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:

  1. 2D6. This gives values 2-12.
  2. 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).

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