House Rule: Using dice other then d6 in hero

[Tanis Frey]

Has anyone considered figuring our how much other dice would cost to buy in Hero for the various different powers? d4s, d8s, d10s, d12s, and d20s

[unclevlad]

Mm...well, just off the top of my head...

 

For normal damage, for STUN, or for adjustment powers where you're counting pips (same as STUN, IOW), I'd compare the mean.

 

d4:  2.5

d6:  3.5

d8:  4.5

d10:  5.5

d12:  6.5

d20:  10.5

 

So 1d12 would be about 2d6;  d20 about 3d6.  Those'd be pretty straightforward.  d4, d8, d10...not so much.  Roughly, 3d8 would be about 4d6;  2d10 would be 3d6.  3d4 would be 2d6.

 

These would have different distributions, tho.  The standard deviations are different.  The SD of N s-sided dice is SQRT(N * (s^2 -1) / 12).  The mean of 3d8 is then just under 4;  of 4d6, it's 3.4.  So the 3d8 will average very slightly less (mean of 3d8 is 13.5, of 4d6 it's 14)...but the 3d8 will be notably more variable.

 

But also note that 3d8 normal will do less BODY, simply because there's fewer dice, unless you change the BODY counting method.  

[Christopher R Taylor]

There's also the reverse effect: a 4 on a d4 shows up 25% of the time (so does a 1), so you can rely on getting more Body from a d4 than a d6.  You'd have to come up with a different system entirely for resolving body on dice.

[unclevlad]

OK, so that's the starting point, but talking about point costs, we run into the hassle that costs are almost always in integer points.  

 

If we retain that...we have, for example, 3d8 is very similar to, but slightly less effective than, 4d6.  4d6 is 20.  So...d8's can't be 7 points, that's too high.  6 points?  Mmm, that feels a bit too low.  Extend to 9d8 vs. 12d6.  Mean on 9d8 is 40.5;  on 12d6, 42.  We're talking a difference of 3 BODY too.  Still, the STUN's usually the key.  9d8 @ 6 points per, would be 54 points;  12d6 is 60.  That's a pretty significant cost savings for not much lower effectiveness.

 

OK, so...what, 6.5 points per die?  If you're willing to do that, well...yeah, OK, it'd probably work well enough.

 

 

20 minutes ago, Christopher R Taylor said:

There's also the reverse effect: a 4 on a d4 shows up 25% of the time (so does a 1), so you can rely on getting more Body from a d4 than a d6.  You'd have to come up with a different system entirely for resolving body on dice.

 

FALSE.  Because a 1 also shows up 25% of the time.  The mean BODY damage is 1 regardless of die size.

EDIT:  you'd get more BODY because, to get the same STUN, you'd be rolling more dice, so that reverse effect does hold.

[dmjalund]

rolling body on different dice:

on any dice
rol1 1 -> 0 body
roll 2-5 -> 1 body
roll 6-9 -> 2 body
roll 10-13 -> 3 body
roll 14-17 -> 4 body
roll 18+ -> 5 body

 

this is still slightly less than rolling multiple d6, but it's a lot closer

 

[unclevlad]

Mmm...lessee.  d12 is the simplest, as it's very close to 2d6 overall.

4 chances of 1 body = 4

4 chances of 2 body = 8

3 chances of 3 body = 9

 

So 21/12 or 1.75 BODY for a d12, as opposed to 2 BODY for 2d6.  

 

d10 would be 4 + 8 + 3, or 15, so 1.5 per die.  3d10 would be about 5d6, so 4.5 vs. 5.

 

d4 would be 0.75 per die;  6d4 would be 4.5, vs. 4d6 being 4.  So the d4's are still doing a little more, but yeah, it's nowhere near as bad.

 

Otherwise yeah, this looks accurate.

 

Overall...I just don't see a good reason to do this.  What's the goal?  edit:  that's to OP.  dmj's method is likely good, should alternate die sizes be accepted.

