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New Player Hates All The Dice


Ndreare

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Re: New Player Hates All The Dice

 

No you're not rolling fewer dice. You "rolled" two of them by setting them to 1 and 6 so your are still rolling 10 dice. This is the crux of our argument. You are not getting more predictabilty by reducing the number of dice rolled. Instead you are increasing predictability by setting a portion of the dice rolled to a predetermined result.

 

I don't understand why there would be a difference in predictability between Xd6 and Xd6+Y. While the end result numbers are different (rolling a 5, 3, 6 vs rolling 5, 3, 6, and adding 14), the shape of the bell curve remains the same. Doesn't that mean that the two are equally predictable because the distribution of probabilities (the shape of the curve) is the same?

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Re: New Player Hates All The Dice

 

I don't understand why there would be a difference in predictability between Xd6 and Xd6+Y. While the end result numbers are different (rolling a 5' date=' 3, 6 vs rolling 5, 3, 6, and adding 14), the shape of the bell curve remains the same. Doesn't that mean that the two are equally predictable because the distribution of probabilities (the shape of the curve) is the same?[/quote']

 

Yes, it does mean that. Xd6 and Xd6+Y have equal predictability because they have the same number of randomly determined DC. I don't think anyone has disputed this.

 

Here is the point that we are trying to make. Take a 10 DC attack. Assume two options 10d6 or 2d6+28. 2d6+28 is more predictable than 10d6 because you have predetermined 8DC out of the 10DC.

 

However if you compare a 2 DC attack to a 10DC attack, the 10DC attack will give you a more predictible result.

 

The concept that 2d6+28 is rolling fewer dice ignores the fact that you have, as Phil put it, set 4 dice to 1 and 4 dice to 6. 10 dice were still used. So 2d6+28 must still be consider rolling 10 dice.

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Re: New Player Hates All The Dice

 

Here is the point that we are trying to make. Take a 10 DC attack. Assume two options 10d6 or 2d6+28. 2d6+28 is more predictable than 10d6 because you have predetermined 8DC out of the 10DC.

SteveZilla understood what I was saying. Apparently you and Dust Raven didn't. I was trying to use "shorthand" to keep it simple. I'll try again:

 

a = the predictability of 2d6

b = the predictability of 2d6+28

c = the predictability of 10d6

 

Xd6 and Xd6+Y have equal predictability...

Here, you are saying a = b. Dust Raven said it also.

 

2d6+28 is more predictable than 10d6 because you have predetermined 8DC out of the 10DC.

Here you are saying b > c. Dust Raven said this also.

 

However if you compare a 2 DC attack to a 10DC attack, the 10DC attack will give you a more predictible result.

And here, you have said that a < c. Dust Raven has also said this.

 

So to put those three statements together, you and Dust Raven are saying that:

1) a = b

2) b > c

3) a < c

 

Clear now? Do you see the logical problem? Is it because you're using one definition of "predictable" in (2) and a different definition in (3)? That's my suspicion, but if you have some other rationale how these three statements can all be true, I'd be happy to hear it.

 

The concept that 2d6+28 is rolling fewer dice ignores the fact that you have, as Phil put it, set 4 dice to 1 and 4 dice to 6. 10 dice were still used. So 2d6+28 must still be consider rolling 10 dice.

What if I don't have any dice at all, and I just pick the number 35? Is that still considered "rolling 10 dice"? How's this for a more extreme example:

 

d) Fixed number 35 -- 100% predictable, no dice rolling involved. (And by "dice rolling" I mean actual rolling of dice.)

e) Fixed number 0 -- 100% predictable. No dice involved, even if you define multiples of 3.5 as "dice".

f) 10d6 actually rolled (clatter clunk clatter) -- Not predictable, could generate any number from 6 to 60, inclusive. The average result, 35, would occur only 7.27% of the time.

