If you have a choice of two weapons. One does 2D6 damage. The other does 1D6 + Some Number. What does that Number have to be for the two weapons to be equally interesting choices?
Is it 1D6+3 or 1D6+4? Or it impossible to balance without some additional non-damage aspect to the weapon?
I ask because the RPG I am working on will be using D20 for combat and only D6s for damage. I wanted to see if I could replace +1D6 with some number and still maintain parity.
They can never be equal. 1d6 + "number" and 2d6 have different standard deviations, regardless of what the "number" is.
Quote from: Spinachcat;426011If you have a choice of two weapons. One does 2D6 damage. The other does 1D6 + Some Number. What does that Number have to be for the two weapons to be equally interesting choices?
Is it 1D6+3 or 1D6+4? Or it impossible to balance without some additional non-damage aspect to the weapon?
I ask because the RPG I am working on will be using D20 for combat and only D6s for damage. I wanted to see if I could replace +1D6 with some number and still maintain parity.
1d6+4 is my guess. The extra half a point of damage on average makes up for the lower maximum.
Quote from: Spinachcat;426011If you have a choice of two weapons. One does 2D6 damage. The other does 1D6 + Some Number. What does that Number have to be for the two weapons to be equally interesting choices?
Is it 1D6+3 or 1D6+4? Or it impossible to balance without some additional non-damage aspect to the weapon?
I ask because the RPG I am working on will be using D20 for combat and only D6s for damage. I wanted to see if I could replace +1D6 with some number and still maintain parity.
2d6 yields a wide bell curve from 2 to 12, with the midpoint at 7.
1d6+3 yields a flat curve with results from 4 to 9, all equally probable.
The first gives a centered result with a moderately wide fluctuation - more accuracy, less precision.
The second gives a uniformly varying result within narrower parameters - more precision, less accuracy.
Both are interesting in different ways.
-clash
If I can choose between 1d6+4 and 2d6 I'm going to take the former every single time.
Quote from: Benoist;426025If I can choose between 1d6+4 and 2d6 I'm going to take the former every single time.
Really? For me it would depend greatly on the character choosing, as I see different appeals in both.
-clash
2d6 gives a bell-curve Gaussian probability distribution with an average result of 7. Since it's a bell-curve, this also means 7 is the most likely result.
1d6+x, however, is a linear distribution. Which means that any result between 1+x and 6+x is just as likely. But if you assume fair, unbiased dice, regression towards the mean assures that there will be a trend towards the average damage of 3.5+x.
If you want to match average for average, it's dirt simple:
3.5+x=7
x=7-3.5
x=3.5
So, for both weapons to have equivalent "average" damage, 1d6+3 or 1d6+4 is what you're looking for.
But of course, IMHO, I feel that there should be more than flat numerical damage that makes weapon choice interesting... :D
Quote from: The Butcher;426029But of course, IMHO, I feel that there should be more than flat numerical damage that makes weapon choice interesting... :D
I think we all have added a mental "All other things being equal" there - except maybe Benoist, who seems very definite... :D
-clash
Quote from: Benoist;426025If I can choose between 1d6+4 and 2d6 I'm going to take the former every single time.
You know what, Benoist's on to something here. Since there's an underlying probability distribution, we're supposed to weigh the means with the relative probabilities for any given result.
Am I making any sense? At all?1d6+4 means equal probabilities of a result ranging between 5-10, resulting on a weighted mean of (5+6+7+8+9+10)/6=45/6=8.5
The weighted mean of 2d6 would be
[2+(2x3)+(3x4)+(4x5)+(5x6)+(6x7)+(5x8)+(4x9)+(3x10)+(2x11)+12]/36=
[2+6+12+20+30+42+40+36+30+22+12]=
252/36=7
which is the same as the average, of course, being a Gaussian distribution.
So 1d6+3, which would give a weighted mean of
4+5+6+7+8+9/6=39/6=6.5
might be a closer to what you want.
