Which weapon is better, mathematically?


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A short sword with 19-20/x2 and 1d6 damage, or a kukri with 18-20/x2 and 1d4 damage?
This is a low magic setting so I think things like keen are out the window, but I could get Improved Critical at level 9 (playing a slayer).
One of these will be my light weapon for TWF.

Thanks!


Assuming improved critical, AFAICT the shortsword deals (3.5+X)*1.2, whereas the Kukri deals (2.5+X)*1.6; simple algebra gets you break-even at X less than 1, so, always use the Kukri.


Kukri.

18-20/x2 is flat out better than 19-20/x2, by a long shot, especially with improved critical. The 1d4 vs 1d6 damage dice is only an average of one damage difference, the 18-20 vs 19-20 gap is much larger in favor of 18-20.

TWF with 2 kukris, with Improved Critical, and you can dish out some ridonkulous damage.


I know the maths people will say otherwise but I prefer x4 crit multipliers as a crit will either kill or seriously, seriously hurt your opponent. A light pick is a nice option for 2 weapon fighting.

I know in terms of mathematical progression the 'raw' DPR gives a fixed number to compare weapons with but high crit multipliers do seriously ramp up the element of randomness in combats and so I wouldn't get too hung up on 'just' DPR.


Kukri. 18-20/x2 beats everything (even the falcata at 19-20/x3). Especially once you throw Keen or improved critical on it, but even before that.


Could someone explain to me why 18-20 critical threat range is better than x4 critical damage multiplier?


Under A Bleeding Sun wrote:
Kukri. 18-20/x2 beats everything (even the falcata at 19-20/x3). Especially once you throw Keen or improved critical on it, but even before that.

This is actually untrue.

The Falcata is mathematically superior.

17-20/x3 is better than 15-20/x2.


Barathos wrote:
Could someone explain to me why 18-20 critical threat range is better than x4 critical damage multiplier?

Technically speaking x4 is "better" damage-wise as I recall, but most of it is overkill damage. It comes up rarely, and often ends up doing more damage than is strictly necessary, which is in stark contrast to the 18-20/x2 (and especially 15-20/x2) crit, which comes up much more often, and tends to get the job done just as well anyway.


In the long run the kurki is better.
Without improved critical (or keen) the formula is 1.1(3.5+x) for the short sword (10% of hits become critical) and 1.15(2.5+x) for the kurki (15% of hits are crits), so when x (damage bonus) equals 20 they do the same and when x is less than 20 the short sword is better.

With improved critical the formula becomes 1.2(3.5+x) vs 1.3(2.5+x), so when x (damage bonus) is above 10 the kurki is better.

Also any effects which trigger on a critical favor the kurki, but that is beyond a straight numbers comparison. In a low magic setting using slashing grace build you might find that the short sword is better until you can get improved critical, but that will depend on how low the amount of magic is.

---forgot to mention that the formula changes if there are bonuses to confirming crits, bonuses to confirming crits favor the kurki, but I cannot think of any likely to be available before level 9.

Silver Crusade

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If you are even a moderately well-built melee damage-dealer, your static damage bonuses will be enough that even a x2 crit will basically doom an enemy, even if it doesn't outright kill them in one hit.


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18-20 weapons are better if you're going to take any of the Staggering/Blinding/Tiring Critical feats.


Scavion wrote:
Under A Bleeding Sun wrote:
Kukri. 18-20/x2 beats everything (even the falcata at 19-20/x3). Especially once you throw Keen or improved critical on it, but even before that.

This is actually untrue.

The Falcata is mathematically superior.

17-20/x3 is better than 15-20/x2.

I remember seeing this mapped out. 17-20/x3 did ultimately win out, but I think it took some pretty insane static modifiers. Granted they are numbers your likely to hit, but not until pretty late in the game(I think about 10+), and as others have said it may be unlikely to matter as the x2 may be enough to kill them anyway.


Ignoring overkill and extra effects that kick in on criticals, all else being equal the 17-20/x3 is definitely better.
If the falcata isn't better at low levels, it's for reasons other than the critical bonus.

(I won't include confirmation chances in this because they should affect them all equally.)
20/x4: 5% chance of extra damage equal to 3 regular hits = 0.05 * 3 = 0.15
18-20/x2: 15% chance of extra damage equal to 1 regular hit = 0.15 * 1 = 0.15.
So ignoring overkill, 18-20/x2 is equal to 20/x4.

