Also, as per the probabilities - it’s recommended that if you have both Savage Attacker and Piercer, you should reroll with Piercer first on any roll from 1-5, then if you roll 1-4 on the reroll use Savage Attacker on the second roll.
Your average damage for the first reroll will be 5.5. Your average with two rerolls is 6.0625.
I remember doing this for a character I had once with GWF as well:
What's interesting about this is it does mean with optimal play (always rerolling 4 or less), Piercer is only marginally better than taking an ASI. If your attacking stat is Odd or you have a maxxed attack stat then piercer is worth considering. But if you are sitting on an even attacking stat then getting the additional +1 in that gives you the same result 95% of the time (when you don't crit) and is more simple for gameplay.
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Founding Member of the High Roller Society.(Currently trying to roll max on 4d6)
So since piercer and GWF both say you must use the new roll that means you can't use them both on the same dice roll right?
Use savage attacker, roll a 1 and a 2, so use piercer to reroll, roll another 1...at that point "you must use the new roll" so you cannot GWF that?
Yeah, that’s why you’re more optimal to use Savage Attacker first, before anything else. Then afterwards, a 1-2 is rerolled with GWF, 3-5 is rerolled with Piercer.
I think that Piercer and Great Weapon Fighting Style are just saying that if you reroll using their abilities you have to use the new roll and not the old roll, not that you can't use another feature to also reroll. Since they are features that have different names, they should all be able to stack with each other. Piercer and Savage Attacker are both once per turn whereas Great Weapon Fighting Style is only limited by a once per die (since you must use the new roll instead of the previous roll). As always, discuss this with your DM, especially since you could potentially be rolling a lot to accomplish very little, which places a little more of the attention on you. Additionally, you may want to ensure that you have enough dice to represent each type of reroll to simplify things. Not that you'd necessarily want to roll all of the dice every time to save time, since you could simply say that you were using a feature or not based on what roll was better for you.
Finally, it should be pointed out that piercer and Savage attacks are once per turn features and not once per round features. This means that they pair well with Sentinel, PAM, Commander's Strike (from another source), Mage Slayer, or other features that help you to reliably get an OA or other attack off of your reaction. As such, they work remarkably well with Cavaliers with their 18th level ability.
Would it be complicated to calculate the piercer feats reroll potential while combining different die sizes?
I am still starting to figure out exactly how effective the piercer feat is with a rapier+sneak attack or Heavy crossbow+sneak attack.
steady aim and elven accuracy could increase the likelihood of a crit occurring for the extra die added.
rolling a bunch of die with one hit would potentially make it easier to choose the lowest die to reroll.
It should be noted that Great Weapon Fighting Style and Savage Attacker both say that they don't work with Divine Smite and (in the case of Savage Attacker) Sneak attack in the official SAC. The language is different for piercer, but it's close enough that you'll want to discuss with your DM whether piercer applies to Sneak Attack. I didn't see anything outside of forum discussions in my quick search and didn't want to go down those rabbit holes.
That said, there isn't a great way to account for them together in one simple string, but you could set up strings to compare how much potential gain you would have by using 3.5 in the place of any potential reroll numbers for a d6 (ie. 3.5, 3.5, 3, 4, 5, 6 for 1s and 2s), 4.5 for d8s, and 5.5 for d10s.
If the D8/D10 rolls the same number as the lowest D6, you should reroll the larger die due to the greater potential. The question becomes when should you reroll a d6 over the d8 or the d10. The answer is likely going to be that you reroll 1s on d6s if your d8 is a 3 or above or your d10 is a 4 or above, but could be a 4/5 or above respectively. I'll have to do the math later to verify, but the increase in value of rerolling diminishes as you approach the average damage. Using the data below from post #22, rerolling a 4 on a d8 would be an expected increase of 1.5 points of damage while a 3 would bring 2.4375 (the expected value of the reroll minus the actual roll). Finding the corresponding values for the d6 will give you your comparison points. Rerolling a 1 on a d6 is 3.9167, giving an increase of 2.9167, which confirms that rerolling a 1 on a d6 is of greater value than rerolling a 3 or a 4 on a d8. Having a cheat sheet ready would give you the comparisons on the fly. Rerolling a 4 on a D10 gives an expected increase of 2.7 whereas the rerolling a 3 gives an expected increase of 3.55, so the 4 is where rerolling the d10 is less valuable than rerolling the 1 on the d6.