[my bad. I am not a mathematician, or engineer, or anything partciularly math-y] :o
Quote from: the butcher;4260341d6+4 means equal probabilities of a result ranging between 5-10, resulting on a weighted mean of (5+6+7+8+9+10)/6=45/6=8.5
45/6 = 7.5
Quote from: flyingmice;426027Really? For me it would depend greatly on the character choosing, as I see different appeals in both.
-clash
Ah if you put it that way, I completely agree! I was completely ignoring the concept of role playing here, to concentrate on the pure mathematical appeal between the two. :)
Going on with that ex-RP argument, It's nearly always better for me as a player to take a fixed value over a die, because then I can strategize better and randomness plays a lesser role in how I plan actions. This is why just comparing the average numbers of the two possibilities, 1d6+3 vs. 2d6, isn't actually an *equal* choice in my mind. I'll take 1d6+3 as well. Choosing between 1d6+2 and 2d6 makes the choice equal to me psychologically, though it is obviously not equal mathematically.
Quote from: ggroy;42603645/6 = 7.5
Told you I suck at math. :o
Quote from: Benoist;426042Ah if you put it that way, I completely agree! I was completely ignoring the concept of role playing here, to concentrate on the pure mathematical appeal between the two. :)
Ah - that's the game designer part of me. When I am designing things, statistical probability is
extremely important to me. When I am a GM or player, I need to know this as well, but the choice would be based on the character, not what
I like. Some characters would enjoy the uncertainty of 2d6, while others would prefer the certainty of 1d6+3, and yet others wouldn't know or care - close enough for hand-grenades, bocce, and head-bashing. That's why God didn't make everyone as handsome as Pundit - choice is important.
-clash
I'm with Benoist. 2d6 is not as good as 1d6+4. If we roll damage a million times, the guy with the 1d6+4 is going to win. For all the times I've knocked a bad guy down to 1 hit point, I think I'll take the higher average.
Quote from: flyingmice;426078Ah - that's the game designer part of me. When I am designing things, statistical probability is extremely important to me.
As it should be! I mean: I can hardly imagine how anyone could come up with some rules sub/system (whether as a house rule or printed material) and not care at all for statistical outcomes. That'd be the equivalent of walking in the dark, with the highest probability to crash into a wall at some point. Then you can't really be surprised you did.
Quote from: flyingmice;426078When I am a GM or player, I need to know this as well, but the choice would be based on the character, not what I like. Some characters would enjoy the uncertainty of 2d6, while others would prefer the certainty of 1d6+3, and yet others wouldn't know or care - close enough for hand-grenades, bocce, and head-bashing. That's why God didn't make everyone as handsome as Pundit - choice is important.
-clash
I agree on principle as well. I mean, personally, as a player, I would make choices based on both what I as a player want and what my character wants. Sometimes the two will be perfectly in tune, and sometimes, they are going to clash, with the character's wishes winning most of the time (I'm thinking suboptimal tactical choices like here, for instance), depending on the situation. Though there are times (I'm thinking deeply disruptive stuff, here) where I as a player need to step in and make a choice to play my character some other way, as to not wreck the game. I don't see how that could occur with the choice between the types of dice proposed, but there you go.
Quote from: Benoist;426103As it should be! I mean: I can hardly imagine how anyone could come up with some rules sub/system (whether as a house rule or printed material) and not care at all for statistical outcomes. That'd be the equivalent of walking in the dark, with the highest probability to crash into a wall at some point. Then you can't really be surprised you did.
You would be surprised - or maybe you wouldn't! - at how many designers have no clue about using statistics to predict and model.
QuoteI agree on principle as well. I mean, personally, as a player, I would make choices based on both what I as a player want and what my character wants. Sometimes the two will be perfectly in tune, and sometimes, they are going to clash, with the character's wishes winning most of the time (I'm thinking suboptimal tactical choices like here, for instance), depending on the situation. Though there are times (I'm thinking deeply disruptive stuff, here) where I as a player need to step in and make a choice to play my character some other way, as to not wreck the game. I don't see how that could occur with the choice between the types of dice proposed, but there you go.