17-20/x3: 20% chance of extra damage equal to 2 regular hits = 0.4
15-20/x2: 30% chance of extra damage equal to 1 regular hit = 0.3


Rynjin wrote:

Kukri.

18-20/x2 is flat out better than 19-20/x2, by a long shot, especially with improved critical. The 1d4 vs 1d6 damage dice is only an average of one damage difference, the 18-20 vs 19-20 gap is much larger in favor of 18-20.

TWF with 2 kukris, with Improved Critical, and you can dish out some ridonkulous damage.

This + consider that with weapon damage the majority of the damage you deal comes from your bonuses not the actual weapon dice. So when you crit you don't just have 1/10 attacks with 2d6 vs 2/10 attacks with 2d4, but your strength bonus and things like power attack or whatever is your game being doubled as well.


The easy way I've always seen this derived is with a simple table of all values between 2 and 20 (attack rolls). At each value you include how much damage the weapon does and sum the totals. So a 19-20/x2 weapon does double damage on 19 and 20 for 21x weapon damage, an x4 weapon does extra damage only on 20 for 22x weapon damage, and so on. This makes an 18-20/x2 weapon the same as an x4 weapon. This only gives you a very simplistic view of it though. Powers that trigger on a crit, actual hit chances, lots of other information changes the actual value. Short answer more crits are better, usually.


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Mathematically the better weapon is the one your gm doesn't get the impression you chose only for the purposes of being mathematically superior.


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Oh no more cheese never make a choice based purely on math takes away from the soul of the game


The issue with DPR calculation is that few fights last 20 rounds (to cover all the mathematical possibilities of a d20). Combats are shorter and dice rolls more random (what would the chance of rolling a d20 20 times and getting every number once) and so for DPR mechanics to fully capture the 'true' properties of a weapon these variables should be factored in.

Essentially an 18-20/x2 crit range weapon has to crit 3 times to be better than a 20/x4 weapon if it crits once. If it crits twice the 18-20 weapon will be equal and if it crits once it will be unlucky but inferior.

So this means that high armour classes can play into the favour of the x3 and x4 weapons (e.g. if you need a straight 20 to hit and therefore to confirm the critical).

In a given game there is also the variable of tactical changes from having delivered massive damage to an opponent - for example on the probability that they only have a few hit points left you may stop power attacking in order to increase you chance to hit or you may fight more defensively in order to 'control' the fight more. This is without considering morale.

That is why, whilst I accept the mathematics favour the 18-20 weapon I prefer a 20/x4 weapon in actual game play.


Calculating the expactation value has nothing to do with "fights lasting 20 rds" or something. Not at all.

Thing is - x4 is often the same as x3 or even x2 as you just over damage your enemies in case of a crit. Yes, sometimes you get to crit the bbeg and it really is super effective but when you calcuklate all this stuff into your DPR-math you end up seeing x4 is not giving you close as much advantages in a fight as 18-20 weapons.

Grand Lodge

Not to question by your choice of weapon, but why not the rapier or scimitar? Same crit as a kukri, more dmg. Both are light one handers....just makes more sense....unless there are specific reasons why they aren't chosen.


both are no light weapons.


Barathos wrote:
Could someone explain to me why 18-20 critical threat range is better than x4 critical damage multiplier?

Overkill.

First,

When you do 876 points of damage to the thing that only had 100 hit points left, all that extra crit damage goes to waste

Furthermore, unless that creature was about to act next you may not have done anything really. if your cleric or rogue friend is about to bash it for 50, then anything you do over 50 is a little pointless.


Also 18-20 enables all thos crit fisher builds.

Scarab Sages

The rapier and scimitar are not light weapons. You cannot dual wield them without substantial penalties.


Wasum wrote:

Calculating the expactation value has nothing to do with "fights lasting 20 rds" or something. Not at all.

Thing is - x4 is often the same as x3 or even x2 as you just over damage your enemies in case of a crit. Yes, sometimes you get to crit the bbeg and it really is super effective but when you calcuklate all this stuff into your DPR-math you end up seeing x4 is not giving you close as much advantages in a fight as 18-20 weapons.

The length of the fight is significant in that the length of the fight dictates the number of attempts to critical that you have. Therefore in order to have a possibility of rolling every possible outcome on a single d20 you theoretically need 20 attempts to roll a critical. Anything less and you start to introduce the chance that no criticals will be scored (and therefore this argument will be meaningless).