What's interesting about this is it does mean with optimal play (always rerolling 4 or less), Piercer is only marginally better than taking an ASI. If your attacking stat is Odd or you have a maxxed attack stat then piercer is worth considering. But if you are sitting on an even attacking stat then getting the additional +1 in that gives you the same result 95% of the time (when you don't crit) and is more simple for gameplay.
So without going and doing the math, if I were using a lance, which is 1D12, and an average of 6.5, I'm guessing that it'd be optimal for me to reroll 1-6?
So without going and doing the math, if I were using a lance, which is 1D12, and an average of 6.5, I'm guessing that it'd be optimal for me to reroll 1-6?
I am no maths wizard and a lot of this discussion made my head hurt, BUT, I did manage to take from it, that with the rules of probability or some such, you are correct. Apparently rerolling on half or less of what the die can yield will work out best in the long run.
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Talk to your Players.Talk to your DM. If more people used this advice, there would be 24.74% fewer threads on Tactics, Rules and DM discussions.
For 1d12, your average die roll is 6.5 without any rerolls. Rerolling on 1-5 increases it to 7.95833, and rerolling on 1-6 increases it to 8. (Somebody check my math on that?)
So yes, if you include your 6es in your rerolls, you get a small benefit over time. However, for each individual reroll of a 6, you only have a 50% chance of getting any benefit, and you have a 41.6% chance of a lower result. With that in mind, you might get more enjoyment out of only rerolling on 1-5 because you've cut out a chunk of those disappointing results, without a meaningful loss in damage output. But that's just my opinion.
For 1dN (where N is even), if you reroll any outcome less than average (e.g. 1-3 on d6), then the expected value of the outcome increases by N/8. So on 1d6, it's 0.75, 1d8 it's 1, 1d10 it's 1.25, 1d12 it's 1.5. This is the optimal strategy for a single attack per turn, absent any other reroll rules.
Does any of this take into account having the ability to choose the lowest die to reroll when multiple are dice are used?
piercer would potentially be applicable with sneak attack, crits, and even spells making use of piercing damage if they stem from an attack.
the 2nd bullet from piercer states “Once per turn, when you hit a creature with an attack that deals piercing damage, you can reroll one of the attack's damage dice, and you must use the new roll.”
so as written it seems that the die chosen to be rerolled doesn’t even have to be piercing damage, so long as it is a single damage roll that also incorporates piercing damage. A rogue casting booming blade or green flame blade while delivering the attack seems to be able to choose freely between the fire/thunder/rapier/sneak attack dice and reroll the lowest one.
the 3rd bullet states “When you score a critical hit that deals piercing damage to a creature, you can roll one additional damage die when determining the extra piercing damage the target takes.” this extra die on a crit would be limited to the piercing damage die.
It improves a lot with multiple simultaneous dice. With MdN, the limit as M gets large is (N+1)/2-1, so like +2.5 damage on Md6, M->infinity, though it approaches this limit slowly. My guess is that the best case there is with a piercing cantrip at high level, basically Thorn Whip, which goes up to 4d6, at which point there's over a 50% chance of rolling at least one 1, so the .75 damage bonus roughly doubles in that case. Leveled spells with piercing damage are better obviously, but adding a couple points of damage to those is not likely to be relevant. My sense is the best case mechanically is for fighters that have already maxed out STR and use heavy piercing weapons a lot, like a mounted Fighter using a lance. With two (successful) attacks and rerolling the first below average roll, you can get the damage bonus up to 2.25/round on a d12, and three attacks gives 2.625, so maybe for a 20 STR low-mid level fighter who does a lot of mounted combat, it's worth it, even if only because they get lots of feats anyway. In a European medieval milieu, it's something every mounted knight would want. It's unfortunate that there aren't any 2dN piercing weapons in the SRD, like there are with bludgeoning and slashing, but if one of those existed, like in a homebrew, it would make Piercer look much better.
Also, as per the probabilities - it’s recommended that if you have both Savage Attacker and Piercer, you should reroll with Piercer first on any roll from 1-5, then if you roll 1-4 on the reroll use Savage Attacker on the second roll.
