New Player Hates All The Dice

[Silbeg]

To sum up...

 

Ok,

We can all agree on the following, I believe.

1. More dice means more range of possible results.
   
2. More dice also means that it is more likely that the results will be "near average" (within one standard deviation of the norm).

Phil has been using #1 to state that fewer dice means a more "predictable" result. I believe he is stating that this is partially due to the reduced range of possibilities, and to the precision to predict a specific value rolled.

 

Others have been using #2 to show that the more dice you use the more "predictable" the roll will be. More dice are more likely have an "average" roll with more dice. This doesn't mean you are more likely to roll a specific number, just that you are more likely to be "near average".

 

I believe that in the contexts of the two (separate) arguments, that both are correct, but that the base definition of what you are calling "predictable" is different.

[Conduit]

Re: To sum up...

 

Ok,

We can all agree on the following, I believe.

1. More dice means more range of possible results.
   
2. More dice also means that it is more likely that the results will be "near average" (within one standard deviation of the norm).

Phil has been using #1 to state that fewer dice means a more "predictable" result. I believe he is stating that this is partially due to the reduced range of possibilities, and to the precision to predict a specific value rolled.

 

Others have been using #2 to show that the more dice you use the more "predictable" the roll will be. More dice are more likely have an "average" roll with more dice. This doesn't mean you are more likely to roll a specific number, just that you are more likely to be "near average".

 

I believe that in the contexts of the two (separate) arguments, that both are correct, but that the base definition of what you are calling "predictable" is different.

 

You've hit the nail on the head. Phil is only concerned with absolute variance which means little to nothing in the world of probabilty. The more dice used the closer the average roll you will be and thus more predictable (no quotes needed).

 

See the following example using the formula provided by Phil for the standard deviation of Nd6 on page 10 of this thread. (Namely (35N/12)^0.5).

Nd6    Average Roll     Standard Deviation  Coefficient of Variation(StD/Mean)
1               3.5                   1.7                         48.8%
2               7.0                   2.4                         34.5%
3              10.5                   3.0                         28.2%
4              14.0                   3.4                         24.4%
5              17.5                   3.8                         21.8%
6              21.0                   4.1                         19.9%
7              24.5                   4.5                         18.4%
8              28.0                   4.8                         17.3%
9              31.5                   5.1                         16.3%
10             35.0                   5.4                         15.4%

So what exactly does the coefficient of variation mean? What it gives us is a way to compare standard deviations of different populations. In other words it is the ideal measure to compare the predictability of throws of different amounts of dice. As you can see, the CoV decreases as the number of dice thrown increases. This means that the standard deviation becomes less and less significant and therefore the throw more predictible.

 

A throw of dice has a perfectly normal distribution. Therefore we know that 68.2% of the throws will total within one standard deviation from the mean. What the CoV tells us is how much of a difference to that mean it will make. For 10d6, 68.2% of the time the throw will be 35 + or - 15.4%. While the absolute value of that 15.4% may be larger than the 48.8% on 1d6, it is more predictible because being off by 5 when you start at 35 is less significant than being off by 2 when you start at 3.5.

 

So, to be specific 10d6 is more than twice as predictible as 2d6.

[Basil]

Re: New Player Hates All The Dice

 

This thread certainly proves the old saying "a little learning is a dangerous thing." Speaking from what I learned in college, I can tell you, flat out, that the absolute difference (not "absolute deviance" which is unimportant) is what you need to look at in this situation.

 

HERO, as all gaming systems I know of, depends on an actual number, not a ratio between the number rolled and the predicted average (nor maximum nor minimum). Hence standard deviation/average, and other ratios, are of no importance. What's important is the probability of the numerical difference; that is, the probability of a linear difference, not a ratio "difference."

 

At least as far as predictability is concerned. The absolute results are only important once you have them. Never before.

But the probability of the absolute results can be determined before the roll is made. Which is what Phil and I are trying to do; I grant that you are, too, but you are (it seems) concerning yourself with the standard deviation/average, or "so-and-such close to the extreme," or "X% up/down from the lowest/highest." In those terms, the more dice the "pointier" the graph of probabilities is if all graphs are made the same size.

 

Before, what matters is weighing the probability of achieving a certain predictable range of numbers.

 

As for the elements of the Hero System you describe, they have nothing to do with probability, they have to do with actual numbers.

But you, and others, are changing the size of the "certain predictable range of numbers" with the change in the number of dice. I'm not, nor is Phil.

 

Look at it this way: Determine the chances of rolling 41 or more points of (potential) damage with 8 Damage Classes, doing it as:

8d6

6d6+7

4d6+14

2d6+21

28 pips

 

You will find that the probability decreases, and the predictability increases, with fewer dice.

 

It really is that simple. And it has nothing to do with standard deviations, SD/average, percentages of average, maximium, or minimum.

