The Half Orc race gets it racial ability Savage Attacks.
Savage Attacks
When you score a critical hit with a melee weapon attack, you can roll one of the weapon’s damage dice one additional time and add it to the extra damage of the critical hit.
So if the Half orc is Wielding a GreatAxe it does an additional 1d12 damage, because the value of 1 greataxe attack is 1d12 ... if it is weilding great sword does it do an additional 1d6 ... or 2d6 because the value of the great sword attack is 2d6?
If the thought of your half orc swinging around a massive sword seems more awesome to you, go with the greatsword. If the thought of your half orc swinging around a massive axe seems more awesome to you, go with the greataxe.
Keep in mind the inconsistency that a D12 weapon can bring. Yes, it is much more likely to max out it’s damage (1 in 12 chance vs 1 in 36 for 2d6) but it also goes the other way. Rolling 4d6 (or in this case 5d6) will give you a good chance of doing decent damage. On a greataxe doing 2d12 (or 3d12) there is still a realistic chance of getting less than 6 damage. Of course that is why fighting styles like great weapon fighting exist.
Personally, I just like really rolling more dice. It’s more satisfying to grab a handful of d6s than it is to pick a couple of d12s.
If my numbers are right (and lord knows they're often wrong) you will do an average of 19.5 points of damage on a savage attack with a greataxe (3d12) and an average of 17.5 points of damage (5d6) with a savage attack with a greatsword. That being said, your normal hit with a greatsword will do half a point of damage more than the greataxe on average. That means that as long as you're getting an average of at least four normal hits for every savage attack, you're breaking even.
In the end, swing the weapon that makes you smile.
Just for clarification, you double the dice, correct? So on a crit, wouldn't you be rolling 4D6 (Without savage attacks) The rules say "Roll all of the attack's damage dice twice and add them together" Thats why a sneak attack does double on a crit, and divine smites are best used on crits? Because you straight up double the damage dice?
You have to build heavily towards high critical chance and damage before the average damage you gain from half orc savage attacks with a greataxe outweighs what you get from a greatsword.
As mentioned in Netzach's answer, a barbarian's brutal critical is better when used with a 1d12 weapon instead of a 2d6 weapon. However, he doesn't account for the probability of a critical hit. Therefore, I wanted to provide a calculation whether a barbarian actually has a higher average damage when using a 1d12 weapon, compared to a 2d6 weapon, and if so, at which barbarian level.
I will be assuming that rolls of 8 and lower (leaving 12 other possible results) don't hit at all.
Instead of the in-post calculation, I switched to using Libre Office Calc. See the results below, now in the form of a graph:
The calculations with Reckless Attack were done using probabilities taken from this website, using the "Dice Roll String" 2d12D1+8.
Note that the Superior Critical and Reckless Superior Critical bars are the same values for 1, 2, 3 or 4 extra damage dice, since Superior Critical cannot be combined with Brutal Critical due to the character cap at level 20. One extra damage dice is, however, possible by choosing the Half-Orc race.
I've seen this mistake for the "average" rolls all over the place. Greatsword is strictly better for a fighter given you take the Great Weapon Fighting style even if with the Half-Orc ability only rolling 5d6 vs the 6d6 people hope for. The actual calculation for damage dice is the expected value of the roll which, given that you take the reroll as is for 1s and 2s, gives an expected dice value of 7.333 for a d12 and 4.167 for a d6 meaning 2d6 always does more damage (most people get). The mistake comes on the next step. The expected value of a roll is the sum of odds of getting the value times that value. The table will show the layout for the half-orc given the rerolls from the fighting style. The great weapon fighting style makes a huge difference on the smaller die to the point of strictly making it better for a fighter. The crits aren't going to happen that often (27.75% cap on advantage unless you're a halfling) (this is done on a binomial distribution of 2 attempts at the dice prob. if you're wondering) so the one more dice damage on the crit is never worth giving up one on every other hit.
Half-Orc fighter w/ GWF style (reroll 1s and 2s and take the reroll)
I get most of this except how you calculated the “exp damage by crit range” section. Sure a 20 crit happens 5% of the time, but you don’t get a regular hit 95% of the time. That is to say, If you only count hits, more than 5% will be crits.
