If the final number is omitted, it is typically assumed to be a six, but in some contexts, other defaults are used.
For example, if a game would call for a roll of
1d4 this would mean, "roll one 4-sided die."
3d6 would mean, "roll three six-sided dice." Commonly, these dice are added together, but some systems could direct the the player to choose the best die rolled.
To this basic notation, an additive modifier can be appended, yielding expressions of the form, AdX+B. The plus is sometimes replaced by a minus sign ("−") for subtraction. B is a number to be subtracted from the final total. So,
1d20+10 would indicate a roll of a single 20-sided die with 10 being added to the result. These expressions can also be chained (e.g.
2d6+1d8), though this usage is less common.
Some games extend the standard notation to AdX(kY)+B where, in addition to the above, Y is the number of dice kept from the roll. Whether the dice omitted are the highest, lowest, or the player's choice depends on the game in question. Seventh Sea only uses 10-sided dice, and uses notation of the form 8k6, meaning "Roll eight ten-sided dice, keep the highest six, and sum them."
An alternative notation used by the OpenRoleplaying.org die roller allows the use of a plus or minus followed by L or H instead of the modifier B, to denote dropping or re-adding the lowest or highest roll on a single die, respectively.
Blood Bowl, also a Games Workshop product, introduces the block die with special notation Xdb or roll block dice X times, blocker/defender chooses (if more than 1 die) with X being one of 3, 2, 1 (usually omitted), -2, -3. Alternatively words for & against can be used to describe a Xdb (in this case X > 0). As an example 2db against is equal to -2db which are both short ways of saying 2 dice block, defender chooses from the results rolled.
In Nomine, a game about Angels and Demons from Steve Jackson Games, uses a three-dice variation called the d666. However, this is actually a combination of 2d6 (for determining success / failure) and 1d6 (for determining degree of success / failure). The notation of d666 is a reference to The Number of the Beast.
The FUDGE role-playing system uses a die marked with minus signs, plus signs and blank sides, meaning -1, +1 and 0 respectively. The default is one third of each, usually represented by a six-sided die with two of each, known as dF.2 or just dF. Four of these (4dF) are rolled to determine results from -4 to +4, which is equivalent to 4d3-8.Variants include dF.1, which is a six-sided die with four blanks, one plus and one minus.