How can we quantify how useful re-rolls are? The table below shows the probability of rolling a 2+, 3+, &c. on a D6:

  • Unmodified so a 2+, or 2, 3, 4, 5 or 6 out of 6 is $\frac{5}{6}$ or 83.3%.
  • Rerolling 1s means if the first roll is a one ($\frac{1}{6}$ or 17% chance) then a second unmodified attempt is made.
  • Rerolling Any means if the roll fails then roll again; so for a 5+ roll (33.3% unmodified) you only fail if you roll 1, 2, 3 or 4 both times, which gives a probability of $1 - (\frac{4}{6}\times\frac{4}{6})$ or 55.6%.

Probability Grid

This shows a simple rule of thumb; Rerolling Any roughly equivalent to (but slightly better than) a +1 modifier.