Ripping the stuff at the bottom straight from https://en.wikipedia.org/wiki/Expected_value... but the expected dice roll is exactly that. you have a 5% chance of a crit (p1) that gives the crit damage (x1) and then a 95% chance (p2) of rolling a non-crit given you are guaranteed a hit that give normal damage (x2). This seems like a big assumption, but it is not meaningful to the comparison. Here's why: the higher expected damage weapon, sword or axe, remains higher for any AC value and attack bonus combination (with one caveat). It may not be intuitive, but here's the edge example. Lets say you need to roll a 14 to hit with crits down to 18, 1-13 on the die gives no damage for either weapon, and the 14-17 is the same range for both dice and therefor the same probability. For this calculation the E[d12] = 4.77 and E[2d6] = 4.79 which still has swords as better. Now for the caveat, there is a turnover point when the probability of getting a crit is higher than the probability of hitting without a crit (the exact point is the when (crit prob)*(crit damage diff) = (hit prob)*(hit damage diff) which for the example gave is a hit probability of 17.44%)
This boils down to as long as you need one more die number to hit without a crit than the numbers needed for a crit, swords are better (e.g. a crit range of 19,20 needing to roll 16 or less to hit, sword is better). I would assume needing to roll that high just to hit wouldn't come up often enough (if at all) during a campaign given the leveling and items are designed to keep the rolls lower as you go (and you don't get 18-20 until level 15 which should have a +10 to hit with STR 20. How often is the AC of a monster over 24?).
Sorry for the length of this, it kind of kept growing as I didn't want to answer with just "because it won't really ever matter in real play" and look rude. The point you bring up is very valid and I should have explained it in the original post.
Finite case
Let be a random variable with a finite number of finite outcomes occurring with probabilities respectively. The expectation of is defined ashttps://wikimedia.org/api/rest_v1/media/math/render/svg/519542ccdb827d224e730020a1f0c0ce675297d3" alt="{\displaystyle \operatorname {E} [X]=\sum _{i=1}^{k}x_{i}\,p_{i}=x_{1}p_{1}+x_{2}p_{2}+\cdots +x_{k}p_{k}.}">
The Half Orc race gets it racial ability Savage Attacks.
So if the Half orc is Wielding a GreatAxe it does an additional 1d12 damage, because the value of 1 greataxe attack is 1d12 ... if it is weilding great sword does it do an additional 1d6 ... or 2d6 because the value of the great sword attack is 2d6?
1d6...
so basically if you are a half orc you are nerfing yourself by using a great sword ?
A Greatsword (or a Maul) still deals more average and consistent damage than a Greataxe, so not so much.
Bye the rules yes...but a non savage attack two handed sword averages more damage. Also with two handed fighting style great sword is also better.
In the first place the crit gives you 2d6
I stole my pfp from this person: https://mobile.twitter.com/xelart1/status/1177312449575432193
If the thought of your half orc swinging around a massive sword seems more awesome to you, go with the greatsword. If the thought of your half orc swinging around a massive axe seems more awesome to you, go with the greataxe.
"Not all those who wander are lost"
Keep in mind the inconsistency that a D12 weapon can bring. Yes, it is much more likely to max out it’s damage (1 in 12 chance vs 1 in 36 for 2d6) but it also goes the other way. Rolling 4d6 (or in this case 5d6) will give you a good chance of doing decent damage. On a greataxe doing 2d12 (or 3d12) there is still a realistic chance of getting less than 6 damage. Of course that is why fighting styles like great weapon fighting exist.
Personally, I just like really rolling more dice. It’s more satisfying to grab a handful of d6s than it is to pick a couple of d12s.
Yes.
The mechanic is there to encourage the trope of barbarians and axes.
If my numbers are right (and lord knows they're often wrong) you will do an average of 19.5 points of damage on a savage attack with a greataxe (3d12) and an average of 17.5 points of damage (5d6) with a savage attack with a greatsword. That being said, your normal hit with a greatsword will do half a point of damage more than the greataxe on average. That means that as long as you're getting an average of at least four normal hits for every savage attack, you're breaking even.