 

However, I do not think it likely those with a smattering of knowledge in statistics are going to understand the (only too common) error they are making, so I am not going to bother continuing to participate in this thread.

 

A little learning is a dangerous thing;

Drink deep, or else touch not, the Pierian spring.

[Conduit]

Re: New Player Hates All The Dice

 

 

But you, and others, are changing the size of the "certain predictable range of numbers" with the change in the number of dice. I'm not, nor is Phil.

 

Look at it this way: Determine the chances of rolling 41 or more points of (potential) damage with 8 Damage Classes, doing it as:

8d6

6d6+7

4d6+14

2d6+21

28 pips

 

You will find that the probability decreases, and the predictability increases, with fewer dice.

 

It really is that simple. And it has nothing to do with standard deviations, SD/average, percentages of average, maximium, or minimum.

 

However, I do not think it likely those with a smattering of knowledge in statistics are going to understand the (only too common) error they are making, so I am not going to bother continuing to participate in this thread.

 

A little learing is a dangerous thing;

Drink deep, or else touch not, the Pierian spring.

 

Here's the point you are not changing the number of dice rolled. You are mearly predefining the number rolled on them.

 

You are saying roll 8d6 and let the total of the first 6 equal 21 (the 2d6+21 method). This obviously increases the predictibilty of the result of rolling 8 dice because you have predetermined 6 of 8 results. This is a whole different matter than the predictibilty of 2d6 versus 8d6.

 

But you, and others, are changing the size of the "certain predictable range of numbers" with the change in the number of dice. I'm not, nor is Phil.

 

Actually you are. The mean of the 2d6+21 method is 28 and its Std Deviation is 2.4. This means that 68.2% of the rolls will be between 26 and 30 and 95% between 23 and 33. With the 8d6 method the mean remains 28 but 68.2% are between 23 and 33 and 95% are between 18 and 38. So you are changing the range of predictible number significantly, but you are not doing it by "rolling two dice" you are doing it by "rolling" 6 dice and always getting 21 and accepting a random result from the last 2 dice.

 

It remains a proven, mathmatical fact that the more dice you roll, the more predictable the result. Let me prove it to you.

 

DC	d6	+	StD	Average	StD as % Average
2	1	3.5	1.7	7	24.40%
4	2	7	2.4	14	17.25%
6	3	10.5	3.0	21	14.09%
8	4	14	3.4	28	12.20%
10	5	17.5	3.8	35	10.91%
12	6	21	4.2	42	9.96%
14	7	24.5	4.5	49	9.22%
16	8	28	4.8	56	8.63%
18	9	31.5	5.1	63	8.13%
20	10	35	5.4	70	7.72%

 

As you can see even with your method, the more dice you throw the more predictible the results.

[SteveZilla]

Re: New Player Hates All The Dice

 

You are always more likely to roll any specific number if you roll fewer dice because there are fewer numbers that are possible to roll.

 

I didn't say anything about a specific number. I picked the "top" of the bell curve in both examples. 'Top' being (possibly poorly) defined as that part of the curve where the lower dice method produces greater individual odds for those results. Outside of my selected range, the lower dice method had lesser chance for each result.

 

I also thought that was the crux of what PhilFleischmann was saying -- that more dice are more unpredictable (IMUO 'unpredictable' means it is easier/more likely to roll a larger distance from the 'peak' of the bell). Note: IMUO = In My Uneducated Opinion.

 

What some of us are saying Phil is wrong about is how he is calculating the probability (assuming that's what he's been trying to say' date=' I'm not sure now). The probability of rolling dice is not linear, so it can not be calculated that way.[/quote']

 

I'm not sure what you mean by your last sentence. Could you explain further, possibly by illustrating with an example?

[SteveZilla]

Re: New Player Hates All The Dice

 

It's no more blasphemous than the 3d6 + (N x 3.5) method. I'd even say it's less so.

 

Actually, that isn't blasphemous now. In 5re, p 104, doing a partial standard effect on a power is given as a GM's option.

[prestidigitator]

Re: New Player Hates All The Dice

 

What the heck does, "predictability," mean anyway? It's not something we can really put an objective value on in the system. It is an aesthetic value that different people are going to have different opinions on. If you mean the probability that you will do any damage to a target, I have already shown that more or less dice (with Standard Effect used to make up the difference in means) are going to be effective depending on the amount of defense present.

 

What is a measurable and invariable system effect is that, "the roll with more dice is always going to average at least the same amount (and usually more) of damage against targets with a given amount of defense."

 

If we want to argue over touchy-feely stuff, why don't we argue over whether we should charge more for players to roll with low-contrast dice, or in a box where no one else can actually see the roll.

