How good is re-rolling 1s on damage dice? (i.e. Tavern Brawler)
I'm sure someone has crunched the numbers, but couldn't find anything concrete. It triggers more on smaller the die, but potentially benefits more on higher the dice? So does that even out?
If we say Advantage on a d20 is roughly like a +5 boost, is re-rolling a d10 roughly like a +2.5 boost? On a d10 that's 1 out of 10 times. So for a Monk doing 3 attacks, that's a 30% chance to get it once (+2.5 dmg), a 20% chance to get it twice (+5 dmg), and a 10% chance to get it thrice (+7.5 dmg).
Does that sound remotely right? Very back of the napkin in my brain. Thoughts?
Some maths - All of which ignore the fact that you actually have to hit first
Whenever you roll a die, you will (on average) get the average. Therefore, the benefit of re-rolling a 1 on a die is the average of the die minus 1, you originally rolled. Ergo, the benefit of rerolling a d10 would be 5.5-1 or +4.5
the chance of rolling a 1 is 10% (or .1), so, for each successful hit, the benefit of rerolling 1's would be .1 * 4.5, or .45
3 successful attacks would result in an expected benefit 1.35 No need to worry about how often the benefit would kick in: on average, every 3 successful attacks will do 1.35 more damage with the benefit of rerolling 1's
It was right up to this point, however on a d6 theire is a 1/6 chance of getting a 1 (and the expected increase when you reroll is indeed 2.5) so the benefit is 1/6 * 2.5 = 0.417
On 6d6 it is 2.5
This assumes you must accept the second roll (which is usually the case) if you can keep rolling until you do not get a one you are effectivley turning a d6 into a d5+1 (as you are equally likely to get anything between 2 and 6. The gain is then 0.5 whatever die you are rolling.
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How good is re-rolling 1s on damage dice? (i.e. Tavern Brawler)
I'm sure someone has crunched the numbers, but couldn't find anything concrete. It triggers more on smaller the die, but potentially benefits more on higher the dice? So does that even out?
If we say Advantage on a d20 is roughly like a +5 boost, is re-rolling a d10 roughly like a +2.5 boost? On a d10 that's 1 out of 10 times. So for a Monk doing 3 attacks, that's a 30% chance to get it once (+2.5 dmg), a 20% chance to get it twice (+5 dmg), and a 10% chance to get it thrice (+7.5 dmg).
Does that sound remotely right? Very back of the napkin in my brain. Thoughts?
Some maths - All of which ignore the fact that you actually have to hit first
Whenever you roll a die, you will (on average) get the average. Therefore, the benefit of re-rolling a 1 on a die is the average of the die minus 1, you originally rolled. Ergo, the benefit of rerolling a d10 would be 5.5-1 or +4.5
the chance of rolling a 1 is 10% (or .1), so, for each successful hit, the benefit of rerolling 1's would be .1 * 4.5, or .45
3 successful attacks would result in an expected benefit 1.35 No need to worry about how often the benefit would kick in: on average, every 3 successful attacks will do 1.35 more damage with the benefit of rerolling 1's
On a d6, the benefit would be .1*2.5 or .25
On 6d6, the benefit would be 1.5
That makes sense. Thank you.
A concentrated benefit you feel when it happens, but infrequent enough that its net damage boost is thin, round-over-round.
Compared to say a flat +1 to damage, which does more than double the net damage of rerolling but doesn't give targeted boost on the low roll.
Or compared to the Graze weapon mastery, which would do roughly the same damage but trigger more often?
Rerolling is also another thing to remember to do, lol.
It was right up to this point, however on a d6 theire is a 1/6 chance of getting a 1 (and the expected increase when you reroll is indeed 2.5) so the benefit is 1/6 * 2.5 = 0.417
On 6d6 it is 2.5
This assumes you must accept the second roll (which is usually the case) if you can keep rolling until you do not get a one you are effectivley turning a d6 into a d5+1 (as you are equally likely to get anything between 2 and 6. The gain is then 0.5 whatever die you are rolling.