Your average damage for the first reroll will be 5.5. Your average with two rerolls is 6.0625.
I remember doing this for a character I had once with GWF as well:
Pike (1st hit)
If 1-6, use Savage Attacker
- If 1-2, use GWF
- If 3-5, use Piercer
Pike (2nd hit+)
If 1-2, use GWF
If 3-5, use Piercer (if available)
Okay...I was looking at it wrong. Sorry for raving like a madman.
Does means all my math was incorrect earlier...@SaldivenWurmfood, are you still paying attention to this thread? We need to redo the averages.
Reroll 1s: 4.9375
Reroll 2s: 5.25
Reroll 3s: 5.4375
Reroll 4s: 5.5
Reroll 5s: 5.4375
Reroll 6s: 5.25
Reroll 7s: 4.9375
What's interesting about this is it does mean with optimal play (always rerolling 4 or less), Piercer is only marginally better than taking an ASI. If your attacking stat is Odd or you have a maxxed attack stat then piercer is worth considering. But if you are sitting on an even attacking stat then getting the additional +1 in that gives you the same result 95% of the time (when you don't crit) and is more simple for gameplay.
Founding Member of the High Roller Society. (Currently trying to roll max on 4d6)
So since piercer and GWF both say you must use the new roll that means you can't use them both on the same dice roll right?
Use savage attacker, roll a 1 and a 2, so use piercer to reroll, roll another 1...at that point "you must use the new roll" so you cannot GWF that?
Founding Member of the High Roller Society. (Currently trying to roll max on 4d6)
Yeah, that’s why you’re more optimal to use Savage Attacker first, before anything else. Then afterwards, a 1-2 is rerolled with GWF, 3-5 is rerolled with Piercer.
I think that Piercer and Great Weapon Fighting Style are just saying that if you reroll using their abilities you have to use the new roll and not the old roll, not that you can't use another feature to also reroll. Since they are features that have different names, they should all be able to stack with each other. Piercer and Savage Attacker are both once per turn whereas Great Weapon Fighting Style is only limited by a once per die (since you must use the new roll instead of the previous roll). As always, discuss this with your DM, especially since you could potentially be rolling a lot to accomplish very little, which places a little more of the attention on you. Additionally, you may want to ensure that you have enough dice to represent each type of reroll to simplify things. Not that you'd necessarily want to roll all of the dice every time to save time, since you could simply say that you were using a feature or not based on what roll was better for you.
Finally, it should be pointed out that piercer and Savage attacks are once per turn features and not once per round features. This means that they pair well with Sentinel, PAM, Commander's Strike (from another source), Mage Slayer, or other features that help you to reliably get an OA or other attack off of your reaction. As such, they work remarkably well with Cavaliers with their 18th level ability.
@Bounces: Yes, I had a 17 Dex, so Piercer both gave a stat bonus increase and a couple of added benefits.
Thanks for the additional clarification.
Would it be complicated to calculate the piercer feats reroll potential while combining different die sizes?
I am still starting to figure out exactly how effective the piercer feat is with a rapier+sneak attack or Heavy crossbow+sneak attack.
steady aim and elven accuracy could increase the likelihood of a crit occurring for the extra die added.
rolling a bunch of die with one hit would potentially make it easier to choose the lowest die to reroll.
It should be noted that Great Weapon Fighting Style and Savage Attacker both say that they don't work with Divine Smite and (in the case of Savage Attacker) Sneak attack in the official SAC. The language is different for piercer, but it's close enough that you'll want to discuss with your DM whether piercer applies to Sneak Attack. I didn't see anything outside of forum discussions in my quick search and didn't want to go down those rabbit holes.
That said, there isn't a great way to account for them together in one simple string, but you could set up strings to compare how much potential gain you would have by using 3.5 in the place of any potential reroll numbers for a d6 (ie. 3.5, 3.5, 3, 4, 5, 6 for 1s and 2s), 4.5 for d8s, and 5.5 for d10s.