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Re: New Player Hates All The Dice

 

Relative deviance is important to HERO despite your protestations otherwise. A player uses relative deviance to determine whether or not to even attempt the attack (or at any rate should). If they know there is little chance that a given attack will push through damage because of the likely roll of that attack' date=' they will pick a different attack that is likely to push through damage. That though process is entirely dependant upon relative deviance.[/quote']

No. A player is interested in the probability of rolling an absolute number:

 

Player: "Wow! This guy is tough! He's got a DEF of 40! What is the likelihood of my being able to roll higher than 40 on my 10 DC attack? Hmmm... It's about 15%. That means I'll only do damage to him between 1/6 and 1/7 of the time. If it takes four damaging hits to put him down, that means it'll take about 26 phases. Can I last 26 of my phases in combat with this guy?"

 

Granted, most players won't be taking the math this far, but what matters is the absolute number of pips of effect that get past defenses. The number we add up on the dice is an absolute number. The defense we subtract is an absolute number. The final effect that gets past defenses is an absolute number. No player ever says:

 

"Wow! This guy is tough! His DEF is 14% higher than the average of my 10 DC attack! What is the likelihood of my being able to roll over 14% above the mean?"

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Re: New Player Hates All The Dice

 

Most players I know of don't put that much thought into it in the first place. They grab three dice and toss them and see if they hit. After that, they grab however many dice they need if they did hit.

 

If they actually put as much thought into the mechanics of the game, as opposed to just playing the game, as went into this thread, most of them would find another hobby.

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Re: New Player Hates All The Dice

 

SteveZilla understood what I was saying. Apparently you and Dust Raven didn't. I was trying to use "shorthand" to keep it simple. I'll try again:

 

a = the predictability of 2d6

b = the predictability of 2d6+28

c = the predictability of 10d6

 

 

Here, you are saying a = b. Dust Raven said it also.

 

 

Here you are saying b > c. Dust Raven said this also.

 

 

And here, you have said that a < c. Dust Raven has also said this.

 

So to put those three statements together, you and Dust Raven are saying that:

1) a = b

2) b > c

3) a < c

 

Clear now? Do you see the logical problem? Is it because you're using one definition of "predictable" in (2) and a different definition in (3)? That's my suspicion, but if you have some other rationale how these three statements can all be true, I'd be happy to hear it.

 

Yeah, this is the place where we are talking past one another.

 

Let me see if I can more clearly explain my position.

 

Xd6 and xd6+y have the same distribution curve except that xd6+y is shifted east on the axis by y. I think we all agree on this, and this is what I mean when I said xd6 and xd6+y have the same predictibilty (and I spoke poorly at that point; I should not have said predictibility but distribution).

 

The more dice you roll, the more likely that any two of them will add up to 7. Do I have your agreement with this statement? If so, then I think you can see that as the number of dice rolled increases the chances of having a mean value roll {the number of dice rolled time 3.5 (or the number of pairs of dice rolled times 7)} also increases. This is what Dust Raven and I mean by predictability.

 

Rolling just 2d6 is much more likely to have a relatively large variance from the average roll than 10d6 is likely to have. 10d6 can have large absolute variances but those variance will not have very often. It is more predictible because 68.2% of the rolls will be between 30 and 40 (roughly, I didn't go back and check StD for 10d6). When you substitute 8 set dice and only roll 2, you do infact make it more predictible than actually rolling 10 dice because now 68.2* will be between 33 and 37. But it is the change relative to the total that makes it predictible. Rolling 2d6 always provides a result that is with in plus or minus ~2 of the mean. But when that mean is 7 the difference is much more significant than when it is 35 and that is why we say 2d6 by itself is less predictible.

 

What if I don't have any dice at all, and I just pick the number 35? Is that still considered "rolling 10 dice"? How's this for a more extreme example:

 

d) Fixed number 35 -- 100% predictable, no dice rolling involved. (And by "dice rolling" I mean actual rolling of dice.)

e) Fixed number 0 -- 100% predictable. No dice involved, even if you define multiples of 3.5 as "dice".

f) 10d6 actually rolled (clatter clunk clatter) -- Not predictable, could generate any number from 6 to 60, inclusive. The average result, 35, would occur only 7.27% of the time.

 

Well, we generally don't deal with specific numbers in HERO, we generally deal with ranges. To steal an example from your next post, a typical range we would deal with is "greater than 40." Beyond that a full standard effect is still considered by me to be rolling 10 dice and yes, it would be a predictible result. 10d6 fully rolled is predictible. It will be between 30 and 40 68.2% of the time. It will be over 40 15.9% of the time.

