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.
I wonder what the math is for Savage Attacker damage roll
1d4 = +?
1d6 = +?
1d8 = +?
1d10 = +?
1d12 = +?
2d6 = +?
Savage Attacker
Origin Feat
You’ve trained to deal particularly damaging strikes. Once per turn when you hit a target with a weapon, you can roll the weapon’s damage dice twice and use either roll against the target.
I wonder what the math is for Savage Attacker damage roll
1d4 = +?
1d6 = +?
1d8 = +?
1d10 = +?
1d12 = +?
2d6 = +?
With Savage Attacker, the boosts to the average are (where "ish" indicates that the decimal goes on and on and I didn't feel like typing more of it):
1d4: +0.625
1d6: +0.97 ish
1d8: +1.3125
1d10: +1.65
1d12: +1.99 ish
2d6, though, depends on how exactly you do it. If you roll 2d6, get the total, then roll 2d6 again, get that total, and take the higher of the two totals, then you've got +1.37 (ish). If you reroll each die individually, you're effectively just doing the 1d6 version twice, and so you get more like +1.94 (ish). I think the former is how it's meant to work.
I wonder what the math is for Savage Attacker damage roll
2d6, though, depends on how exactly you do it. If you roll 2d6, get the total, then roll 2d6 again, get that total, and take the higher of the two totals, then you've got +1.37 (ish). If you reroll each die individually, you're effectively just doing the 1d6 version twice, and so you get more like +1.94 (ish). I think the former is how it's meant to work.
It is. It says "use either roll". Each instance of 2d6 is a damage roll.
I wonder what the math is for Savage Attacker damage roll
2d6, though, depends on how exactly you do it. If you roll 2d6, get the total, then roll 2d6 again, get that total, and take the higher of the two totals, then you've got +1.37 (ish). If you reroll each die individually, you're effectively just doing the 1d6 version twice, and so you get more like +1.94 (ish). I think the former is how it's meant to work.
It is. It says "use either roll". Each instance of 2d6 is a damage roll.
Which interestingly means the average goes up by a bit less than it would for 1d12, though it also intensifies 2d6's increased likelihood of rolling a number closer to the average.
I wonder what the math is for Savage Attacker damage roll
1d4 = +?
1d6 = +?
1d8 = +?
1d10 = +?
1d12 = +?
2d6 = +?
With Savage Attacker, the boosts to the average are (where "ish" indicates that the decimal goes on and on and I didn't feel like typing more of it):
1d4: +0.625
1d6: +0.97 ish
1d8: +1.3125
1d10: +1.65
1d12: +1.99 ish
2d6, though, depends on how exactly you do it. If you roll 2d6, get the total, then roll 2d6 again, get that total, and take the higher of the two totals, then you've got +1.37 (ish). If you reroll each die individually, you're effectively just doing the 1d6 version twice, and so you get more like +1.94 (ish). I think the former is how it's meant to work.
Thank you for data! Weirdly enought, i imagined it would be better based on the notion of Advantage where 1d20 = +5 but i'm guessing actually it's slightly lower in the 4.ish
The average of a d20 is 10.5; the average with advantage is 13.825, so it's an increase of +3.325. How much this actually increases the probability of success obviously depends on what the DC is, and is complicated further on attack rolls because of the special behavior of 1s and 20s.
Rollback Post to RevisionRollBack
pronouns: he/she/they
To post a comment, please login or register a new account.
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 1/6*2.5 or .417
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.
thank you for correcting my math!
I wonder what the math is for Savage Attacker damage roll
1d4 = +?
1d6 = +?
1d8 = +?
1d10 = +?
1d12 = +?
2d6 = +?
With Savage Attacker, the boosts to the average are (where "ish" indicates that the decimal goes on and on and I didn't feel like typing more of it):
2d6, though, depends on how exactly you do it. If you roll 2d6, get the total, then roll 2d6 again, get that total, and take the higher of the two totals, then you've got +1.37 (ish). If you reroll each die individually, you're effectively just doing the 1d6 version twice, and so you get more like +1.94 (ish). I think the former is how it's meant to work.
pronouns: he/she/they
It is. It says "use either roll". Each instance of 2d6 is a damage roll.
Which interestingly means the average goes up by a bit less than it would for 1d12, though it also intensifies 2d6's increased likelihood of rolling a number closer to the average.
pronouns: he/she/they
Thank you for data! Weirdly enought, i imagined it would be better based on the notion of Advantage where 1d20 = +5 but i'm guessing actually it's slightly lower in the 4.ish
The average of a d20 is 10.5; the average with advantage is 13.825, so it's an increase of +3.325. How much this actually increases the probability of success obviously depends on what the DC is, and is complicated further on attack rolls because of the special behavior of 1s and 20s.
pronouns: he/she/they