[David Blue]

Re: New Player Hates All The Dice

 

I must confess I am at a loss as to why this discussion has aroused such heat. We're talking about statistics! These are simple mathematical facts. There's no subjectivity or opinion involved here. We're not talking about politics or aethetics. What emotional stake do people have in this?

I can only speak for myself on that.

 

I sympathise with the new player who hates all the dice. I think the game plays better and faster with less dice-rolling, pip counting, multiplication, division, addition and subtraction. Less, not none but less, is desirable.

 

I think that Champions creates many perverse incentives, including one to clog up play with dice-rolling.

 

A "bad" player, from my point of view, benefits by default from increased average Stun totals and greater variability of the kind that punches more damage through defenses. A "good" player, from my point of view, one who wants less dice-rolling, is penalised twice, by default, through less average damage and more of the kind of predictability that leads to not putting damage through respectable defences in serious fights.

 

If everybody follows the incentives built into the game, play slows to what seems to me to be an unpleasant crawl. What's good for the individual is not good for the group.

 

For best outcomes for everyone, from my point of view, the gamemaster should see to it that "good" players are at least not penalised.

 

I like to see the following things acknowledged:

 

1) Damage classes are not equal in value, only in cost. In the general case, a damage class consisting of one pip of normal Body and three pips of Stun is inferior to a damage class consisting of 1d6 normal damage, with the double gain of 0.5 more Stun on average and greater variability.

 

2) The claim that with Standard Effect the player gains the benefit of predictability in return for the penalty of less damage is bogus. Less average damage is a penalty, and in the general case less variability of the kind that punches damage through normal, respectable defenses is an additional penalty.

 

3) The claim that the player with Standard Effect gains by never rolling below average is bogus. Rather, the "good" player who takes Standard Effect simply for what I see as the "right" reasons - less dice-rolling, faster and simpler play, which benefits everyone - is penalised by always rolling below average. And as the dice mount up, quite a bit below average.

 

4) In team fights against "boss villains" with high defenses, the penalty of greater predictability of the kind that in the general case leads to not punching damage through defenses is high, and can even render the player character nearly useless.

 

5) Therefore, if you regard with genuine sympathy the desire of the new player to play with less dice, if you want not to penalise them, and if you want an incentive structure in your game that favours or at least does not penalise faster and simpler play with less dice, then just telling the new player to use Standard Effect does not cut it.

 

Nobody seems to be arguing against these positions at the moment, so I'm placidly watching the artillery fire go back and forth.

[Conduit]

Re: New Player Hates All The Dice

 

I can only speak for myself on that.

 

I sympathise with the new player who hates all the dice. I think the game plays better and faster with less dice-rolling, pip counting, multiplication, division, addition and subtraction. Less, not none but less, is desirable.

 

I think that Champions creates many perverse incentives, including one to clog up play with dice-rolling.

 

A "bad" player, from my point of view, benefits by default from increased average Stun totals and greater variability of the kind that punches more damage through defenses. A "good" player, from my point of view, one who wants less dice-rolling, is penalised twice, by default, through less average damage and more of the kind of predictability that leads to not putting damage through respectable defences in serious fights.

 

If everybody follows the incentives built into the game, play slows to what seems to me to be an unpleasant crawl. What's good for the individual is not good for the group.

 

For best outcomes for everyone, from my point of view, the gamemaster should see to it that "good" players are at least not penalised.

 

I like to see the following things acknowledged:

 

1) Damage classes are not equal in value, only in cost. In the general case, a damage class consisting of one pip of normal Body and three pips of Stun is inferior to a damage class consisting of 1d6 normal damage, with the double gain of 0.5 more Stun on average and greater variability.

 

2) The claim that with Standard Effect the player gains the benefit of predictability in return for the penalty of less damage is bogus. Less average damage is a penalty, and in the general case less variability of the kind that punches damage through normal, respectable defenses is an additional penalty.

 

3) The claim that the player with Standard Effect gains by never rolling below average is bogus. Rather, the "good" player who takes Standard Effect simply for what I see as the "right" reasons - less dice-rolling, faster and simpler play, which benefits everyone - is penalised by always rolling below average. And as the dice mount up, quite a bit below average.

 

4) In team fights against "boss villains" with high defenses, the penalty of greater predictability of the kind that in the general case leads to not punching damage through defenses is high, and can even render the player character nearly useless.

 

5) Therefore, if you regard with genuine sympathy the desire of the new player to play with less dice, if you want not to penalise them, and if you want an incentive structure in your game that favours or at least does not penalise faster and simpler play with less dice, then just telling the new player to use Standard Effect does not cut it.

 

Nobody seems to be arguing against these positions at the moment, so I'm placidly watching the artillery fire go back and forth.

 

If you want to add heat, this is the way to do it. Using terms such as good players and bad players, even in quotes, is periously close to flaming. Now, it's your opinion that the game is better when less dice are used and that's fine. My group just loves grabbing two fist full of dice and letting them fly. Neither of us are wrong.