 

No. A player is interested in the probability of rolling an absolute number:

 

Player: "Wow! This guy is tough! He's got a DEF of 40! What is the likelihood of my being able to roll higher than 40 on my 10 DC attack? Hmmm... It's about 15%. That means I'll only do damage to him between 1/6 and 1/7 of the time. If it takes four damaging hits to put him down, that means it'll take about 26 phases. Can I last 26 of my phases in combat with this guy?"

 

Granted, most players won't be taking the math this far, but what matters is the absolute number of pips of effect that get past defenses. The number we add up on the dice is an absolute number. The defense we subtract is an absolute number. The final effect that gets past defenses is an absolute number. No player ever says:

 

"Wow! This guy is tough! His DEF is 14% higher than the average of my 10 DC attack! What is the likelihood of my being able to roll over 14% above the mean?"

Here's where you contradict yourself. You say the player is interested in his ability to roll an absolute number and then immediately turn around and talk about his ability to roll within a range. The player will look at a fully rolled 10d6 and know they will push damage through, on average, once in every five attempts. Whereas the 2d6+28 player know for sure they never will.

 

You know predictible probable is a bad word for what we mean. All dice rolls of any size follow the same rules consistently over time. In that way they are all equally "predictable." Instead maybe the word I want is reliable. At any rate the point I am trying to make is that as dice rolled gets larger the standard deviation becomes less significant relative to the mean and you can become more assured that you will roll the average roll (after all what significance does a StD of 5 mean to an average of 35 when you need to roll over 40 to get damage through? You know you won't be doing much). Yes, larger absoulte variance become possible but they also become less likely.

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Re: New Player Hates All The Dice

 

Relative deviance is important to HERO despite your protestations otherwise. A player uses relative deviance to determine whether or not to even attempt the attack (or at any rate should). If they know there is little chance that a given attack will push through damage because of the likely roll of that attack' date=' they will pick a different attack that is likely to push through damage. That though process is entirely dependant upon relative deviance.[/quote']

Cool. So you want to attack me. Your mean damage is 10 Stun less than my PD. The Standard Deviation of your damage roll is 25% of the mean of your damage roll. Should you make the attack? If you do, how likely are you to do damage? If your statement is correct, I have given enough information for you to judge the probable results.

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Re: New Player Hates All The Dice

 

Xd6 and xd6+y have the same distribution curve except that xd6+y is shifted east on the axis by y. I think we all agree on this' date=' and this is what I mean when I said xd6 and xd6+y have the same predictibilty (and I spoke poorly at that point; I should not have said predictibility but distribution).[/quote']

Fine. They are equally predictable, meaning they have an equal chance of rolling near the means of their respective ranges. (However you chose to define "near")

 

The more dice you roll, the more likely that any two of them will add up to 7. Do I have your agreement with this statement?

I'm not sure what you mean by that statement. What do you mean by "any two of them"? Do you mean two individual dice picked at random will be more likely to add up to 7 if there are 10 dice total than if there are only two to choose from? That certainly isn't true. Two specific dice rolled (chosen randomly before or after the roll) will add up to 7 one sixth of the time. It doesn't matter how many additional dice you roll.

 

Or do you mean that the more dice you roll, the more likely you'll be able to find two of them that add to 7? That certainly is true, but it doesn't seem to have much to do with the discussion. It doesn't have much bearing on the total of all the dice rolled. If I roll 12 dice, I can almost certainly pick out two to add to any number I want between 2 and 12, but that won't tell me what the total is.

 

Rolling just 2d6 is much more likely to have a relatively large variance from the average roll than 10d6 is likely to have.

Large as a percentage of the mean, yes. Large as an absolute number, no. Are we in agreement on this?

 

10d6 can have large absolute variances but those variance will not have very often. It is more predictible because 68.2% of the rolls will be between 30 and 40 (roughly, I didn't go back and check StD for 10d6). When you substitute 8 set dice and only roll 2, you do infact make it more predictible than actually rolling 10 dice because now 68.2* will be between 33 and 37. But it is the change relative to the total that makes it predictible.

