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Alternative Dice
Need more dice? Want a D16, D24, D36 or D64? The good news is that you have more dice in your pocket than you think. Below is a system that gives you access to new dice that you (probably) didn’t know you had.
Picture this: You ask your players to roll a D96, offering them a D8 and D12 – a 5 and 10 appear on the pips. You sagaciously announce “Hrmmm … 70 huh, but is that enough …”. DM mystique leveled up, player mutiny probable!
Background
Everyone knows that two D10s can be used to make a (‘composite’) D100 die. One D10 is the ‘biggie’ die (hereafter the ‘boss’ die), and the other D10 is the ‘smallie’ die (hereafter the ‘slave’ die). When the ‘boss’ die and ‘slave’ die are combined a random number from 1 to 100 is generated.
In the dice shown left/above a roll of 96 is obtained when the red die is the ‘boss’ die and the white die is the ‘slave’ die.
We are so used to the ‘D100 concept’ that we often don’t realize that we are actually using a simple mathematical procedure to work this result out.
That is, we are multiplying the 9 by 10 (i.e. 9 × 10 = 90) before adding the 6 to get 96 (i.e. 90 + 6 = 96). Obviously, if the white die were the ‘boss’ die, then the roll would have been 69 instead (i.e. (6 × 10) + 9 = 69).
So far, so good!
Plot Twist
There is nothing stopping us using the same (mathematical) procedure with any kinds of dice (i.e. not just with two D10s). By using any two dice you gain access to lots of new ‘composite’ dice (see the table below).
The only catch is that the maths is a bit more complicated than with the simple case of using two D10s. However, fear not, by using three simple rules, the procedure becomes relatively simple.
That said, if you prefer a nonmathematical option, see the ‘grid’ option at the end of this article.
Die Size (the ‘D’ number)
The size of the ‘composite’ die (the ‘D’ number) is set by multiplying the maximum possible values of both dice together. That is, two D10s give a ‘composite’ D100 die, so likewise, a D4 together with a D6 gives a ‘composite’ D24 die (i.e. 4 × 6 = 24), and a D6 and D10 give a D60 (i.e. 6 × 10 = 60). The table below gives the ‘composite’ dice that are available using standard polyhedral dice:
Composite Dice 
1st Die 