I think what you are saying here is that if the difference is large enough, the player needs to step in and make sure the character - who just might prefer a banana to that .45 - makes the choice that won't make him a liability in the party; but if the difference is relatively minor, as in the current example, the player can allow the character to move as he would list. I agree entirely! Especially for those games where that sort of thing is important! In some games, of course - and here I am staring directly into the baby blues of Toon - the banana
is the rational choice...
-clash
If I am playing the reckless dwarf barbarian with the great axe, I want the 2d6. Because the rare opportunity to roll two sixes is worth it for that kind of character.
If I am playing the logical rapier wielding elf fighter, I want the 1d6+4. Because the increased reliability of the damage fits better with the character concept for me.
Quote from: Mistwell;426121If I am playing the reckless dwarf barbarian with the great axe, I want the 2d6. Because the rare opportunity to roll two sixes is worth it for that kind of character.
If I am playing the logical rapier wielding elf fighter, I want the 1d6+4. Because the increased reliability of the damage fits better with the character concept for me.
I honestly can't get, for the life of me, what the spread of the damage dice has to do with the character concept. Better numbers equal more skill and luck, worse numbers, the opposite.
This thread is the first time, ever, I've heard anyone suggest picking a weaker damage spread to enhance their character concept.
I kind of see where you guys are coming from, I just don't see the point.
"Wow guy, you did 2 damage that strike and 12 the next! What flair!" Who would notice but you?
If you have armor that subtracts from damage, then that technically will make the 2d6 a little bit more attractive. However, the extra +0.5 average of 1d6+4 basically counter-balances this.
For example, let's say the opponent has armor that subtracts 9 from damage.
2d6 does average 0.28 damage per hit.
1d6+3 can't damage at all.
1d6+4 does average 0.17 damage per hit.
If the opponent has armor that subtracts 6 from damage.
2d6 does average 1.56 damage per hit.
1d6+4 does average 1.67 damage per hit.
1d6+3 does average 1.00 damage per hit.
On a practical note, you could make 1d6+3 more attractive by giving a minor extra effect if the player rolls maximum damage. This is likely for 1d6+3, but rare for 2d6.
Quote from: Cranewings;426136I honestly can't get, for the life of me, what the spread of the damage dice has to do with the character concept. Better numbers equal more skill and luck, worse numbers, the opposite.
Strange. I have the opposite reaction, and entirely understand what Mark means. If you have a random spread of damage, this might indicate a more erratic, less precise, more blunt behavior, with a higher risk for different types of outcome, whereas a precise amount of damage might simulate some precision and care in the way the attack is carried out. So it totally can be part of role playing the character concept or emotion at the moment, in my mind.
Quote from: Cranewings;426136This thread is the first time, ever, I've heard anyone suggest picking a weaker damage spread to enhance their character concept.
That is even weirder to me.
Quote from: Cranewings;426136I kind of see where you guys are coming from, I just don't see the point.
"Wow guy, you did 2 damage that strike and 12 the next! What flair!" Who would notice but you?
Somebody needs to notice besides yourself for you to be actually role playing?
I'm role playing my characters' (PCs or NPCs) emotions silently in my head all the time!
The difference in the shape of the distributions (between a linear 5-11 or the v-shaped 2-12) may be important from a practical min/maxing perspective.
The raw average damage isn't as important as how many hits it takes to kill a monster. If most monsters have 12 hit points say, then the 2-12 might be better because you have at least some chance, even if its only 1 in 36, of popping the monster on the first go, even though the average damage is slightly lower.
But, if alot of monsters have 3 or 4 hit points, then 2d6 is worse since its not a guaranteed splatter vs. the goblins.
Of course you expect a range of HP totals, but which type is more common can still inform your decision.
If we compare 1D6+3 and 1D6+4 vs. 2D6...
How often does the 2D6 weapon do the minimum or less than the 1D6+X one?
How often does the 2D6 weapon do the maximum or more than the 1D6+X one?