E.G. A six round fight with low level characters is likely to give you 6 attempts to hit. If a 20/x4 weapon crits in that fight then it is likely to kill the opponent, if an 18-20/x2 does it may well also but it might not. However it also gives a better chance of more criticals (which may spread the damage over multiple enemies) in terms of 'weight' of damage the x4 crit is fewer 'big spikes' of damage and the 18-20/x2 is more consistent damage but without the big variation.

Likewise it is easy to ignore but as I said earlier high armour class opponents can render the higher crit range meaningless. It ultimately is a matter of taste but looking at it in terms of DPR as a raw calculation is not enough.

Scarab Sages

High AC renders all crits meaningless, as you still need to confirm. If you need a 20 to hit, you need a 20 to confirm.


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This is something I wrote for myself and my D&D 3.5 campaign players in 2008:

A weapon does D average damage, its threat range spans T numbers (i.e., 19-20 = 2 numbers), and it scores C times as much damage when it scores a critical.

Assume you need to roll an N or higher to hit. To make it simpler, assume that 2 <= N <= 20-T. This ensures that the chance of a threat remains constant -- if, for instance, the threat range was 19-20 and N could be 20, then T is not constant.

M = # of misses = N-1
H = # of rolls that produce normal hits = 20 - T - M = 21 - T - N
Chance of hitting = P = (21-N)/20

Expected damage = D * (H/20 + (T/20)*(1-P) + (T/20)*P*C)
= D * (H + T - T*P + T*P*C) / 20
= D * (H + T + T*P*(C-1)) / 20 = D * (21 - T - N + T + T*(C-1)*(21-N)/20) / 20
= D * (21 - N + (21-N)*T*(C-1)/20) / 20
= D * (21-N)/20 * (1 + T*(C-1)/20)

We want to find a number that we can use to compare weapons, so we can take that number and just multiply it be the chance of hitting to get the expected damage. That is, Expected damage = V * (21-N)/20. We have just that in the equation above,

V = D*(1 + T*(C-1)/20)

We can make a table:

Critical T C V
x2 1 2 1.05*D
x3 1 3 1.1*D
x4 1 4 1.15*D
19-20/x2 2 2 1.1*D
18-20/x2 3 2 1.15*D

Let's compare a longsword (1d8, 19-20/x2) with a battleaxe (1d8, x3) and a scimitar (1d6, 18-20/x2).
longsword, V = 1.1*D = 1.1*4.5 = 4.95
battleaxe, V = 1.1*D = 1.1*4.5 = 4.95
scimtar, V = 1.15*3.5 = 4.025

To check this, assume the chance of hitting is 50% (needs to roll an 11 or greater), the expected damage is:
longsword: normal hit on 11-18 (40%), threat 10% of the time. A threat yields normal damage 50% of the time and double damage 50% of the time. Expected damage = 4.5*(40% + 10% * 50% + 10% * 50% * 2) = 4.5 * (40% + 5% + 10%) = 2.475
2.475 / 50% (the chance of hitting) = 4.95
battleaxe: normal hit on 11-19 (45%), threat 5% of the time. A threat yields normal damage 50% of the time and triple damage 50% of the time. Expected damage = 4.5*(45% + 5% * 50% + 5% * 50% * 3) = 4.5 * (45% + 2.5% + 7.5%) = 2.475
2.475 / 50% (the chance of hitting) = 4.95
scimitar: normal hit on 11-17 (35%), threat 15% of the time. A threat yields normal damage 50% of the time and double damage 50% of the time. Expected damage = 3.5*(35% + 15% * 50% + 15% * 50% * 2) = 3.5 * (35% + 7.5% + 15%) =
2.0125, 2.0125 / 50% (the chance of hitting) = 4.025.

Getting back to the original question,
"A short sword with 19-20/x2 and 1d6 damage, or a kukri with 18-20/x2 and 1d4 damage?"

Short sword, D=3.5, T=2, C=2. V = 3.5*(1+2*(2-1)/20) = 3.5*1.1 = 3.85
Kukri, D=2.5, T=3, C=2. V = 2.5*(1+3*(2-1)/20) = 2.5*1.15 = 2.875

If we increase the damage both weapons do, because of the wielder's Strength modifier, Weapon Specialization, etc., let that increase be X. From the above,
Short Sword, V = 3.85 + 1.1*X
Kukri, V = 2.875 + 1.15*X

These are equal when 0.975 = 0.05*X, or X=19.5

So, if your choice is use a swortsword doing 1d6+19 damage, or a kukri doing 1d4+19, use the shortsword (Vshortsword = 24.75 vs Vkukri = 24.725). If your choice is use a swortsword doing 1d6+20 damage, or a kukri doing 1d4+20, use the kukri (Vshortsword = 25.85 vs Vkukri = 25.875).