D2* 
D3* 
D4 
D5* 
D6 
D8 
D10 
D12 
D20 
2nd Die 
D2* 
D4^{‡} 
D6^{‡} 
D8^{‡} 
D10^{‡} 
D12^{‡} 
D16 
D20^{‡} 
D24 
D40 
D3* 
– 
D9 
D12^{‡} 
D15 
D18 
D24 
D30 
D36 
D60 
D4 
– 
– 
D16 
D20^{‡} 
D24 
D32 
D40 
D48 
D80 
D5* 
– 
– 
– 
D25 
D30 
D40 
D50 
D60 
D100^{‡} 
D6 
– 
– 
– 
– 
D36 
D48 
D60 
D72 
D120 
D8 
– 
– 
– 
– 
– 
D64 
D80 
D96 
D160 
D10 
– 
– 
– 
– 
– 
– 
D100^{‡} 
D120 
D200 
D12 
– 
– 
– 
– 
– 
– 
– 
D144 
D240 
D20 
– 
– 
– 
– 
– 
– 
– 
– 
D400 
* = D2, D3 and D5 can be made from the repeating units found in larger dice. For example a D2 could be made by making the odd numbers on a D6 equate to 1, and the even numbers equate to 2. In a related way, a D3 can be obtained from a D6, and a D5 from a D10.
^{‡ }= polyhedral dice of this kind already exist, but this is an alternative option, that might be used to mess with your players. For example, a ‘composite’ D20 (D4 with a D5*) could be used to keep players from knowing if they have passed their saving throw/ability check, or not. This is more so if they don’t know which die you are using as the ‘boss’ die.
Please note, the above table does not include Dungeon Crawl Classics polyhedral dice, which also include D3, D5, D7, D9, D11, D14, D16, D18, D22, D24 and D30s, giving rise to still further possible composite dice.
Dashed cells are repeat combinations and have not been shown in the table for simplicity.
Three Simple Rules (Method 1)
As mentioned above, this system uses any two dice to make a ‘composite’ die (e.g. two D10s are used to make a ‘composite’ D100). Decide which die is the ‘boss’ die and which is the ‘slave’ die, and then roll the two dice:
 Rule 1: Multiply the ‘boss’ die roll by the Dsize of the ‘slave’ die
 Rule 2: If the ‘boss’ die roll is the maximum value for that die (for a D6 that’s a 6), then the ‘boss’ roll equates to zero.
 Rule 3: Add together the ‘boss’ die value from above to the ‘slave’ die roll
D10’s – Please note: For the system to work properly the ‘0’ on a D10 should be treated as 10. This is because no other die has a ‘0’ on it.
(Method 2)
Method 2 is the same as Method 1, only Rule 2 is different:
 Alternative Rule 2: the maximum value on ANY die equates to ZERO, unless both dice roll their maximums, then the maximum values should be taken instead.
In the traditional two D10s method, there are no “10’s” shown on the dice, they are replaced with zeros. It is only when you get two zeros that the zeros flip over and become 10s, and so give 100! Alternative Rule 2 replicates this by ‘replacing’ the maximum values on the dice with zeros.
Therefore, Method 2 works exactly the same as the traditional two D10s system, except the maths is a bit more awkward (because you need to flip maximums to zeros most of the time). Method 2 might work best if you simply paint over the maximum values on the dice, and perhaps paint a zero or add a wildcard ‘star’ symbol. Kickstarter anyone?
Worked examples (using Method 1 only)
:: Example 1: D24
A D24 is rolled (i.e. using a D4 and D6). It is decided to make the D6 the ‘boss’ die and the D4 the ‘slave’ die.
3 (on the ‘boss’ die) and 4 (on the ‘slave’ die) are rolled.
Rule 1: 3 × D4 = 12
Rule 2: This rule does not apply
Rule 3: 12 + 4 = 16 rolled on the D24
:: Example 2: D24 (revisited)
Please note, if in Example 1 the D4 were the ‘boss’ die and the D6 were the ‘slave’ die, then a different result would have been obtained, i.e.:
Rule 1: The ‘boss’ die roll of 4 is the maximum roll possible on the D4. Therefore, Rule 2 applies!
Rule 2: The boss die result is deemed to be 0
Rule 3: 0 + 3 = 3 is rolled on the D24
So why is Example 1 different to Example 2? Think about a D100 where one die roll is a 9 and the other die roll is a 6. Depending on which you decide is the ‘boss/slave’ die you get either 69 or 96. Therefore, it is very important to decide which is the ‘boss’ die and ‘slave’ die before you roll. Or have a system in place like the smallest die is always the ‘boss’ die (the maths is usually a bit simpler if the ‘boss’ die is the smaller die), or the when the dice are rolled the leftmost die is the ‘boss’ die, etc.
:: Example 3: D60
A D60 is rolled (i.e. using a D6 and D10). It is decided to make the D6 the ‘boss’ die and the D10 the ‘slave’ die.
2 (on the ‘boss’ die) and 6 (on the ‘slave’ die) are rolled.
Rule 1: 2 × D10 = 20
Rule 2: This rule does not apply
Rule 3: 20 + 6 = 26 is rolled on the D60
If the ‘boss’ and ‘slave’ dice were reversed then the result would be (6 × 6) + 2 = 38.
Combining Examples 1 and 3 (i.e. D24:D60) we can generate a random time of day i.e. 16:26.
Grid Option
Not everyone will enjoy doing this kind of mental gymnastics. Thankfully, if that applies to you, then the maths can be eliminated by making a simple reference grid as explained below:
On one axis (e.g. the horizontal axis) write out the numbers of the first die. On the other axis (e.g. the vertical axis) write out the numbers of the second die. Make a grid. Then simply write 1 up to the ‘D’ number in the grid formed.
For example, for a D24 make a 6 by 4 grid, and write the numbers 1 to 24 in the boxes formed:
D24 

1st Die roll (i.e. the D6) 


1 
2 
3 
4 
5 
6 
2nd Die
Roll
(i.e. the D4) 
1 
1 
2 
3 
4 
5 
6 
2 
7 
8 
9 
10 
11 
12 
3 
13 
14 
15 
16 
17 
18 
4 
19 
20 
21 
22 
23 
24 
Using this D24 reference grid as a tool, the result of a D24 can be easily determined when the two dice are rolled.
For example, if the D4 rolls a 4 and the D6 rolls a 5, then by simply cross‑referencing the rolls on the grid, a value of 23 is obtained (i.e. the red cell). Likewise, rolling two 3s would give 15 (not shaded in this case). Simples!
No doubt, a DM type screen with such reference grids could be made up. Also, I’m sure a program/app could be whipped up to do the same.
I suspect, you’ll either like this idea or hate it.
:O
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Me on DriveThruDriveThru; at the moment I’m mainly pimping my procedural adventure ‘Carapace‘ about a giant ant colony.