cases where you need to roll exploding dice of a large die rank, just let each actual die in the roll explode individually, as normal. That is, if you are rolling 2d16!, just roll 3d10!+1 instead, with each d10 exploding on a result of "10." This isn't a mathematically perfect substitute for 2d10!, but it's close enough, statistically, for game purposes.
Modifying Stat Dice
Some conditions or circumstances can modify the die rank of a given stat die. Modifications do not affect the value of the stat itself, but affect all die rolls based on that stat as long as the condition persists. Stat die modifications are applied before the dice are rolled, to each die thrown. For example, a hero with Brawn 8 contracts an illness that applies a modifier of -2 to Brawn; until that illness is cured, he will have to roll his modified Brawn dice, d6's, instead of his normal Brawn dice, which are d8's.
Modifiers vs. Adjustments
Note the difference between modifiers and adjustments. A modification is applied to dice before the roll, while an adjustment is added or subtracted from the total after the roll.