In the end, swing the weapon that makes you smile.
"Not all those who wander are lost"
i appreciate all the input .... i just gave him a polearm for the reach lol
Just for clarification, you double the dice, correct? So on a crit, wouldn't you be rolling 4D6 (Without savage attacks) The rules say "Roll all of the attack's damage dice twice and add them together" Thats why a sneak attack does double on a crit, and divine smites are best used on crits? Because you straight up double the damage dice?
You have to build heavily towards high critical chance and damage before the average damage you gain from half orc savage attacks with a greataxe outweighs what you get from a greatsword.
This graph was posted by user PixelMaster on a Stackexchange thread (https://rpg.stackexchange.com/questions/120604/is-greatsword-superior-to-greataxe):
I've seen this mistake for the "average" rolls all over the place. Greatsword is strictly better for a fighter given you take the Great Weapon Fighting style even if with the Half-Orc ability only rolling 5d6 vs the 6d6 people hope for. The actual calculation for damage dice is the expected value of the roll which, given that you take the reroll as is for 1s and 2s, gives an expected dice value of 7.333 for a d12 and 4.167 for a d6 meaning 2d6 always does more damage (most people get). The mistake comes on the next step. The expected value of a roll is the sum of odds of getting the value times that value. The table will show the layout for the half-orc given the rerolls from the fighting style. The great weapon fighting style makes a huge difference on the smaller die to the point of strictly making it better for a fighter. The crits aren't going to happen that often (27.75% cap on advantage unless you're a halfling) (this is done on a binomial distribution of 2 attempts at the dice prob. if you're wondering) so the one more dice damage on the crit is never worth giving up one on every other hit.
I get most of this except how you calculated the “exp damage by crit range” section. Sure a 20 crit happens 5% of the time, but you don’t get a regular hit 95% of the time. That is to say, If you only count hits, more than 5% will be crits.
Ripping the stuff at the bottom straight from https://en.wikipedia.org/wiki/Expected_value... but the expected dice roll is exactly that. you have a 5% chance of a crit (p1) that gives the crit damage (x1) and then a 95% chance (p2) of rolling a non-crit given you are guaranteed a hit that give normal damage (x2). This seems like a big assumption, but it is not meaningful to the comparison. Here's why: the higher expected damage weapon, sword or axe, remains higher for any AC value and attack bonus combination (with one caveat). It may not be intuitive, but here's the edge example. Lets say you need to roll a 14 to hit with crits down to 18, 1-13 on the die gives no damage for either weapon, and the 14-17 is the same range for both dice and therefor the same probability. For this calculation the E[d12] = 4.77 and E[2d6] = 4.79 which still has swords as better. Now for the caveat, there is a turnover point when the probability of getting a crit is higher than the probability of hitting without a crit (the exact point is the when (crit prob)*(crit damage diff) = (hit prob)*(hit damage diff) which for the example gave is a hit probability of 17.44%)
This boils down to as long as you need one more die number to hit without a crit than the numbers needed for a crit, swords are better (e.g. a crit range of 19,20 needing to roll 16 or less to hit, sword is better). I would assume needing to roll that high just to hit wouldn't come up often enough (if at all) during a campaign given the leveling and items are designed to keep the rolls lower as you go (and you don't get 18-20 until level 15 which should have a +10 to hit with STR 20. How often is the AC of a monster over 24?).
Sorry for the length of this, it kind of kept growing as I didn't want to answer with just "because it won't really ever matter in real play" and look rude. The point you bring up is very valid and I should have explained it in the original post.
Finite case
Let be a random variable with a finite number of finite outcomes occurring with probabilities respectively. The expectation of is defined ashttps://wikimedia.org/api/rest_v1/media/math/render/svg/519542ccdb827d224e730020a1f0c0ce675297d3" alt="{\displaystyle \operatorname {E} [X]=\sum _{i=1}^{k}x_{i}\,p_{i}=x_{1}p_{1}+x_{2}p_{2}+\cdots +x_{k}p_{k}.}">