AKA, we know the 1D6+3 does 9 points about 17% of the time and the D6+4 does 10 pts the same rate. How often does the 2D6 weapon do 9 or more? How often does it do 10 or more?
And we can look at the converse. How often does a 2D6 weapon do 4 pts or less?
Quote from: Benoist;426025If I can choose between 1d6+4 and 2d6 I'm going to take the former every single time.
How do you feel about 1D6+3 vs. 2D6?
Also, does your feeling change when comparing 2D6+3 vs. 3D6?
How about 2D6+6 vs 4D6?
Quote from: The Butcher;426029But of course, IMHO, I feel that there should be more than flat numerical damage that makes weapon choice interesting... :D
YES!
I will be designing other aspects of weapons (accuracy, usefuless in variety of situations, etc), but at the moment I wanted to focus just on thoughts about the damage range. Thus, if people are really down are D6+3 and thrilled with D6+4 vs. 2D6, that would tell me the D6+3 and 2D6 weapons need some sort of "boost" versus a 2D6 one.
Quote from: Cranewings;426136"Wow guy, you did 2 damage that strike and 12 the next! What flair!" Who would notice but you?
Why would I care what anyone else thinks?
-clash
Quote from: Benoist;426138Strange. I have the opposite reaction, and entirely understand what Mark means. If you have a random spread of damage, this might indicate a more erratic, less precise, more blunt behavior, with a higher risk for different types of outcome, whereas a precise amount of damage might simulate some precision and care in the way the attack is carried out. So it totally can be part of role playing the character concept or emotion at the moment, in my mind.
That is even weirder to me.
Somebody needs to notice besides yourself for you to be actually role playing?
I'm role playing my characters' (PCs or NPCs) emotions silently in my head all the time!
I agree entirely, in every way, with everything you have said here, Benoist! :D
-clash
Quote from: flyingmice;426120You would be surprised - or maybe you wouldn't! - at how many designers have no clue about using statistics to predict and model.
I can't say I'm really surprised, but at the same time, that's just mind-boggling to me. I'm no math wizard (I'm not completely uneducated on the matter either - I was in Sciences in high school), but I can't for the life of me understand why a designer wouldn't care about statistics as far as dice outcomes are concerned.
As I said earlier about the 2d6 vs 1d6+N choice earlier, a strictly equal mathematical choice might not equal to a strictly equal choice in the context of the game, and there are indeed other considerations (human, tactical, RP and otherwise) you'd take into account for sure, but that shouldn't stop someone from looking at the basic mathematics involved.
Alright kidz, check my maths! (I am rounding up %)
AVERAGE TO HIGH END ROLLS
2D6
03% to get 12
08% to get 11 or higher
17% to get 10 or higher
28% to get 9 or higher
42% to get 8 or higher
58% to get 7 or higher
1D6+4
17% to get 10
33% to get 9 or higher
50% to get 8 or higher
67% to get 7 or higher
1D6+3
17% to get 9
33% to get 8 or higher
50% to get 7 or higher
LOW END ROLLS
2D6
17% to get 4 or lower
28% to get 5 or lower
42% to get 6 or lower
1D6+4
17% to get 5
33% to get 6 or lower
1D6+3
17% to get 4
33% to get 5 or lower
50% to get 6 or lower
SO....ANOTHER QUESTION....
Assuming a D20 style combat system, are these weapons balanced (all other factors being equal)???
1) 1D6+4 weapon with a +0 Attack bonus
2) 2D6 weapon with a +1 Attack bonus
3) 1D6+3 weapon with a +2 Attack bonus
AND....EVEN ANOTHER QUESTION....
Do the math make sense with higher dice? AKA, how does 2D6+6 compare to 4D6?
To answer the original question, as soon as you go with "all other things being equal", you have to go with the higher mean, d6 + 4, since you've got nothing else to go on.
Playing a game where all monsters have DR 10? Then 2d6 makes sense.
Playing a game where all monsters have 4 hp or less? Then D6 + 3 makes sense.