 

So the question is how does your group find a satisfactory way of rolling less dice? I think any of the methods discribed will work for your group, if everyone in the group uses them and the GM adjusts NPC defenses accordingly. Otherwise, Standard Effect and Partial Standard Effect (xd6+y) just never seem to match up to the full dice roll.

[Dust Raven]

Re: New Player Hates All The Dice

 

But you, and others, are changing the size of the "certain predictable range of numbers" with the change in the number of dice. I'm not, nor is Phil.

 

Look at it this way: Determine the chances of rolling 41 or more points of (potential) damage with 8 Damage Classes, doing it as:

8d6

6d6+7

4d6+14

2d6+21

28 pips

 

You will find that the probability decreases, and the predictability increases, with fewer dice.

 

It really is that simple. And it has nothing to do with standard deviations, SD/average, percentages of average, maximium, or minimum.

 

I agree. I stopped agruing this point long ago, once I realized this is what Phil was talking about. It was his statements that the predictability was dependant solely upon the number of dice rather than predetermining the value of a number of additional "dice" which were involved but not actually being rolled.

[Dust Raven]

Re: New Player Hates All The Dice

 

I didn't say anything about a specific number. I picked the "top" of the bell curve in both examples. 'Top' being (possibly poorly) defined as that part of the curve where the lower dice method produces greater individual odds for those results. Outside of my selected range, the lower dice method had lesser chance for each result.

 

I also thought that was the crux of what PhilFleischmann was saying -- that more dice are more unpredictable (IMUO 'unpredictable' means it is easier/more likely to roll a larger distance from the 'peak' of the bell). Note: IMUO = In My Uneducated Opinion.

The reason I disagree with this perspective as being a valid assessment of the predictability is that the top of the bell curve is representitive of single value, i.e. a specific number.

 

I'm not sure what you mean by your last sentence. Could you explain further, possibly by illustrating with an example?

 

I'm not sure exactly how to explain it any further really. I suppose you could look at it a bit more abstractly to start. A roll of 1d6 will yeild any result from 1 to 6, a range of 6 values, with an equal chance of getting any of those values. These 6 values represent all of (100%) of the possible results of rolling 1d6. If you roll 1d6 three times and total the results, you'll get a result ranging from 3 to 18, a range of 16 values. The difference is that you don't have an equal chance of getting each value from 3 to 18. Most likely you'll get a result somewhere in the vicinity of 10.5. If you try to assess the predictability of these rolls and compare them by looking at the chance of rolling specific number range (say a set of 6 numbers centered on the average), it looks like 1d6 is 100% predictable because you will always get such a number. With a roll of 3d6, you only have a 67.6% chance of rolling a value within that range of 6 numbers (any value from 8 to 13). This is pointless because you might as well just look for a specific number. 1d6 has a 16.7% chance of rolling a 4, a number withing .5 of the average, and 3d6 has only a 12.5% chance of rolling an 11, also a number within .5 of the average. The problem is that these probabilities aren't representitive of all the results. You also have a 16.7% chance of rolling a 1 or a 2 or a 6 on 1d6, but you don't have a 12.5% chance of rolling a 3, or an 8 or a 15 on 3d6. The chance of rolling any of those numbers is less than 12.5%.

 

Going back to specific, linear, sets of numbers, let's take a set of 3 numbers centered on the mean of the 1d6 roll, 2, 3 and 4 (not exactly centered, but since you have an equal chance of any number, it makes no difference which we choose). The chance of rolling a 2, a 3 or a 4 on a single roll is 50%. Take that 50% and look at how many numbers in the 3d6 roll fall within that range. You'll find 9, 10, 11 and 12 fall within 50% (48.15% actually, but close enough). If you look at this linerarly, it appears that 1d6 is more predictable because there are only 3 values in the set you have a 50% chance of rolling where the 3d6 roll has 4. However, the calculations do not end here. You need to compare these values to the number of possibilities. You'll find that the 3 values of the 1d6 roll make up 50% of the possible results, but the 4 values of the 3d6 roll make up a tiny 25% of the possible results. Unlike a 1d6 roll, half of your rolls will only represent one fourth of the possible results, making the roll of 3d6 more predictable.

 

Of course, this is really nothing more than a long winded proof of the law of averages, which just states the more dice your roll, the more predictable the result will be.

[Dust Raven]

Re: New Player Hates All The Dice

 

I like to see the following things acknowledged:

 

1) Damage classes are not equal in value, only in cost. In the general case, a damage class consisting of one pip of normal Body and three pips of Stun is inferior to a damage class consisting of 1d6 normal damage, with the double gain of 0.5 more Stun on average and greater variability.

