Which one produces the best results the most? Or how about 2d6 against 1d12? Or 3d4 against 1d12?What about the generic case: ndm against 1d(nm)?in short, ndm is always better than 1d(nm) which, written mathematically, looks like:

Truth be told this is an oversimplification; an ndmis more consistent than a1d(nm)for dealing damage, however, the probability that a 1d(nm) produces an extreme is higher than the probability an ndm will. Personally though, if given the choice, I'd always take the ndmbut that's just me.

"Which one produces the best results the most?" is literally asking "which has the higher average?" If you disagree, please explain. If you agree, some simple counting will tell you that the average for a d8 is 4.5 not 4 and the average of a d4 is 2.5, so 2d4 has a slightly higher average than 1d8. Would you rather roll 1d8 or 8d1 for damage? Clearly 8d1 is the better choice. The average for 1d(nm) is nm/2+.5 while the average for ndm is n(m/2+.5).

You bring up an interesting point about the distribution of results. Certainly 1d8 is more likely to roll extreme values than 2d4, but it's equally likely to roll extremely low as roll extremely high. The probability of rolling a 1 on 2d4 is 0.

The only time 1d8 is better than 2d4 is if you're in a situation where it's absolutely imperative that you deal more than 5 damage for whatever reason, since the 1d8 weapon has a higher chance of doing so. In general, you're better off with the more consistent and higher average damage of 2d4.

If you have abilities that let you add 1 more of your weapon's damage die then 1d8 might be more appealing, but those features usually onlyworkon a critical hit and generally don't make up for the lower average damage you have when not scoring crits.

The only time 1d8 is better than 2d4 is if you're in a situation where it's absolutely imperative that you deal more than 5 damage for whatever reason, since the 1d8 weapon has a higher chance of doing so. In general, you're better off with the more consistent and higher average damage of 2d4.

If you have abilities that let you add 1 more of your weapon's damage die then 1d8 might be more appealing, but those features usually onlyworkon a critical hit and generally don't make up for the lower average damage you have when not scoring crits.

This is also an interesting point. Average damage isn't everything. If you can do 5 damage exactly per hit or roll 1d8, in general I would say that the d8 is inferior. If the enemy has 6 hp, it'sdefinitelybetter to take the risk on the d8 to kill the enemy in one hit instead of 2. I need to think about it more and there's probably a better way to quantify/describe this phenomenon.

2d4 is a good deal better than 1d8 in almost all situations. Rather obviously, you have a higher average, but that's not even the only thing that makes 2d4 better. In addition to its higher average output, it has a more consistent, bell-curved output (which is more tactically useful than a more unpredictable output in many situations) and a higher minimum output (2 instead of 1) which means it has more reliable "you can't fail" situations.

Pretty much the only case where 1d8 is better is if you are in a situation where rolling higher than 5 is extremely important, such as it being the only possible way to do enough damage to finish off a very dangerous foe before they can move.

My philosophy on this is the you will always get at least 2 damage with the 2d4, 2d6, 2d10, and so on. So even on a string of the worst rolls you will be guaranteed at least 2 damage.2d(X)also provides a better chance to roll consistently higher. 1d8 vs. 2d4 If you look at the chance to roll 4 or above on a single roll using1d8 is 62.5%. Using 2d4 your chance jumps to 81.25% of rolling the same 4 or above. So I will always opt for the ndm when given the choice.

I see what you're saying here I'm hesitant to follow your logic though. Technically the probability doesn't change on either so you still have the same probability of rolling a 1 on the 1st roll as you do on the 2nd. You will never roll below a 2 with 2d4 and have a better chance of rolling at least 3, 4, 5 if you want to have sustained damage output.

I agree Savage Attack is still useful either way because on a bad roll your probability resets, but it doesn't give you any better chance definitively. I personally, would still take the 2d4 for Savage Attack because I am more likely to roll a consistently higher total than just one roll of the d8. However, the 25% chance of rolling 7 or better and the 12.5% chance of rolling the 8 makes me want to rethink this a little more.

"My philosophy on this is the you will always get at least 2 damage with the 2d4, 2d6, 2d10, and so on. So even on a string of the worst rolls you will be guaranteed at least 2 damage.2d(X)also provides a better chance to roll consistently higher. 1d8 vs. 2d4 If you look at the chance to roll 4 or above on a single roll using1d8 is 62.5%. Using 2d4 your chance jumps to 81.25% of rolling the same 4 or above. So I will always opt for the ndm when given the choice."

A 9th lvl Half Orc Barbarian with a Greatsword rolls: 2d6+STR +2d6 (critical) +1d6 (Savage Attacks) +1d6 (Brutal Critical) for 6d6+STR for an average of 18+STR (min 6+STR / max 36+STR)A 9th lvl Half Orc Barbarian with a Greataxe rolls: 1d12+STR +1d12 (critical) +1d12 (Savage Attacks) +1d12 (Brutal Critical) for 4d12+STR for average of 24+STR (min 4+STR / max 48+STR)

Rerolling 2d4 is still going to give a higher average than rerolling 1d8. EDIT: Interestingly, rerolling 1d12 has a slightly higher average than rerolling 2d6though. Also,Savage Attacker isn't worth it if your attacking ability score isn't maxed out. Even then, most classes have a secondary ability score they want to bump and several other compelling feats (e.g. Sentinel, War Caster, Polearm Master, Great Weapon Fighting.)

Also is Savage Attacker worth it?It only applies to the melee weapon, so it won't apply to Sneak Attack (The one place I'd find it useful, because it's a lot of dice once a turn).Is it ever worth it to take Savage Attacker instead of +1 attack/damage stat? I mean unless you're already at a 20?

Savage attacker, assuming a Barbarian with a great axe,is actually rather difficult to quantify, I find. Rerolling your d12 boosts your average damage from 6.5 to 8, so, from a purely mathematical standpoint, its little better than just +1 damage, far weaker than +1 Strength's boost to saves, athletics checks, to hit and to damage rolls. On a crit, you get an extra 1.5 damage per brutal critical feature (plus whatever half-orc's version is called), so that might make up for it.... on a single attack. This is where it all falls apart - you get the feat's bonus once per turn. So, you have to balance your desire to get extra bonus on the critical and holding off, and possibly missing, and then the chance your first damage roll will be good and wasting the feat... And what about the case with a flametongue greataxe or some other damage?

I go for the d8 over 2d4 for the same reason I go for the d12 over 2d6: I like having better odds of rolling the high end of the range even when it means equally greater odds of rolling sub-par, and luck carries me through often enough to not look silly for doing it.

Defining "best results" as "max damage", the objective answer to your question is "1d8", which produces max damage 12.5% of the time, while "2d4" produces max damage half as often (6.25% of the time). You probably didn't mean to ask that, though. =)

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