(empahsis mine) So 10d6 is more predictable, and 2d6 is more predictable? You chose a range of 30-40 (the middle 11 numbers). 68.2% of the rolls of 10d6 will be in that middle 11 numbers. With 2d6, 100% will be in the middle 11 numbers.

 

Rolling 2d6 always provides a result that is with in plus or minus ~2 of the mean.

Always? 2, 3, 4, 10, 11, and 12 happen a total of 1/3 of the time, and they aren't within 2 of the mean.

 

But when that mean is 7 the difference is much more significant than when it is 35 and that is why we say 2d6 by itself is less predictible.

Now you're saying that 2d6 is less predictable than 2d6+28! Pick one definition for "predictable" and stick with it. OK, nevermind. I understand what you are saying. That the percentage variance from the mean is smaller when you roll 2d6+28 than if you just roll 2d6. For example: The maximum on 2d6 is 12 - 171% of the mean. The maximum result on 2d6+28 is 40 - 114% of the mean. With 2d6, the result can vary by up to 71% of the mean. With 2d6+28 the result never varies more than 14%.

 

OK, I get that. I've acknowledged this in so many words earlier in the thread. And I assume (hope) that you acknowledge that the percent differences in the above cases represent an absolute difference of 5 in both cases, so the absolute variance is the same. That's what I meant by equally predictable.

 

I think we agree on these statistical facts, even if we can't come to an agreement on the definition of "predictable" or on the definition of "dice rolled."

 

My other claim is that the absolute numbers, not the percentages of the mean, are what matter in HERO. That seems to be something we disagree on:

 

Well, we generally don't deal with specific numbers in HERO, we generally deal with ranges.

Everything on every character sheet is a specific number! When you add up pips on the dice, you get a specific number. When you subtract defenses, that's a specific number. When you apply damage, that's a specific number. Yes, we also real with ranges occasionally, when we want to know if it's possible, or likely for an attack to be effective. But they are always ranges of specific numbers. We never deal with percentages of the mean, or ranges of percentages of the mean in HERO.

 

To steal an example from your next post, a typical range we would deal with is "greater than 40."

Yes, my point exactly. "Greater than 40" is a range of specific numbers. 40 is a single specific number. "Greater than 114% of the mean" is a relative range, nor a specific number range. It means completely different things with a 10 DC attack and a 6 DC attack, for example. If Captain Goodguy fires his 12d6 EB at the evil Doctor Defense with 40 DEF, he needs >40 to do damage. If Lieutenent Goodguy fires his 10d6 at Doctor Defense, he also needs >40 to do damage. They're both shooting for absolute numbers, not percentages of the mean. And if Private Goodguy only has 6d6 of EB, he won't be able to do damage at all, even if he rolls, 175% of the mean!

 

Beyond that a full standard effect is still considered by me to be rolling 10 dice and yes, it would be a predictible result. 10d6 fully rolled is predictible. It will be between 30 and 40 68.2% of the time. It will be over 40 15.9% of the time.

But the standard effect will be between 30 and 40 100% of the time. It will be over 40 0% of the time, hence it is more predictable.

 

Here's where you contradict yourself. You say the player is interested in his ability to roll an absolute number and then immediately turn around and talk about his ability to roll within a range.

A range of absolut numbers. As I said to Dust Raven earlier, the distinction isn't between single values and ranges, it's between absolute numbers and relative numbers.

 

The player will look at a fully rolled 10d6 and know they will push damage through, on average, once in every five attempts. Whereas the 2d6+28 player know for sure they never will.

Even though they're both capable of rolling 70% above the mean. In fact, the 2d8+28 guy will roll over 70% above the mean more often. But that doesn't mean anything in HERO, since the absolute number is what he needs to get through the defenses, not the percentage of the mean.

 

You know predictible probable is a bad word for what we mean. All dice rolls of any size follow the same rules consistently over time. In that way they are all equally "predictable." Instead maybe the word I want is reliable.

You can use any word you like as long as we're clear and consistant on the definition we're using.