 

2) The claim that with Standard Effect the player gains the benefit of predictability in return for the penalty of less damage is bogus. Less average damage is a penalty, and in the general case less variability of the kind that punches damage through normal, respectable defenses is an additional penalty.

 

3) The claim that the player with Standard Effect gains by never rolling below average is bogus. Rather, the "good" player who takes Standard Effect simply for what I see as the "right" reasons - less dice-rolling, faster and simpler play, which benefits everyone - is penalised by always rolling below average. And as the dice mount up, quite a bit below average.

 

4) In team fights against "boss villains" with high defenses, the penalty of greater predictability of the kind that in the general case leads to not punching damage through defenses is high, and can even render the player character nearly useless.

 

5) Therefore, if you regard with genuine sympathy the desire of the new player to play with less dice, if you want not to penalise them, and if you want an incentive structure in your game that favours or at least does not penalise faster and simpler play with less dice, then just telling the new player to use Standard Effect does not cut it.

 

Nobody seems to be arguing against these positions at the moment, so I'm placidly watching the artillery fire go back and forth.

 

Consinder them acknowledged.

 

I really couldn't agree more. I've said before (on this thread I think) that Standard Effect, even if placed at 3.5 instead of 3 per die, is a bad deal unless the attack is NND. The more DEF the target has versus the attack, the more useful a completely randomly roll is, at least over time. Sure, if you have an 8 DC attack SE 28 points (3.5 per die) and the target has a DEF of 20, you'll know you'll bet 8 points through every time. If you randomly roll, you sometimes get less than 8 and sometimes more, but in the sometimes more you'll also roll enough to Stun the target, something that would be impossible with only 8 points of effect (assuming the target has a CON of 8 or higher, which I think if a fair assumption). Also, if you total the damage past defenses for every roll over the course of many attacks, the average amount that gets past defenses will be higher than 8 (even taking into account those roll that fall under 20).

 

As far as using SE as a possible solution to this player's problem with rolling dice, I do recomend against it (I specifically suggested using NNDs and AVLDs, which use less dice but still have high effective DCs). But if rolling less dice is really that important to the player, to the point where the game is that much less fun to roll all those dice, it may be that being less effective because of using SE is insignificent by comparison.

[Ndreare]

Re: New Player Hates All The Dice

 

Well here is that latest update. Since I posted we have had a chance to play some more and she is coming around. She still does not like having all the dice, but we have worked around that. Now she is starting to see the game in a better light. Her husband is loving the game and I know he will be playing more.

[David Blue]

Re: New Player Hates All The Dice

 

Well here is that latest update. Since I posted we have had a chance to play some more and she is coming around. She still does not like having all the dice' date=' but we have worked around that. Now she is starting to see the game in a better light. Her husband is loving the game and I know he will be playing more.[/quote']Woo hoo! That's what matters.

[SteveZilla]

Re: New Player Hates All The Dice

 

Well here is that latest update. Since I posted we have had a chance to play some more and she is coming around. She still does not like having all the dice' date=' but we have worked around that. Now she is starting to see the game in a better light. Her husband is loving the game and I know he will be playing more.[/quote']

 

Cool! I had a thought. If counting the dice twice using two different methods (Body & Stun) is difficult for her, here is a suggestion:

 

Use dice with pips instead of numbers, (like black dice with white pips), and color a single pip in with red on the 2, 3, 4, and 5 faces, and color two pips red on the 6 face. Now, there is a visible reminder of each way of counting the dice.

[PhilFleischmann]

Re: New Player Hates All The Dice

 

I mean range of of percentages of the mean. This is what determines the predictability of greater numbers of dice being rolled. It's a really simple concept that has been more than clear many times.

Well, you've said it many times, but you've never explained what it means. You seem to be saying that the probability of rolling a certain range of percentages "determines" the probability of rolling a certain range of numbers. This makes no sense to me. The number and the percentage are just different mathematical ways of describing results. Neither "determines" the other. It's sort of like saying the percentage of people who get the flu determines the number of people who get the flu.

 

The chart you made proves nothing. You are comparing identical damage classes, with the only difference being that some of the dice involve have a preset result.

Of course I'm comparing identical damage classes! That's the whole point of the thread! The question was, "How can I have a 12 DC attack but not have to roll so many dice?" What would be the point of comparing two attacks with different damage classes? Don't we already know how those compare?

 

That is not the same as rolling fewer dice.

Yes, it is. If I roll 10 dice, them I'm rolling 10 dice. If I set aside two of those dice and set them to 1 and 6, and then roll 8 dice. I'm rolling fewer dice. 8 dice is fewer than 10 dice. More dice are not being rolled, therefore fewer dice are being rolled.