This only applies when the roll you need to hit, N, is ≤ 21-T, or in this case N ≤ 18. When you need to roll a 19 to hit, you're removing part of the kukri's threat range, making it essentially have an 19-20 threat range.


Imbicatus wrote:
High AC renders all crits meaningless, as you still need to confirm. If you need a 20 to hit, you need a 20 to confirm.

And on those odds I'd rather have a x4 multiplier than a x2.


BigNorseWolf wrote:
Barathos wrote:
Could someone explain to me why 18-20 critical threat range is better than x4 critical damage multiplier?

Overkill.

First,

When you do 876 points of damage to the thing that only had 100 hit points left, all that extra crit damage goes to waste

Furthermore, unless that creature was about to act next you may not have done anything really. if your cleric or rogue friend is about to bash it for 50, then anything you do over 50 is a little pointless.

Even if you ignore the overkill concern, at best the two are the SAME value, and the 18-20 crit weapons tend to be sexier.

Though there is a certain charm in the scythe-wielding gothy-pants type.


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strayshift wrote:
Imbicatus wrote:
High AC renders all crits meaningless, as you still need to confirm. If you need a 20 to hit, you need a 20 to confirm.
And on those odds I'd rather have a x4 multiplier than a x2.

A 1 in 400 chance of a critical is so low as to be best ignored. If you aren't hitting on an 18, you should probably be running away.

One thing in favor of x4 weapons: they're great for coup de grace if you're teamed up with casters using Color Spray, Hold Person, etc.

Sovereign Court

I'd say that in a low magic campaign - the shortsword is far superior unless you're going one of the builds which gets extra bonuses on crit. This is because in a low magic campaign, static bonuses are going to be harder to come by.

Does anyone really think he can get a +10 static modifier on an off-hand weapon without magic? And that's with Improved crit!

Before level 9 and improved crit (which costs a feat) you'd need a +20 static modifier to make the reduced damage worth it statistically. (not gonna EVER happen in low magic - except maybe with a two-handed weapon, and in that case there's a 3 point damage gap between greatsword & falchion, in which case you'd need a 60 point static modifier)

The only advantage to the kukri is if you're in love with one of the extra bonuses you get on crits. (a few feats etc)

Sovereign Court

Under A Bleeding Sun wrote:
Kukri. 18-20/x2 beats everything (even the falcata at 19-20/x3). Especially once you throw Keen or improved critical on it, but even before that.

For coolness factor - maybe. But not mathematically.

Sovereign Court

Pupsocket wrote:
Assuming improved critical, AFAICT the shortsword deals (3.5+X)*1.2, whereas the Kukri deals (2.5+X)*1.6; simple algebra gets you break-even at X less than 1, so, always use the Kukri.

Your math is bad and you should feel bad.

It's (3.5+X)*1.2 & (2.5+X)*1.3. The only way the kukri would be *1.6 is if you somehow got a crit of 8-20. Not possible.

Therefore X would need to be 10. (even using your wrong formular X would need to be 2.5)


Charon's Little Helper wrote:

I'd say that in a low magic campaign - the shortsword is far superior unless you're going one of the builds which gets extra bonuses on crit. This is because in a low magic campaign, static bonuses are going to be harder to come by.

Does anyone really think he can get a +10 static modifier on an off-hand weapon without magic? And that's with Improved crit!

Before level 9 and improved crit (which costs a feat) you'd need a +20 static modifier to make the reduced damage worth it statistically. (not gonna EVER happen in low magic - except maybe with a two-handed weapon, and in that case there's a 3 point damage gap between greatsword & falchion, in which case you'd need a 60 point static modifier)

The only advantage to the kukri is if you're in love with one of the extra bonuses you get on crits. (a few feats etc)

A 5th human fighter can achieve this with no magic. He will need a 20 DEX but only a 10 STR which is easily done. He takes weapon finesse, slashing grace, piranha strike, double slice, and two Weapon fighting. He will be at +9 to hit, doing 1d4+12 for the primary hand, and +9 to hit, doing 1d4+10 with the secondary.

