I'd be happier with "roll twice, and take the better result" on healing that the character boosts. However, that does take extra time.
You could allow each die to be rerolled separately (and only once), which amusingly actually is faster than requiring every die to be rerolled.
Another idea would be "any die that lands on less than half die size, is boosted to die size". Another idea would be "any die that lands on 1 is boosted to the max value for the die", or "any die that lands on 1 can be rerolled, indefinitely".
Power of the above options:
Reroll once per die =~ 25% boost
Less than half boosted to half =~ 25% boost (bit less)
Any die that lands on 1 boosted to max =~ 1 point per die boost, getting closer to 1 with larger die sizes (dN gets +(N-1)/N average boost)
Any die that lands on 1 rerolled, recursively = 0.5 point per die boost.
You could allow each die to be rerolled separately (and only once), which amusingly actually is faster than requiring every die to be rerolled.
Another idea would be "any die that lands on less than half die size, is boosted to die size". Another idea would be "any die that lands on 1 is boosted to the max value for the die", or "any die that lands on 1 can be rerolled, indefinitely".
Power of the above options:
Reroll once per die =~ 25% boost
Less than half boosted to half =~ 25% boost (bit less)
Any die that lands on 1 boosted to max =~ 1 point per die boost, getting closer to 1 with larger die sizes (dN gets +(N-1)/N average boost)
Any die that lands on 1 rerolled, recursively = 0.5 point per die boost.