 

The table you provided does not show the difference in the probability between 6d6 and 4d6. It shows the difference between 6d6 (6 DC) and 4d6+7 (6 DC with 2 of the DC predetermined). .... You are right that adding any fixed number does not change the probability curve,

Do you see how you've just contradicted yourself here? I'm showing the difference between 6d6 and 4d6. If you add 7 to the 4d6, the curve is the same. The predictability is the same. The average on 4d6 is 14. The average on 4d6+7 is 14+7.

 

but you are wrong in your assumption that the probability curve of more dice demonstrates a less predictable result than the probability curve of less dice.

O don't see how you can read my chart correctly and still make that statement. That middle range of values is clearly more likely on 4d6 than it is on 6d6.

 

You are not just wrong, you are just confusing yourself even more by only adding your fixed result to only one side of your examples. Try the table of yours again but ad 7 to both the 4d6 and the 6d6 and take a look. You aren't providing fair comparisons.

Why add 7? Why not add 0 to both sides? How you you imagine adding a fixed number changes the probability? I've looked at the chart many different ways, no matter what fixed number I add to both sides, 6d6 still produces fewer average results than 4d6.

 

Your chart does no such thing. Do you even know what your own chart shows?

Yes, I do. It shows that average results are more likely with 4d6 than with 6d6.

 

As to your question regarding the predictability of 2d6 versus 2d6+28, mathematically they are equally predictable. In both cases you are rolling only 2d6. If you are intending this as a comparison of 2 DCs and 10 DCs, then there is nothing to compare.

Here you are agreeing with me that 2d6 (a) and 2d6+28 ( are equally predictable. You also seem to agree with me now that 2d6+28 is more predictable than 10d6 ©. But you still seem to be saying that 2d6 is less predictable than 10d6. Check your logic:

 

a = b

b > c

a < c

 

I think part of the confusion here is that you're using an inconsistent definition of "predictable". We need to pick one definition and stick with it. The one I have been using this whole time is the one that is useful in HERO - the one that deals with absolute numbers.

 

It is wrong because you are not taking into account the relative deviance of the mean, but instead taking an absolute deviance.

I don't take into account the relative deviance, because it is irrelevent to the HERO System.

[PhilFleischmann]

Re: To sum up...

 

Ok,

We can all agree on the following, I believe.

1. More dice means more range of possible results.
   
2. More dice also means that it is more likely that the results will be "near average" (within one standard deviation of the norm).

No. I, for one, do not agree with #2. And when you define "near average" as "within one standard deviation", then no one who knows what standard deviation means will agree with #2. For any normal distribution curve, the standard deviation will always include about 68.2% of the results. In other words, if you roll 3d6, 68.2% of the results will be within one standard deviation of the mean. If you roll 10d6, 68.2% of the results will be within one standard deviation of the mean. If you roll 20d6, 68.2% of the results will be within one standard deviation of the mean. (Because we're dealing with dice rolling discrete numbers, there will be "round off" variances from this figure.)

 

Others have been using #2 to show that the more dice you use the more "predictable" the roll will be. More dice are more likely have an "average" roll with more dice. This doesn't mean you are more likely to roll a specific number, just that you are more likely to be "near average".

It depends on what you mean by "near average":

 

a) If you mean "within a standard deviation" or "within half a standard deviation" or "within two srandard deviations" or "within any specific multiple or fraction of a standard deviation," then any number of dice will be equally "predictable."

 

If you mean "within a certain percentage of the mean" then, yes, more dice will be more "predictable." You are more likely to roll within 10% of the mean with 12d6 than with 6d6.

 

c) If you mean "within a certain specific distance from the mean", then no, more dice are less "predictable." You are more likely to roll within 5 of the mean on 6d6 than on 12d6. (Note that I said "within 5" not "within 5%".) In other words, the range 16-26 is more likely on 6d6, than the range 37-47 is on 12d6. (both are ranges of 11 numbers centered on the average.)

 

I believe that in the contexts of the two (separate) arguments, that both are correct, but that the base definition of what you are calling "predictable" is different.

Absolutely right! The definition I've been using for "predictable" is ©. That's the one that matters in HERO.

[PhilFleischmann]

Re: To sum up...

 

Phil is only concerned with absolute variance which means little to nothing in the world of probabilty.

Actually it means a good deal in the world of probability, but we don't have to argue that. The only thing that I'm concerned with here is that absolute variance is the only thing that matters in the HERO System (and as Basil mentions, just about every other game system). Relative variance means nothing in any game I've ever played.

 

Which does your GM tell you:

"The bad guy blasts you for 45 STUN."

or

"The bad guy blasts you for 29% more STUN than the mean."

?

 

The more dice used the closer the average roll you will be and thus more predictable (no quotes needed).

Like I said in the last post, it depends on your definition of "predictable". If we use the HERO-relevent definition, that statement is false. Is it too much to ask that we use the HERO-relevent definition?

 

So what exactly does the coefficient of variation mean?

It means nothing in the world of HERO.

 

So, to be specific 10d6 is more than twice as predictible as 2d6.