Sovereign Court

Mysterious Stranger wrote:
Charon's Little Helper wrote:

I'd say that in a low magic campaign - the shortsword is far superior unless you're going one of the builds which gets extra bonuses on crit. This is because in a low magic campaign, static bonuses are going to be harder to come by.

Does anyone really think he can get a +10 static modifier on an off-hand weapon without magic? And that's with Improved crit!

Before level 9 and improved crit (which costs a feat) you'd need a +20 static modifier to make the reduced damage worth it statistically. (not gonna EVER happen in low magic - except maybe with a two-handed weapon, and in that case there's a 3 point damage gap between greatsword & falchion, in which case you'd need a 60 point static modifier)

The only advantage to the kukri is if you're in love with one of the extra bonuses you get on crits. (a few feats etc)

A 5th level fighter with an 18str and no magic can achieve this. That assumes he has an 18 STR and 15 DEX. He needs power attack, double slice, weapon specialization, and desperate battler.

Sure - with all of those things he'd be at just a +10 static modifier.

However, power attack kinda sucks with TWF, and desperate battler certainly isn't going to be working every round.

Finally - at 5th level he can't have access to improved crit yet, so you'd need to be at +20 static mod to make it worth it.

Edit: But OP said he's playing a slayer - so no weapon specialization or fighter bonus - so he'd be at +7 max following your build as close as he could at level 5.


Why choose? Buy a bladed belt.


strayshift wrote:
Imbicatus wrote:
High AC renders all crits meaningless, as you still need to confirm. If you need a 20 to hit, you need a 20 to confirm.
And on those odds I'd rather have a x4 multiplier than a x2.

Statistical outlier, any AC that high isn't getting beat by martial prowess anyway, you need to RUN because it's going to beat you down.

Silver Crusade

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Well, the OP said he was playing a slayer, so he gets partial sneak attack but no Weapon Specialization.

Edit: Also, just take Exotic Weapon Proficiency (wakizashi) and get 1d6 and an 18-20 critical range.


Matthew Downie wrote:
strayshift wrote:
Imbicatus wrote:
High AC renders all crits meaningless, as you still need to confirm. If you need a 20 to hit, you need a 20 to confirm.
And on those odds I'd rather have a x4 multiplier than a x2.

A 1 in 400 chance of a critical is so low as to be best ignored. If you aren't hitting on an 18, you should probably be running away.

One thing in favor of x4 weapons: they're great for coup de grace if you're teamed up with casters using Color Spray, Hold Person, etc.

They're also just fun sometimes. To dial it back down for a moment, in greatsword vs. greataxe the greatsword CLEARLY wins (half point higher average damage, the crit mod thing we just discussed) but the "one hit, one kill" moment you get with the axe crit can be quite viscerally satisfying.

And some people have a perverse love of d12s.


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cnetarian wrote:
In a low magic setting using slashing grace build you might find that the short sword is better until you can get improved critical, but that will depend on how low the amount of magic is.
Mysterious Stranger wrote:
A 5th human fighter can achieve this with no magic. He will need a 20 DEX but only a 10 STR which is easily done. He takes weapon finesse, slashing grace, piranha strike, double slice, and two Weapon fighting.

Correct me if I'm wrong, but I don't believe Shortsword or Kukri qualify for Slashing Grace. Neither are one-handed slashing weapons (shortsword is piercing).


Majuba wrote:
cnetarian wrote:
In a low magic setting using slashing grace build you might find that the short sword is better until you can get improved critical, but that will depend on how low the amount of magic is.
Mysterious Stranger wrote:
A 5th human fighter can achieve this with no magic. He will need a 20 DEX but only a 10 STR which is easily done. He takes weapon finesse, slashing grace, piranha strike, double slice, and two Weapon fighting.
Correct me if I'm wrong, but I don't believe Shortsword or Kukri qualify for Slashing Grace. Neither are one-handed slashing weapons (shortsword is piercing).

You appear to be correct. Shortsword is also light rather than one-handed (this distinction matters, I assume). Cutlass works, but presumably isn't on the character's proficiency list or doesn't work with class abilties or summat.