So answering most of your questions are about factors outside of just 'the mean'.
But, 2d6 +6 is 'worse', all other things being equal, than 4d6.
The mean of a sum is the sum of a mean, for independent variables like dice. The expected value of a d6 roll is 3.5, so all your questions can be answered (if you're only looking at the mean) by taking expected values.
Quote from: Benoist;426138Somebody needs to notice besides yourself for you to be actually role playing?
I'm role playing my characters' (PCs or NPCs) emotions silently in my head all the time!
Well, you can pretend anything in your head that you want. One of the main points of the rules and the dice and all that (at least to me) is to help everyone have the same thing in their head at the same time. The nuance of your character being unreliable at striking as demonstrated by rolling 2d6 instead of 1d6+3.5 for damage isn't going to be picked up on by anyone. It is completely trivial and no one is going to track or remember it.
The only thing anyone will remember about your character's damage is if he seems to kill quickly or not, if he is good at fighting or not. Picking something that causes him to take an extra round of hitting to make his kill will just make people think you suck, rather than convey the idea that he is (insert whatever 2d6 conveys over 1d6+3.5).
I don't really doubt that you guys really believe it helps you RP better, it just isn't something I've ever seen before this thread. If someone had a choice between doing 100 points every time they hit, or doing 1d100, everyone would pick 100 flat. Even if they wanted to play a wild and crazy guy, they would still pick the high flat number... they would just tell people he looks wild and crazy.
Quote from: flyingmice;426157Why would I care what anyone else thinks?
-clash
If you didn't care what anyone else thinks, you wouldn't bother describing anything about your character.
Telling people that you can prove with dice that he is an unreliable striker because he rolls 2d6 instead of 1d6+4 or whatever is so trivial, no one I've ever met would care or remember. You could automatically deal 7 very time and no one would care. If you said, "he may technically deal 7 every time, but he seems wild and crazy when he fights" then people will picture a wild guy. Modeling it with your damage dice is too trivial to matter to anyone I've ever met in real life.
Quote from: Spinachcat;426261Assuming a D20 style combat system, are these weapons balanced (all other factors being equal)???
1) 1D6+4 weapon with a +0 Attack bonus
2) 2D6 weapon with a +1 Attack bonus
3) 1D6+3 weapon with a +2 Attack bonus
Depending on hit probability...if chance to hit is 50/50 (11+ on d20), then
another +1 attack bonus will increase your average damage by 10%.
For 2d6 that bumps your equivalent damage from 7 to 7.7, compared to 7.5 for the d6+4. Slight net gain, but nothing noticeable. The +1 to hit becomes more significant the lower your actual chance of hitting is, though.
Quote from: Cranewings;426284If you didn't care what anyone else thinks, you wouldn't bother describing anything about your character.
You see, that's just flat out wrong. You come to this wrong conclusion by assuming I value what you value. That basic assumption is incorrect.
QuoteTelling people that you can prove with dice that he is an unreliable striker because he rolls 2d6 instead of 1d6+4 or whatever is so trivial, no one I've ever met would care or remember. You could automatically deal 7 very time and no one would care. If you said, "he may technically deal 7 every time, but he seems wild and crazy when he fights" then people will picture a wild guy. Modeling it with your damage dice is too trivial to matter to anyone I've ever met in real life.
Then you should play a game where you just say "I fight the dragon and beat him, but have a tough time doing it, so I'm all scuffed up and bloody" rather than bothering to play it out. They can all picture it, right? That's all that matters.
I don't *want* to prove with dice that my character is an unreliable striker. It would not ever even occur to me as a possibility. You are approaching roleplaying in such a fundamentally different way than I am that it is like we are alien creatures. You are - in effect - trying to tell me that I tap my lips when I ponder because my snershum juville is horking, when I have no snershum juville, and thus not only can't I hork, I have no concept of what horking is.
-clash
Fair enough. I'm afraid I don't get it.
Quote from: Cranewings;426358Fair enough. I'm afraid I don't get it.
