5d6 Hero

[Gary]

Interestingly enough, if you use more than 3d6 on to hit rolls, it doesn't really affect to hit probabilities that much assuming you adjust the target number accordingly. The probability distribution for 3d6 is:

 

3	0.5%
4	1.9%
5	4.6%
6	9.3%
7	16.2%
8	25.9%
9	37.5%
10	50.0%
11	62.5%
12	74.1%
13	83.8%
14	90.7%
15	95.4%
16	98.1%
17	99.5%
18	100.0%

 

The probability distribution for 5d6 is:

 

5	0.0%
6	0.1%
7	0.3%
8	0.7%
9	1.6%
10	3.2%
11	5.9%
12	9.8%
13	15.2%
14	22.1%
15	30.5%
16	40.0%
17	50.0%
18	60.0%
19	69.5%
20	77.9%
21	84.8%
22	90.2%
23	94.1%
24	96.8%
25	98.4%
26	99.3%
27	99.7%
28	99.9%
29	100.0%
30	100.0%

 

If you set the target number at 18, then here are the to hit probabilities with each difference in CV:

 

3d6	5d6
-5	9.3%	15.2%
-4	16.2%	22.1%
-3	25.9%	30.5%
-2	37.5%	40.0%
-1	50.0%	50.0%
0	62.5%	60.0%
1	74.1%	69.5%
2	83.8%	77.9%
3	90.7%	84.8%
4	95.4%	90.2%
5	98.1%	94.1%

 

There's some difference in to hit probabilities, but not that much.

 

It seems if you want to run a campaign that's somewhat more unpredictable, you can easily switch to 5d6 for attack rolls and a 18 target number without throwing balance off that much.

[digital_lorax]

Re: 5d6 Hero

 

ooo, nice. Thanks.

I like the capacity for more variation, though I wonder at the hassle (or not) of rolling 5 dice instead of 3.

[Thia Halmades]

Re: 5d6 Hero

 

Not really much of a hassle, but - and I would point this out - the more dice you have, the more likely you are to fall to the mean, and you drastically reduce the odds of an extreme roll. I submit that you cannot, actually, increase the number of dice without affecting the outcome, because its on a bell curve. Gary's math may be right, but 9th grade math tells me that the more likely you are to fall into the middle.

[Gary]

Re: 5d6 Hero

 

Not really much of a hassle' date=' but - and I would point this out - the more dice you have, the more likely you are to fall to the mean, and you drastically reduce the odds of an extreme roll. I submit that you cannot, actually, increase the number of dice without affecting the outcome, because its on a bell curve. Gary's math may be right, but 9th grade math tells me that the more likely you are to fall into the middle.[/quote']

 

It depends on what you mean by falling to the mean. In percentage terms, you're right. For example, the odds of rolling less than 1/2 the mean (less than 1.75) for 1d6 is 16.7%, for 3d6 (less than 5.25) is 4.6%, and for 5d6 (less than 8.75) is 0.7%. However in absolute terms, you fall closer to the mean with fewer dice. For example, the odds of being within 1.5 of the mean is 66.7% for 1d6 (2-5), 48.1% for 3d6 (9-12), and 39.0% for 5d6 (16-19).

 

And Hero's combat system uses absolute differences, not relative differences in CV.

[Thia Halmades]

Re: 5d6 Hero

 

Okay, now my head hurts.

 

Walk me through this slowly.

 

I have one die in a perfect world of dice. I have an equal chance of coming up on any given side, 1-6. Straight up, no questions asked.

 

I have two dice. I have the BEST chance of rolling SEVEN, as that's where the most possible combinations are. I have the least chance of rolling 2 or 12, as those are both extremes, and varying percentage chances in between. Correct?

 

I have three dice. I have the BEST chance of rolling ELEVEN, because on three dice, that's where the most possible combinations are. I have a very slim chance of rolling either a 3 or an 18 - those are the extremes and are increasingly unlikely.

 

You're talking about five dice. I have the BEST chance of rolling EIGHTEEN, assuming your math is right (3, 4, 3, 4, 3.5 = 18.5, close enough 18/19, round down, shrug) and an alarmingly slim chance of rolling a 5 or a 30 - ALARMINGLY slim. It'll happen, and I'll get some rolls in the single digits and some in the 25+ range, but the bulk of my rolls are going to fall into the 15-20 range, yes?

 

So - and here's where I need you to use very small words - how is it adding two dice to the bell curve doesn't fundamentally alter how the mechanics work? And this is a no sarcasm intended post - I honestly don't get it, I genuinely believe I'm right, and I really didn't follow your math.