Sovereign Court

boring7 wrote:
Majuba wrote:
cnetarian wrote:
In a low magic setting using slashing grace build you might find that the short sword is better until you can get improved critical, but that will depend on how low the amount of magic is.
Mysterious Stranger wrote:
A 5th human fighter can achieve this with no magic. He will need a 20 DEX but only a 10 STR which is easily done. He takes weapon finesse, slashing grace, piranha strike, double slice, and two Weapon fighting.
Correct me if I'm wrong, but I don't believe Shortsword or Kukri qualify for Slashing Grace. Neither are one-handed slashing weapons (shortsword is piercing).
You appear to be correct. Shortsword is also light rather than one-handed (this distinction matters, I assume). Cutlass works, but presumably isn't on the character's proficiency list or doesn't work with class abilties or summat.

The cutlass can't be used for TWF effectively. The only way I know of to TWF with slashing grace for both hands is to use the sawtoothed sabre and have dipped a level in swashbuckler.

Grand Lodge

There is always the Sawtooth Sabre, which can be used with Slashing Grace.


You can also use Dueling Swords, you just take the extra -2 to attack for not using a Light weapon in the off hand. This also means you don't have to dip Swashbuckler.


For the 4x coup de grace, just carry around a 4x weapon, even without the feats or magic the multiplier probably means it's way more damage.


Majuba wrote:
cnetarian wrote:
In a low magic setting using slashing grace build you might find that the short sword is better until you can get improved critical, but that will depend on how low the amount of magic is.
Mysterious Stranger wrote:
A 5th human fighter can achieve this with no magic. He will need a 20 DEX but only a 10 STR which is easily done. He takes weapon finesse, slashing grace, piranha strike, double slice, and two Weapon fighting.
Correct me if I'm wrong, but I don't believe Shortsword or Kukri qualify for Slashing Grace. Neither are one-handed slashing weapons (shortsword is piercing).

You are correct, I mention the slashing grace build because a strength focused build would likely have a higher static bonus, which shifts the balance to the kurki being the superior choice.


boring7 wrote:
To dial it back down for a moment, in greatsword vs. greataxe the greatsword CLEARLY wins (half point higher average damage, the crit mod thing we just discussed) but the "one hit, one kill" moment you get with the axe crit can be quite viscerally satisfying.

That actually happened to me within the last week. Our group of level 3 characters with no magical equipment met a Lamia Matriarch (CR 8) and things turned hostile. Instead of running away like sensible adventurers, we attacked. A lucky greataxe critical from a raging barbarian took away the majority of her hit points, and we won with no casualties.

Sovereign Court

Matthew Downie wrote:
boring7 wrote:
To dial it back down for a moment, in greatsword vs. greataxe the greatsword CLEARLY wins (half point higher average damage, the crit mod thing we just discussed) but the "one hit, one kill" moment you get with the axe crit can be quite viscerally satisfying.
That actually happened to me within the last week. Our group of level 3 characters with no magical equipment met a Lamia Matriarch (CR 8) and things turned hostile. Instead of running away like sensible adventurers, we attacked. A lucky greataxe critical from a raging barbarian took away the majority of her hit points, and we won with no casualties.

Yes - but you might as well just use an earthbreaker. It has the x3 but retains the 2d6, so it doesn't average less damage than a greatsword. Much of the extra damage will still be overkill, so from that perspective the greatsword is a bit better, though I suppose on the earthbreaker side is that it's harder to sunder. :P (yet another disadvantage of the greataxe for that matter - one of the easiest two-handed weapons to sunder)

Scarab Sages

Charon's Little Helper wrote:
Matthew Downie wrote:
boring7 wrote:
To dial it back down for a moment, in greatsword vs. greataxe the greatsword CLEARLY wins (half point higher average damage, the crit mod thing we just discussed) but the "one hit, one kill" moment you get with the axe crit can be quite viscerally satisfying.
That actually happened to me within the last week. Our group of level 3 characters with no magical equipment met a Lamia Matriarch (CR 8) and things turned hostile. Instead of running away like sensible adventurers, we attacked. A lucky greataxe critical from a raging barbarian took away the majority of her hit points, and we won with no casualties.
Yes - but you might as well just use an earthbreaker. It has the x3 but retains the 2d6, so it doesn't average less damage than a greatsword. Much of the extra damage will still be overkill, so from that perspective the greatsword is a bit better, though I suppose on the earthbreaker side is that it's harder to sunder. :P (yet another disadvantage of the greataxe for that matter - one of the easiest two-handed weapons to sunder)

Not always. There are several deities with greataxe as a favored weapon, and none with Earth Breaker. This makes it more attractive if you are running into proficiency issues, or have feats that require favored weapon.

Or if you are small, they both do 1d10.

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