I'm wondering if this is somehow related to the group you're playing with. The big picture as far as your gaming is concerned, and the problems you are running into with your group. I'm not saying that'd be all your fault or whatnot. Just wondering if this is all interconnected somehow, and I'm not seeing the pattern yet. (trying to be helpful, here)
Quote from: Cranewings;426358Fair enough. I'm afraid I don't get it.
I will attempt to explain:
Let us take Mistwell's example of the "reckless dwarf barbarian with the great axe", which I am playing. The character is reckless, not calculating. He would prefer the weapon with the greatest *potential* damage that he could handle - not because it is optimal, not because doing so would show the other players that I - the player - am playing a reckless character, but because it is an
expression of his character. *He* would prefer that 2d6 weapon over the 1d6+4 weapon. Letting him have this weapon would not cripple him - the difference is minor - so I, the player, choose that weapon for him.
James Bond would never drive a Volvo, no matter that it is very safe, because he's James Fucking Bond! He'd drive that Aston Martin because it's fast, flashy, and sexy. Bond values those characteristics over safe, dependable, and tough, the virtues of a Volvo.
Similarly, the reckless dwarf barbarian cherishes the recklessness of the 2d6 weapon over the dependability of the 1d6+4 weapon. It expresses his character. Similarly, he'd prefer armor that gave him freedom and mobility over armor that protected better at the cost of slowing him down. Again, an expression of character. He'd gamble his gold away on a single throw of teh dice because he is reckless. The thrill of the risk more than compensates for the safety of living defensively.
This has nothing to do with what other players think of me as a player. That is something I care nothing about. That is not a goal, or even a concern. It has to do with getting into the head of the character, and playing him from the inside out. By doing this, it helps my my imagination to allow me to see things through his eyes, and experience the world through his senses. That is, ultimately, my goal.
-clash
Quote from: flyingmice;426391I will attempt to explain:
Let us take Mistwell's example of the "reckless dwarf barbarian with the great axe", which I am playing. The character is reckless, not calculating. He would prefer the weapon with the greatest *potential* damage that he could handle - not because it is optimal, not because doing so would show the other players that I - the player - am playing a reckless character, but because it is an expression of his character. *He* would prefer that 2d6 weapon over the 1d6+4 weapon. Letting him have this weapon would not cripple him - the difference is minor - so I, the player, choose that weapon for him.
James Bond would never drive a Volvo, no matter that it is very safe, because he's James Fucking Bond! He'd drive that Aston Martin because it's fast, flashy, and sexy. Bond values those characteristics over safe, dependable, and tough, the virtues of a Volvo.
Similarly, the reckless dwarf barbarian cherishes the recklessness of the 2d6 weapon over the dependability of the 1d6+4 weapon. It expresses his character. Similarly, he'd prefer armor that gave him freedom and mobility over armor that protected better at the cost of slowing him down. Again, an expression of character. He'd gamble his gold away on a single throw of teh dice because he is reckless. The thrill of the risk more than compensates for the safety of living defensively.
This has nothing to do with what other players think of me as a player. That is something I care nothing about. That is not a goal, or even a concern. It has to do with getting into the head of the character, and playing him from the inside out. By doing this, it helps my my imagination to allow me to see things through his eyes, and experience the world through his senses. That is, ultimately, my goal.
-clash
:hatsoff:
I allways choose weapons that mirror my (characters) persona...:D
Quote from: Benoist;426377I'm wondering if this is somehow related to the group you're playing with. The big picture as far as your gaming is concerned, and the problems you are running into with your group. I'm not saying that'd be all your fault or whatnot. Just wondering if this is all interconnected somehow, and I'm not seeing the pattern yet. (trying to be helpful, here)
Could be. I'm not sure. (; On a side note, I know it isn't my fault at all because I ran a 8 month long game with a stable group last year and didn't have any problems. These friends of mine are just crazy.