How much more predictable is it than 0d6?

[prestidigitator]

Re: To sum up...

 

No. I' date=' for one, do not agree with #2. And when you define "near average" as "within one standard deviation", then no one who knows what standard deviation means will agree with #2. For any normal distribution curve, the standard deviation will always include about 68.2% of the results. In other words, if you roll 3d6, 68.2% of the results will be within one standard deviation of the mean. If you roll 10d6, 68.2% of the results will be within one standard deviation of the mean. If you roll 20d6, 68.2% of the results will be within one standard deviation of the mean. (Because we're dealing with dice rolling discrete numbers, there will be "round off" variances from this figure.)[/quote']

Roughly, yes. Not that it really matters here (because we are talking about the sum of a significant number of random variables), but it is more a function of the Central Limit Theorem than the definition of the standard deviation: no matter the distribution in question, if you add together many random variables with that distribution, the overall distribution (of the sum) approaches a normal distribution (the more random variables, the closer to a normal distribution it becomes). If we talk about the distribution of a single random variable, what you say is not necessarily true (for example, only 57.7...% of a continuous flat distribution is within one standard deviation of the mean). For that matter, we could easily come up with a distribution for which 0% or 100% (depending upon the definition of, "within" ) falls within one standard deviation of the mean (consider a single d2).

[PhilFleischmann]

Re: To sum up...

 

Not that it really matters here (because we are talking about the sum of a significant number of random variables)' date=' but it is more a function of the Central Limit Theorem than the definition of the standard deviation:[/quote']

I didn't say it was because of the "definition" of standard deviation, just that that's the result for a normal distribution curve.

 

If we talk about the distribution of a single random variable, what you say is not necessarily true (for example, only 57.7...% of a continuous flat distribution is within one standard deviation of the mean).

But I wasn't talking about a continuous flat distribution. I specifically said "For any normal distribution curve". A "normal distribution curve" is a specific statistical "shape" - the bell curve that we all know and love. 1d6 doesn't produce it. For Nd6 (N>2), a normal curve is what you get. Disregarding the anomalies caused by the discrete values of dice rolls, you get the 68.2% that I said. We are talking about dice rolls here, right?

[prestidigitator]

Re: To sum up...

 

I didn't say it was because of the "definition" of standard deviation, just that that's the result for a normal distribution curve.

 

But I wasn't talking about a continuous flat distribution. I specifically said "For any normal distribution curve".

Oops. Sorry about that. I missed the one word. It's true that our rolls aren't normal distributions, though (each die is a discrete flat distribution; if it isn't weighted, at least ); they only approach a normal distribution as we add more dice. Once we get above 3d6 it's probably not a very significant difference, however. Like I said, it doesn't matter all that much.

[Ndreare]

Re: New Player Hates All The Dice

 

Cool! I had a thought. If counting the dice twice using two different methods (Body & Stun) is difficult for her, here is a suggestion:

 

Use dice with pips instead of numbers, (like black dice with white pips), and color a single pip in with red on the 2, 3, 4, and 5 faces, and color two pips red on the 6 face. Now, there is a visible reminder of each way of counting the dice.

 

I like that idea, it is easy and we have dozens of those dice.

[Conduit]

Re: New Player Hates All The Dice

 

Yes, it is. If I roll 10 dice, them I'm rolling 10 dice. If I set aside two of those dice and set them to 1 and 6, and then roll 8 dice. I'm rolling fewer dice. 8 dice is fewer than 10 dice. More dice are not being rolled, therefore fewer dice are being rolled.

 

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.

 

Here you are agreeing with me that 2d6 (a) and 2d6+28 ( are equally predictable. You also seem to agree with me now that 2d6+28 is more predictable than 10d6 ©. But you still seem to be saying that 2d6 is less predictable than 10d6. Check your logic:

 

a = b

b > c

a < c

 

a does not equal b. A is 2 DC while b is 10. Therefore b represents more dice than a. Yes, b is more predictable than c but that is because b is c just with some dice set to predetermined results.

 

I think part of the confusion here is that you're using an inconsistent definition of "predictable". We need to pick one definition and stick with it. The one I have been using this whole time is the one that is useful in HERO - the one that deals with absolute numbers.

 

I don't take into account the relative deviance, because it is irrelevent to the HERO System.

 

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, they will pick a different attack that is likely to push through damage. That though process is entirely dependant upon relative deviance.

[Conduit]

Re: To sum up...

 

Actually it means a good deal in the world of probability, but we don't have to argue that. The only thing that I'm concerned with here is that absolute variance is the only thing that matters in the HERO System (and as Basil mentions, just about every other game system). Relative variance means nothing in any game I've ever played.

 

Which does your GM tell you:

"The bad guy blasts you for 45 STUN."

or

"The bad guy blasts you for 29% more STUN than the mean."