 

[Gary]

Re: 5d6 Hero

 

Okay, now my head hurts.

 

Walk me through this slowly.

 

I have one die in a perfect world of dice. I have an equal chance of coming up on any given side, 1-6. Straight up, no questions asked.

 

I have two dice. I have the BEST chance of rolling SEVEN, as that's where the most possible combinations are. I have the least chance of rolling 2 or 12, as those are both extremes, and varying percentage chances in between. Correct?

 

I have three dice. I have the BEST chance of rolling ELEVEN, because on three dice, that's where the most possible combinations are. I have a very slim chance of rolling either a 3 or an 18 - those are the extremes and are increasingly unlikely.

 

You're talking about five dice. I have the BEST chance of rolling EIGHTEEN, assuming your math is right (3, 4, 3, 4, 3.5 = 18.5, close enough 18/19, round down, shrug) and an alarmingly slim chance of rolling a 5 or a 30 - ALARMINGLY slim. It'll happen, and I'll get some rolls in the single digits and some in the 25+ range, but the bulk of my rolls are going to fall into the 15-20 range, yes?

 

So - and here's where I need you to use very small words - how is it adding two dice to the bell curve doesn't fundamentally alter how the mechanics work? And this is a no sarcasm intended post - I honestly don't get it, I genuinely believe I'm right, and I really didn't follow your math.

 

 

Yes it's far more likely to roll a 3 or 18 than a 5 or 30. However, that's looking at it in relative terms not absolute terms. A 3 or 18 is 7.5 points away from the mean. In absolute (Hero) terms, that would correspond to rolling 10 or less or 25 or more. And there's a significantly higher probability of rolling at least 7.5 away from the mean with 5d6 as opposed to 3d6.

 

The bell curve is altered near the tails, but not too much in the middle. It's flattened a bit. Basically, each point of CV is worth more with fewer dice, but not necessarily a whole lot more, at least in the middle of the curve.

 

Fundamentally, you'd get the same mechanic except for the tiny chance of more extreme results.

[Supreme Serpent]

Re: 5d6 Hero

 

Interesting.

 

Good for games where you want significant differences to be even more important. Amber's been on my mind recently, this (or even 7d6, etc) could be a good way to help stretch the gap between good and better.

[Gary]

Re: 5d6 Hero

 

Interesting.

 

Good for games where you want significant differences to be even more important. Amber's been on my mind recently, this (or even 7d6, etc) could be a good way to help stretch the gap between good and better.

 

Thanks. Here are the probabilities with 4d6 (target 14) and 7d6 (target 25)added.

 

3d6	4d6	5d6	7d6
-5	9.3%	9.7%	15.2%	19.2%
-4	16.2%	15.9%	22.1%	25.7%
-3	25.9%	23.9%	30.5%	33.2%
-2	37.5%	33.6%	40.0%	41.4%
-1	50.0%	44.4%	50.0%	50.0%
0	62.5%	55.6%	60.0%	58.6%
1	74.1%	66.4%	69.5%	66.8%
2	83.8%	76.1%	77.9%	74.3%
3	90.7%	84.1%	84.8%	80.8%
4	95.4%	90.3%	90.2%	86.3%
5	98.1%	94.6%	94.1%	90.6%

[Thia Halmades]

Re: 5d6 Hero

 

*blink blink*

 

Color me a moron, I still don't get it.

[Supreme Serpent]

Re: 5d6 Hero

 

*blink blink*

 

Color me a moron, I still don't get it.

 

The more dice you add, you stretch out the bell curve, making the likelihood of falling around the middle more likely, and extremes less likely.

[Thia Halmades]

Re: 5d6 Hero

 

Right, I thought that's what I said in the beginning (note my post) but then Gary is saying something about relative vs. absolute - that's where I'm baffled. I know (again, please see post) if we add dice we flatten the curve. I also know that the curve flattens out fairly quickly and you're far more likely to have a grouping in the center. That's why I'm baffled - why would you want to REDUCE the odds of variety, that's where I'm confused.

 

Seems to me if you have more groupings in the center I see less happening in the far ends of the spectrum, making variety less common.

[Supreme Serpent]

Re: 5d6 Hero

 

Sorry, just responding to last post, not original one.

 

You do end up with less variety. For some settings, that's a good thing. For example, if I were to do Amber or Feng Shui HERO I might want to do something like that - show off the differences between big names and no-names even more - with a greater tendency to the middle, the big names shine more in comparison. If I wanted a more free-wheeling feeling, where agents have a good chance of tagging supers, I'd stick with 3d6.