 

At any rate the point I am trying to make is that as dice rolled gets larger the standard deviation becomes less significant relative to the mean and you can become more assured that you will roll the average roll (after all what significance does a StD of 5 mean to an average of 35 when you need to roll over 40 to get damage through? You know you won't be doing much). Yes, larger absoulte variance become possible but they also become less likely.

(Emphasis mine again) The relative variances become less likely, but the absolute variances become more likely, as illustrated in the chart I posted. And the more dice you roll, the less likely you are to roll the average value. I thought that was settled already.

 

Dice Avg Likelyhood of rolling Average
2d6   7  16.667%
4d6  14  11.265%
6d6  21  9.285%
8d6  28  8.094%
10d6 35  7.269%
12d6 42  6.654%

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Re: New Player Hates All The Dice

 

No. A player is interested in the probability of rolling an absolute number:

Incorrect. A player is interested in the probability of rolling an specific result or greater (for effect dice, it's a specific result or less for Skill and attack rolls). A specific result or greater (or less) represents a range of possibilities, not a single absolute result.

 

"Wow! This guy is tough! His DEF is 14% higher than the average of my 10 DC attack! What is the likelihood of my being able to roll over 14% above the mean?"

Though you have the terms wrong, this is exactly what a player who is interested in knowing the likelihood of doing damage to a particular target is wanting to know. The second thing a player will want to know is how much damage it likely to be done, another aspect of determing the probability of a range of numbers possible.

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Re: New Player Hates All The Dice

 

Yes, it does mean that. Xd6 and Xd6+Y have equal predictability because they have the same number of randomly determined DC. I don't think anyone has disputed this.

 

Here is the point that we are trying to make. Take a 10 DC attack. Assume two options 10d6 or 2d6+28. 2d6+28 is more predictable than 10d6 because you have predetermined 8DC out of the 10DC.

 

However if you compare a 2 DC attack to a 10DC attack, the 10DC attack will give you a more predictable result.

 

The concept that 2d6+28 is rolling fewer dice ignores the fact that you have, as Phil put it, set 4 dice to 1 and 4 dice to 6. 10 dice were still used. So 2d6+28 must still be consider rolling 10 dice.

 

I think we can leave DC calculations out of this discussion. Nobody is (AFAIK) taking the stance of 2d6+(8 * 3.5) ≠ 10d6 in terms of Damage Classes (all other things being equal). Damage Classes don't equally translate to numbers of dice in all instances. A 12 DC attack could be 20, 12, 6, or 4 dice, just to use Base Costs for certain powers.

 

Now, if 2d6 and 2d6+28 are equally predictable, that means that in terms of predictability, the +28 is meaningless. And if 2d6+28 is more predictable than 10d6, that means that 2d6 is also more predictable than 10d6.

 

My conclusions, drawn from only the information above:

 

  1. If we predetermine some of the dice being used, we are not rolling them any more -- they have become a static (fixed) element.
  2. Adding a static (fixed) number to a group of dice doesn’t change the predictability of that group of dice.
  3. Fewer dice used, regardless of a fixed number added to them, is more predictable than a greater number of dice.

 

Thus, saying that “it’s more predictable because some dice are predetermined†seems to be just a roundabout way of saying "it’s more predictable because fewer dice are being used in the roll".

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Re: New Player Hates All The Dice

 

I think we can leave DC calculations out of this discussion. Nobody is (AFAIK) taking the stance of 2d6+(8 * 3.5) ≠ 10d6 in terms of Damage Classes (all other things being equal). Damage Classes don't equally translate to numbers of dice in all instances. A 12 DC attack could be 20, 12, 6, or 4 dice, just to use Base Costs for certain powers.

 

Now, if 2d6 and 2d6+28 are equally predictable, that means that in terms of predictability, the +28 is meaningless. And if 2d6+28 is more predictable than 10d6, that means that 2d6 is also more predictable than 10d6.

 

My conclusions, drawn from only the information above:

 

  1. If we predetermine some of the dice being used, we are not rolling them any more -- they have become a static (fixed) element.
  2. Adding a static (fixed) number to a group of dice doesn’t change the predictability of that group of dice.
  3. Fewer dice used, regardless of a fixed number added to them, is more predictable than a greater number of dice.