The guy playing the party leader was in a funk monday night when I picked him up. He was having some kind of moody depression. I told him on the way, "you know this could be the last game given what you are fighting so you better put on your fucking try-hards and win because everyone needs your genius." Surprisingly enough, they actually won the fight without any casualties. I was pretty shocked.
Flying Mice, I get ya. I wouldn't have ever thought of it that way.
I get pretty into character myself, but it doesn't have anything to do really with his attributes. I've always thought of getting into character as something individuals do because they are inclined to.
In my experience, the same people that actually get into character do no matter what the system or what's on their sheet. The other people just don't.
Quote from: Cranewings;426533Could be. I'm not sure. (; On a side note, I know it isn't my fault at all because I ran a 8 month long game with a stable group last year and didn't have any problems. These friends of mine are just crazy.
Yeah, like I said: I'm not trying to put the blame on you somehow. Just wondering about the paradigm in your game group, because that's twice now I'm really puzzled about them, and I would just love to play with these guys just to see if I could notice something somehow that I did not notice through your descriptions on the board.
Quote from: Cranewings;426533The guy playing the party leader was in a funk monday night when I picked him up. He was having some kind of moody depression. I told him on the way, "you know this could be the last game given what you are fighting so you better put on your fucking try-hards and win because everyone needs your genius." Surprisingly enough, they actually won the fight without any casualties. I was pretty shocked.
HA! Awesome! A win for the group, in many senses of the term! :D
Math hurts my brain.
RPGpundit
Quote from: Spinachcat;426011Is it 1D6+3 or 1D6+4? Or it impossible to balance without some additional non-damage aspect to the weapon?
1d6+3.5 is mathematically the same as 2d6, but since you can't really do that the 1d6+4 is probably your best choice.
Quote from: finarvyn;4266751d6+3.5 is mathematically the same as 2d6, but since you can't really do that the 1d6+4 is probably your best choice.
It's stunning how many people think all there is to a distribution is the mean.
Quote from: Doom;426716It's stunning how many people think all there is to a distribution is the mean.
I'm kind of surprised as well. It's like my earlier point of the consistency vs. randomness, the psychological aspect of tactics and how they relate to planning, expectations and so on flew completely over some people's heads.
Quote from: finarvyn;4266751d6+3.5 is mathematically the same as 2d6, but since you can't really do that the 1d6+4 is probably your best choice.
Or can't you???
Going the other way 1d6+3, rerolling any 1s gives an average value of exactly 7.
(all values possible on the d6: 2,3,4,5,6 = 20, /5 possible results = average value of 4)
If you do that then the only difference becomes the distribution, no change in average damage between the d6+3 and the 2d6 at all.
Hey, that's a clever way to get around the whole "add a 0.5" silliness.
Next to a discussion about police riding unicorns, this is probably the 2nd best fun-but-pointless gaming board discussion I've seen for 2010. ;)
Wonder who (in rpg gaming) pays attention to kurtosis and skewness.
Quote from: Doom;426854Hey, that's a clever way to get around the whole "add a 0.5" silliness.
Next to a discussion about police riding unicorns, this is probably the 2nd best fun-but-pointless gaming board discussion I've seen for 2010. ;)
Think we could make a list? Rule is it has to get to the third page.
Quote from: Bloody Stupid Johnson;426836Or can't you???
Going the other way 1d6+3, rerolling any 1s gives an average value of exactly 7.
(all values possible on the d6: 2,3,4,5,6 = 20, /5 possible results = average value of 4)
If you do that then the only difference becomes the distribution, no change in average damage between the d6+3 and the 2d6 at all.
woooo smart!
Quote from: Cranewings;426947woooo smart!
Go me!! Though maybe its kinda cheating since it really turns the d6 into a d5.
Quote from: ggroy;426864Wonder who (in rpg gaming) pays attention to kurtosis and skewness.
I had to google those, but best use of weird distributions I can think of goes to Gary?
Whoever set up random encounter tables for D&D to use d8+d12 knew what they were doing: all the numbers from (IIRC) about 9 to 12 are equally likely, so you get a "truncated bell curve", a distribution that when you graph it looks like a hill with the top cut off. Good use of this since it makes all the "common" encounters equally likely.