 

Edit: Or the opposite of all that. Brain kinda fuzzy right now. Bed soon. Urr.

[Gary]

Re: 5d6 Hero

 

The odds of being at least 7.5 away from the mean with 3d6 is 0.9%, since you can only get there by rolling a 3 or 18. The odds of being at least 7.5 away from the mean with 5d6 is 6.5% since you can get there by rolling 5, 6, 7, 8, 9, 10, 25, 26, 27, 28, 29, 30.

 

So for the exact same CV difference, you have a higher chance of hitting with 5d6 rather than 3d6 where the 3d6 ends.

[Derek Hiemforth]

Re: 5d6 Hero

 

Seems to me if you have more groupings in the center I see less happening in the far ends of the spectrum' date=' making variety less common. [/quote']Larger bell curves only cluster more to the center on average. In absolute values (which the HERO System uses), larger bell curves give more variation... not less.

 

For example, an OCV 8 trying to hit a DCV 11 needs to beat the "target number" by 3 (the difference between 8 and 11). In the standard rules, where you roll 3d6 and the target number is 11, succeeding by three (rolling an 8) will only happen 25.9% of the time. But if you use 5d6 with a target number of 18, then you succeed by three (rolling a 15) 30.5% of the time.

 

The larger bell curves have less-likely extremes, which does pull values to the center on average. But there are also more possible values in the center, allowing greater granularity in the results in absolute terms.

 

For example, on a 3d6 curve, there are only 5 results (8, 9, 10, 11, and 12) that are in the probability range of roughly 25% to roughly 75%. On a 5d6 curve, there 7 results in that range (14, 15, 16, 17, 18, 19, and 20).

 

Does that help?

[Thia Halmades]

Re: 5d6 Hero

 

The odds of being at least 7.5 away from the mean with 3d6 is 0.9%' date=' since you can only get there by rolling a 3 or 18. The odds of being at least 7.5 away from the mean with 5d6 is 6.5% since you can get there by rolling 5, 6, 7, 8, 9, 10, 25, 26, 27, 28, 29, 30.[/quote']

 

Gary: I don't have a better way of saying this. What i've quoted is precisely what I don't understand. I just keep seeing you post the exact same thing over and over, and no matter how many times you post it, I don't get it. There's nothing for me to connect too - no concept for me to latch onto.

 

So far, I've gotten SS to agree that I'm correct: if you add dice you flatten the curve and push things towards the middle. I got that far - that's, in fact, precisely how far I got on my own. You then said that isn't what's happening. I asked for explanation. You posted what is likely the explanation, but it doesn't do me any good, because I literally do not understand what you're saying. 7.5 of what to what? What?

 

The curve flattens. Odds of variety reduce. If odds of variety reduce, then chance of random occurance drops and curve flattens (i.e., if we look at it directly visually, the 'peak' becomes lower and longer.) I do not understand how you then say "there's no change" because I do in fact see a change, and SS agrees there's a change.

 

I was totally serious when I said "small words" - I'm good with math, but my brain is telling me one thing (flat curve = less variety) and you're saying something else. I still don't get it.

[Thia Halmades]

Re: 5d6 Hero

 

For example, on a 3d6 curve, there are only 5 results (8, 9, 10, 11, and 12) that are in the probability range of roughly 25% to roughly 75%. On a 5d6 curve, there 7 results in that range (14, 15, 16, 17, 18, 19, and 20).

 

Does that help?

 

YES. THANK YOU. Now I get what you're saying. Because you're more likely to have a variety of values in the center, while you lose extreme values, you maintain - and ultimately improve - granulatiry because you can, in fact, note the 'skill roll' and the difficulty mod and then roll the dice against those absolute values. In this case, a difference of 3 between OCV and DCV. Yes, I have heightened comprehension of the concept, thank you very much.

 

Now can you explain how you would modify ALL the numbers to reflect that properly? How would you have the base OCV/DCV change for these purposes? Or would you simply leave everything as is and add a die?

[Derek Hiemforth]

Re: 5d6 Hero

 

CVs wouldn't need to change. Just the target number (18 instead of 11). And maybe GM-applied modifiers if desired, but that probably wouldn't have too much impact anyway.

[Thia Halmades]

Re: 5d6 Hero

 

Sorry, wrong language, right concept. The base number would then become '18' instead of '11.' Yes?

[Gary]

Re: 5d6 Hero

 

Gary: I don't have a better way of saying this. What i've quoted is precisely what I don't understand. I just keep seeing you post the exact same thing over and over, and no matter how many times you post it, I don't get it. There's nothing for me to connect too - no concept for me to latch onto.

