#RPGaDay2021 – Fraction

Dice probabilities and fractions can be a bit of a pig, even though we play with dice all the time, they can still trip you up.

What’s the likelihood of rolling a 6 on a d6? 1/6.

How many times must I roll to all but guarantee getting a 6? 9 times, not 6. You only have a 66.5% chance od rolling a 6 in those 6 rolls.

If you’re making tables using more than one dice, there are more combinations that will hit the middle numbers, so put the things you want to be more common in the middle (on 2d6 5-7) and the things you want to be rarer on the ends (1 and 12).

The chance of rolling an 18 on your 3d6 Ability roll is 1/216, and even with roll 4d6, drop the lowest, it’s not that much better. Yet in our games, the statistics are linear, when they might be better off being logorithmic – to get really complicated.

This is also what drives one of the most important system decisions in many game designs, whether you use a single flat die (d20) or a combination of two or three dice to better represent a probability curve around the average sorts of result.

Something that really hasn’t been explored, given the advent of online random number generators, that can pick between any values, are truly large die ranges (d1000 only seems to have been explored in FATAL of all things) or very specific ranges: An axe that does 1-37 damage potential, for example. There’s interesting possibilities there.

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