?

 

At this time I would like to point out that the statement you intend for me to pick "45 STUN" is not a statement of absolute variance. It is a statement of result. A statement of absolute variance would be "hits you for 10 more than the mean" which obviously no one says. Why? Because noone care a lick for probability after the event occurs. Probabilty is useful in decision making. Once the decision making is done we deal with reality.

 

Like I said in the last post, it depends on your definition of "predictable". If we use the HERO-relevent definition, that statement is false. Is it too much to ask that we use the HERO-relevent definition?

 

Predictible means the same thing whether we are talking about HERO or the chance to draw an inside straight. Your attempt to redefine the word to win the argument is just a logical fallicy.

[Dust Raven]

Re: New Player Hates All The Dice

 

Well' date=' you've said it many times, but you've never explained what it means. You seem to be saying that the probability of rolling a certain range of percentages "determines" the probability of rolling a certain range of numbers. This makes no sense to me. The number and the percentage are just different mathematical ways of describing results. Neither "determines" the other. It's sort of like saying the percentage of people who get the flu determines the number of people who get the flu.[/quote']

It doesn't have to make sense to you for it to be true. You are otherwise correct about what I "seem" to be saying. In any case, it's not like saying the percentage of people (out of all people) who get the flue determine the number of people likely to get the flu, assuming identical or nearly identical circumstances.

 

Yes, it is. If I roll 10 dice, them I'm rolling 10 dice. If I set aside two of those dice and set them to 1 and 6, and then roll 8 dice. I'm rolling fewer dice. 8 dice is fewer than 10 dice. More dice are not being rolled, therefore fewer dice are being rolled.

I think Conduit put this best when he said that you are rolling the same dice, you just already know what two of the results will be.

 

Do you see how you've just contradicted yourself here? I'm showing the difference between 6d6 and 4d6. If you add 7 to the 4d6, the curve is the same. The predictability is the same. The average on 4d6 is 14. The average on 4d6+7 is 14+7.

I have not contracticted myself at all. You are in fact showing the difference between 6d6 and 4d6+7, NOT 6d6 and 4d6.

 

O don't see how you can read my chart correctly and still make that statement. That middle range of values is clearly more likely on 4d6 than it is on 6d6.

Because you don't have the probability range of 4d6 on your chart, you have the probability range for 4d6+7, which is the same as rolling 6d6 with two of the dice's resuls already determined (any two number adding up to 7).

 

Why add 7? Why not add 0 to both sides? How you you imagine adding a fixed number changes the probability? I've looked at the chart many different ways, no matter what fixed number I add to both sides, 6d6 still produces fewer average results than 4d6.

The trick is to add the number to both sides, which you did not do in your chart. You did not present a chart with 4d6+0 vs 6d6+0, or any common number adding to both sides.

 

Yes, I do. It shows that average results are more likely with 4d6 than with 6d6.

No it doesn't. It shows that if you determine what 2 of the 6 dice being rolled are, your end results will be more predictable, which is self evident. You are just persisting in calling it something it's not.

 

Here you are agreeing with me that 2d6 (a) and 2d6+28 ( are equally predictable. You also seem to agree with me now that 2d6+28 is more predictable than 10d6 ©. But you still seem to be saying that 2d6 is less predictable than 10d6. Check your logic:

 

a = b

b > c

a < c

Okay, let's check. But while checking, let's check correctly:

2d6 (2 DC) = a

2d6+28 (10 DC) = b

10d6 (10d6) = c

 

a does not equal b, but they have the same probability curve

b equals c, and b has a more precitable probability curve

a does not equal c, nor does it have the same probability curve.

 

Keep in mind that each element we are comparing here has two factors to consider, it's DC value measured by the Hero System, and the statistical probability determined by the dice randomly rolled. And keep in mind that term: randomly rolled. In the example of 2d6+28, you technically are rolling 10d6, but only 2d6 of that is randomly rolled.

 

I think part of the confusion here is that you're using an inconsistent definition of "predictable". We need to pick one definition and stick with it. The one I have been using this whole time is the one that is useful in HERO - the one that deals with absolute numbers.

I don't see how absolute numbers has anything to do with predictability or probability. Absolute numbers is what you work with after you have determined the result of some random event. Predictability and probability are things you take into account before you have a result so you know the likely hood of the results possible.

 

I don't take into account the relative deviance, because it is irrelevent to the HERO System.

It is not irrelevant, and is actually of great importance ot any game of chance. Perhaps you personally see no value in knowing the likelihood of success or failure over a single roll or continuous rolls, but many players do. It seems you do see value in it though, but refuse acknowledge the mathematical facts surrounding it.

 

In any case, I'm pretty much done with this thread derailment. I (and others) have tried to tell you something you apparently simply didn't know and you have refused to listen to it.