 

So far, I've gotten SS to agree that I'm correct: if you add dice you flatten the curve and push things towards the middle. I got that far - that's, in fact, precisely how far I got on my own. You then said that isn't what's happening. I asked for explanation. You posted what is likely the explanation, but it doesn't do me any good, because I literally do not understand what you're saying. 7.5 of what to what? What?

 

The curve flattens. Odds of variety reduce. If odds of variety reduce, then chance of random occurance drops and curve flattens (i.e., if we look at it directly visually, the 'peak' becomes lower and longer.) I do not understand how you then say "there's no change" because I do in fact see a change, and SS agrees there's a change.

 

I was totally serious when I said "small words" - I'm good with math, but my brain is telling me one thing (flat curve = less variety) and you're saying something else. I still don't get it.

 

The average of 3d6 is 10.5. The average of 5d6 is 17.5.

 

The odds of rolling at least 7.5 from average is higher for 5d6 than 3d6 because there is a much wider range of rolls that fill that condition. Only rolling 3 or 18 fills that conditon for 3d6 (10.5-7.5 or 10.5+7.5), while rolling anywhere from 5-10 or from 25-30 fills that condition for 5d6 (17.5-7.5 or 17.5+7.5).

[Derek Hiemforth]

Re: 5d6 Hero

 

Sorry' date=' wrong language, right concept. The base number would then become '18' instead of '11.' Yes?[/quote']Yes.

[Thia Halmades]

Re: 5d6 Hero

 

Huzzah! Victory is pine scented! I get it. I don't imagine I'll be using it - I'm not well vested enough in HERO to start chucking around house rules - but at the very least, I get it. Thanks!

[Hugh Neilson]

Re: 5d6 Hero

 

CVs wouldn't need to change. Just the target number (18 instead of 11). And maybe GM-applied modifiers if desired' date=' but that probably wouldn't have too much impact anyway.[/quote']

 

To me, the greater the variance (5d6 being more variance than 3d6), the more important the roll of the dice becomes, and the less sgnificance modifiers have.

 

I believe that the odds of success if your OCV is 2 less than the target's DCV, and the odds of failure if your OCV is 2 greater than the target's DCV (for example) will be greater with 5d6 than 3d6. Gary, am I wrong?

 

ie increasing the number of dice means the roll becomes more important, and the charactre's skill becomes less important, in the determination of success.

[Gary]

Re: 5d6 Hero

 

To me, the greater the variance (5d6 being more variance than 3d6), the more important the roll of the dice becomes, and the less sgnificance modifiers have.

 

I believe that the odds of success if your OCV is 2 less than the target's DCV, and the odds of failure if your OCV is 2 greater than the target's DCV (for example) will be greater with 5d6 than 3d6. Gary, am I wrong?

 

ie increasing the number of dice means the roll becomes more important, and the charactre's skill becomes less important, in the determination of success.

 

Yes, but it's only a moderate difference in the grand scheme of things, as long as the modifiers aren't too high. If you look at the first post in this thread, the third chart has a list of to hit probabilities from -5 to +5 CV difference for both 3d6 and 5d6.

[Hugh Neilson]

Re: 5d6 Hero

 

If you set the target number at 18, then here are the to hit probabilities with each difference in CV:

 

3d6	5d6
-5	9.3%	15.2%
-4	16.2%	22.1%
-3	25.9%	30.5%
-2	37.5%	40.0%
-1	50.0%	50.0%
0	62.5%	60.0%
1	74.1%	69.5%
2	83.8%	77.9%
3	90.7%	84.8%
4	95.4%	90.2%
5	98.1%	94.1%

 

There's some difference in to hit probabilities, but not that much.

 

A marginally lower chance to hit at even OCV/DCV probably makes little difference. However, I think characters reliant on DCV, rather than defenses, are placed at a disadvantage. If we assume that results in a 5 point spread between OCV and DCV, the the attacker's chance of connecting has been increased about 63% over the odds in a 3d6 system. He probably needs to invest in 1 or 2 more DCV. Meanwhile, the character reliant on defenses is just as well defended, and need expend no additional points.

 

Not a huge shift in the balance, but certainly there.

[techogre]

Re: 5d6 Hero

 

The HERO system has been balanced at the 3d6 level. Using more or less dice will change the balance, honed over, what, 20+ years?

 

Still, it's an interesting idea, just not one that I would use.

 

Just my $0.02.

 

Pax tecum