If the D8/D10 rolls the same number as the lowest D6, you should reroll the larger die due to the greater potential. The question becomes when should you reroll a d6 over the d8 or the d10. The answer is likely going to be that you reroll 1s on d6s if your d8 is a 3 or above or your d10 is a 4 or above, but could be a 4/5 or above respectively. I'll have to do the math later to verify, but the increase in value of rerolling diminishes as you approach the average damage. Using the data below from post #22, rerolling a 4 on a d8 would be an expected increase of 1.5 points of damage while a 3 would bring 2.4375 (the expected value of the reroll minus the actual roll). Finding the corresponding values for the d6 will give you your comparison points. Rerolling a 1 on a d6 is 3.9167, giving an increase of 2.9167, which confirms that rerolling a 1 on a d6 is of greater value than rerolling a 3 or a 4 on a d8. Having a cheat sheet ready would give you the comparisons on the fly. Rerolling a 4 on a D10 gives an expected increase of 2.7 whereas the rerolling a 3 gives an expected increase of 3.55, so the 4 is where rerolling the d10 is less valuable than rerolling the 1 on the d6.
So without going and doing the math, if I were using a lance, which is 1D12, and an average of 6.5, I'm guessing that it'd be optimal for me to reroll 1-6?
I am no maths wizard and a lot of this discussion made my head hurt, BUT, I did manage to take from it, that with the rules of probability or some such, you are correct. Apparently rerolling on half or less of what the die can yield will work out best in the long run.
Talk to your Players. Talk to your DM. If more people used this advice, there would be 24.74% fewer threads on Tactics, Rules and DM discussions.
For 1d12, your average die roll is 6.5 without any rerolls. Rerolling on 1-5 increases it to 7.95833, and rerolling on 1-6 increases it to 8. (Somebody check my math on that?)
So yes, if you include your 6es in your rerolls, you get a small benefit over time. However, for each individual reroll of a 6, you only have a 50% chance of getting any benefit, and you have a 41.6% chance of a lower result. With that in mind, you might get more enjoyment out of only rerolling on 1-5 because you've cut out a chunk of those disappointing results, without a meaningful loss in damage output. But that's just my opinion.
For 1dN (where N is even), if you reroll any outcome less than average (e.g. 1-3 on d6), then the expected value of the outcome increases by N/8. So on 1d6, it's 0.75, 1d8 it's 1, 1d10 it's 1.25, 1d12 it's 1.5. This is the optimal strategy for a single attack per turn, absent any other reroll rules.
Does any of this take into account having the ability to choose the lowest die to reroll when multiple are dice are used?
piercer would potentially be applicable with sneak attack, crits, and even spells making use of piercing damage if they stem from an attack.
the 2nd bullet from piercer states “Once per turn, when you hit a creature with an attack that deals piercing damage, you can reroll one of the attack's damage dice, and you must use the new roll.”
so as written it seems that the die chosen to be rerolled doesn’t even have to be piercing damage, so long as it is a single damage roll that also incorporates piercing damage. A rogue casting booming blade or green flame blade while delivering the attack seems to be able to choose freely between the fire/thunder/rapier/sneak attack dice and reroll the lowest one.
the 3rd bullet states “When you score a critical hit that deals piercing damage to a creature, you can roll one additional damage die when determining the extra piercing damage the target takes.”
this extra die on a crit would be limited to the piercing damage die.
It improves a lot with multiple simultaneous dice. With MdN, the limit as M gets large is (N+1)/2-1, so like +2.5 damage on Md6, M->infinity, though it approaches this limit slowly. My guess is that the best case there is with a piercing cantrip at high level, basically Thorn Whip, which goes up to 4d6, at which point there's over a 50% chance of rolling at least one 1, so the .75 damage bonus roughly doubles in that case. Leveled spells with piercing damage are better obviously, but adding a couple points of damage to those is not likely to be relevant. My sense is the best case mechanically is for fighters that have already maxed out STR and use heavy piercing weapons a lot, like a mounted Fighter using a lance. With two (successful) attacks and rerolling the first below average roll, you can get the damage bonus up to 2.25/round on a d12, and three attacks gives 2.625, so maybe for a 20 STR low-mid level fighter who does a lot of mounted combat, it's worth it, even if only because they get lots of feats anyway. In a European medieval milieu, it's something every mounted knight would want.
It's unfortunate that there aren't any 2dN piercing weapons in the SRD, like there are with bludgeoning and slashing, but if one of those existed, like in a homebrew, it would make Piercer look much better.