 

Thus, saying that “it’s more predictable because some dice are predetermined†seems to be just a roundabout way of saying "it’s more predictable because fewer dice are being used in the roll".

 

No, no, no. You've gone all sideways on me. 2d6 is going to give a less predictible result than 10d6 will. We know, because of the rules of probabilty, normal distribution and the law of large numbers that 10d6 will, over time, present results much closer to the mean result than 2d6 will. It is, that extent, more predictible. If you change a portion of the 10d6 to a static element and roll the rest you will make it even more predictible.

 

The confusion you have is that 2d6 and 2d6+28 are 2DC and 10DC respectively (Assume an EB if you must). They do not have the same distribution curve or mean. If you define predictibility as the likely hood to roll close to mean, 2d6 will be more predictible because the possible variance is small relative to the mean.

 

The problem is that we never do your statement two. Instead of adding a number to dice, we change dice to a number.

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Re: New Player Hates All The Dice

 

Incorrect. A player is interested in the probability of rolling an specific result or greater (for effect dice' date=' it's a specific result or less for Skill and attack rolls). A specific result or greater (or less) represents a range of possibilities, not a single absolute result.[/quote']

Fine, but you're just quibbling with words. You may take me to mean "a range of absolute numbers". Is it so hard to understand the difference between an absolute result/number/range and a relavite result/number/range? That's the distiction I'm trying to make.

 

If the GM says, "The bad guy hits you for 114% of the mean," you have no idea what to do with this information. What you need is for the GM to say, "The bad guy hits you for 40 STUN." Then you know what to do: subtract your appropriate defense from 40 and apply the rest to your STUN, etc. "114% of the mean" is a relative result. "40 STUN" is an absolute result. 114% or more of the mean" is a relative range. "40 or more STUN" is an absolute range.

 

The absolutes are what matter in HERO (and AFAIK, every other game that uses dice, RPG or otherwise).

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Re: New Player Hates All The Dice

 

2d6 is going to give a less predictible result than 10d6 will. We know' date=' because of the rules of probabilty, normal distribution and the law of large numbers that 10d6 will, over time, present results much closer to the mean result than 2d6 will.[/quote']

That depends on what you mean by "closer to the mean". If you mean closer by percentage of the mean, then you're right. If you mean closer in terms of absolute difference, then that is not the case. The absolute difference from the mean will be much greater with 10d6 than with 2d6. In that sense, 10d6 is less predictable. And since absolute results are what matter in HERO, that's why Steve and I are saying that 10d6 is less predictable than 2d6.

 

And just to be clear, as an example if you roll 10d6 and get a result of 40, the percentage of the mean is 114% (or if you want to express it as a fraction, 8/7). The absolute difference is 5. "5 STUN" means something in HERO. The relative numbers "114%" and "8/7" do not come into play.

 

The confusion you have is that 2d6 and 2d6+28 are 2DC and 10DC respectively (Assume an EB if you must). They do not have the same distribution curve or mean. If you define predictibility as the likely hood to roll close to mean, 2d6 will be more predictible because the possible variance is small relative to the mean.

Now you've got this part backwards. In relative terms, 2d6 will be less predictable because results can vary by up to 71% of the mean. With 2d6+28, results can vary by only 14% of the mean. I assume you know this and just got it wrong when you typed it in. Steve and I (and formerly both you and Dust Raven) say that they are equally predictable because in absolute terms, they both vary by up to 5.

 

The problem is that we never do your statement two. Instead of adding a number to dice, we change dice to a number.

Really? Would you actually take out ten dice, set four of them to 2 and four of them to 5 and then roll the remaining two and then add them up? I certainly wouldn't. I'd just roll two dice, add them, and then add 28.

 

And BTW, we could also do a 10 DC attack by rolling 12d6-7, or 18d6-28. Whould you call these more predictable or less predictable than 10d6?

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Re: New Player Hates All The Dice

 

Well, since I as yet see no new thread ( :P ), here's a chart of the probability distributions of {2d6-7, 4d6-14, 6d6-21, 8d6-28, 10d6-35}. Take from it what you will.

 

(Click to see larger image)

nd6probdens3ak.th.png

 

Geez! Give me a minute. I'm at work here, okay? :)

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