I am not a role-player, but I *am* a mathematician.

There are those role-players who may be tempted to take short-cuts when rolling dice. Rather than rolling a large number of low-value dice, they may roll a larger die, and devise a scheme for discarding invalid results.

Surely this is pretty accurate?

*Well, no! It isn't!*

Consider two simple cases:

- 2D6. This gives values 2-12.
- D11, which doesn't exist, but let's assume it does, and it's marked 2-12.

*What is the chance of rolling 2?*

The D11 has a 1/11 (9%) chance.

The 2D6 has 6×6 or 36 possible outcomes. Only one of these (1+1) equals 2. So there's a 1/36 (2.7%) chance.

*What about other values?*

This table gives the probabilities for our simple case:

Value Chance D11 Chance 2D6
2 1/11 (9%) 1/36 (2.7%)
3 1/11 (9%) 2/36 (5.5%)
4 1/11 (9%) 3/36 (8.3%)
5 1/11 (9%) 4/36 (11%)
6 1/11 (9%) 5/36 (14%)
7 1/11 (9%) 6/36 (16%)
8 1/11 (9%) 5/36 (14%)
9 1/11 (9%) 4/36 (11%)
10 1/11 (9%) 3/36 (8.3%)
11 1/11 (9%) 2/36 (5.5%)
12 1/11 (9%) 1/36 (2.7%)

*Conclusion*

If a die-roll involves multiple dice, it was probably designed that way, and short-cuts will mess with your game. If killing a god requires a roll of 18 on 3D6, it's *meant* to be nigh on impossible! (0.46% probability, actually).