But other than that, I don't know why someone would be deliberately trying to make a skewed distribution?? A mechanic like Tunnels and Trolls' "roll 2d6, doubles roll up" would I think give you a weird probability curve when drawn out (either a fat tail, or maybe a series a progressively smaller bulges like the spine of an iguana ?) but that's probably unintentional on the part of the designers.
To answer the original question as best I can:
Those who pointed out the importance of armor absorption are absolutely right. That needs to be nailed down in order to proceed.
Secondly, the typical amount of hit points of the target are also important. Reason: the more hit points the target has, the more individual hits it's going to take to kill them. (Duh.) That means, at some point, you're summing enough hits that the standard deviations of the sums start to look similar. And that means that the mean & standard deviation in # of hits to kill the opponent will be about the same.
I mean, if the opponent has 20 hp, you'd figure it'll take "about 3" hits to kill them. That means in one case you're rolling 6d6 (mean 21.5, sd 4.58), and in the other you're rolling 3d6+3X (mean 10.5+3X, sd 3.24). In relation to the range of results, these standard deviations are about 15% and 20%/
If the opponent has 40 hp, you're looking at "about 6" hits to kill. The standard deviations are then 6.48 and 4.58, respectively. While these are larger numbers, they're smaller in relation to the range of results--about 11% and 15%, respectively.
If you turn this around and look at this in terms of the mean and standard deviation in "# of hits to kill", you'll see that two methods basically converge as the target damage goes up.
Third, there's the question of how long you have to take out the opponent. If you're facing someone who has a high chance of killing you in one or two rounds, then you'd want a damage roll that's got at least a chance of doing the same to him, even if it offers a lower mean. So here, you'd probably go for the 2d6 because of the higher standard deviation. You don't care that it might dink him for 2-3 points; what you care about is that it can wallop him for 11 or 12 points.
Quote from: Doom;426716It's stunning how many people think all there is to a distribution is the mean.
Sorry. I mis-spoke. :o
I was looking at the distribution range and not the exact values. Naturally a linear addition of 3.5 cannot give a total distribution the same as the bell shape of 2d6 (even if you could add a half point). Basic mathematics.
With 2d6 you get 36 combinations that form a bell shape. With 1d6+something you get a simple linear shape. My point was that the "typical" roll for each would be similar.
2d6 is actually a wedge curve. Each number is 1/36th more likely than the number before it until you hit the mid point, and then each number is 1/36th less likely until you get to the final number.
That being said, which is better depends on what I am being asked to do. If I am expecting to fight Orc warriors and Goblins who only have 4 hit points, I'd rather do d6+4 or even a d6+3 damage. If my opponents have 8 hit points, then I would rather do a d6+4 (6/12 kill) than 2d6 (5/12 kill), and rather do 2d6 than d6+3 (4/12 kill). If my enemies are gnolls who have 11 hit points, I would rather do 2d6 than a d6+3 or even a d6+4. The d6+3 does half a point less on average than 2d6 and the d6+4 does half a point more. Furthermore, the 2d6 has a higher chance of doing an average amount of damage, but it also has a higher chance of doing extreme edge damage. If I am happier to roll an extreme high edge case than I am sad to roll an extreme low edge case (such as when the enemy has a large number of hit points), then I want the extra dice. If I am sadder to roll very low than I am happy to roll very high (such as when the enemy has very few hit points), then I want the extra fixed bonus.
By the way, if we go to 3d6, we could have the same average on 3d6 or 1d6+7. And then if the enemy had 11 hit points we seriously wouldn't care either way - it's a 50% chance to drop the enemy regardless. But if the enemy had 10 hit points we'd rather roll d6+7 (67% drop instead of 63%), and if the enemy had 12 hit points we'd rather roll 3d6 (38% drop instead of 33%).
-Frank
Frank, I think you've just convinced me that weapons should never do more than one die of damage.