[Christopher R Taylor]

 

Quote

FALSE.  Because a 1 also shows up 25% of the time.  The mean BODY damage is 1 regardless of die size.

 

OK there's a misunderstanding here.  What I meant was that every 4 times you roll the die you're likely to get 4 on a d4.  On a d6, you're only likely to get a 6 every 6 times you roll (obviously odds don't work exactly like that, but 25% of the time vs 16.666%).  Hence, you are more likely to roll 2 body on a d4 than a d6 on any one given roll of the dice.  This shifts the odds of getting better body in the favor of the d4 than the d6. 

 

The average body is the same on all dice, which is what you are correctly pointing out.  I'm just as likely to roll a 1 on a d4 as a 4.  But since the 4 gives you 2 Body, that's rising the chance of a good roll over a d6 because of the fewer die faces.  In other words, the fewer faces on the dice, the greater the odds of a higher body roll.

 

And the more die faces, the more pronounced this effect becomes.  D20 is a 5% chance, for example.  And the rules would have to somehow take that into account.

Edited November 25 by Christopher R Taylor

[Hugh Neilson]

1 hour ago, Christopher R Taylor said:

OK there's a misunderstanding here.  What I meant was that every 4 times you roll the die you're likely to get 4 on a d4.  On a d6, you're only likely to get a 6 every 6 times you roll (obviously odds don't work exactly like that, but 25% of the time vs 16.666%).  Hence, you are more likely to roll 2 body on a d4 than a d6 on any one given roll of the dice.  This shifts the odds of getting better body in the favor of the d4 than the d6.

 

You are also 25% likely to roll a 1 on 1d4, rather than the 16.666% chance to roll a 1 on 1d6. The average remains precisely 1 BOD per die. As unclevlad notes, however, if you have more d4s, you will roll more dice and do more BOD. Larger dice will generate less BOD.

Way back in 1e, Hero published a newsletter and did an article on "funny shaped dice" where they suggested prices for the various dice, but this simplistically assumed a 1 remained 0 BOD, the highest number was 2 BOD and all numbers in between were 1 BOD.  IIRC, they went up to 1d100 with a cost of 72 points for normal damage and 216 for a 1d6 Killing Attack.

[Tech]

There's also the problem of having to buy alot of dice other than D6, which can get expensive.

[unclevlad]

1 hour ago, Christopher R Taylor said:

 

 

OK there's a misunderstanding here.  What I meant was that every 4 times you roll the die you're likely to get 4 on a d4.  On a d6, you're only likely to get a 6 every 6 times you roll (obviously odds don't work exactly like that, but 25% of the time vs 16.666%).  Hence, you are more likely to roll 2 body on a d4 than a d6 on any one given roll of the dice.  This shifts the odds of getting better body in the favor of the d4 than the d6. 

 

 

And your odds of a 1 go from 1 in 6 to 1 in 4...so you get 0 BODY.  That shifts it right back.

 

1 hour ago, Christopher R Taylor said:

The average body is the same on all dice, which is what you are correctly pointing out.  I'm just as likely to roll a 1 on a d4 as a 4.  But since the 4 gives you 2 Body, that's rising the chance of a good roll over a d6 because of the fewer die faces.  In other words, the fewer faces on the dice, the greater the odds of a higher body roll.

 

 

So you're just as likely to roll BELOW average because you'll see more 1's.

 

They CANCEL each other, for the mean, which is going to be what matters...especially because the mean becomes the dominant factor as the # of dice increase...central limits and all.

 

Now, yes, the variance per die IS higher.  BODY is really simple, because the results are 0, 1, or 2...the mean's 1.  The variance is (result - mean) ^2 * prob(result).  Well, that's 1 twice, and 0 for the rest...regardless of the number of sides, and the prob(result) for the 1 is 2/sides.  So the variance for BODY is always 2/sides, using standard counting.  

 

BODY SD of 3d4 would then be sqrt(3 * 2/4) or sqrt(1.5) or about 1.22.  BODY SD of 2d6 would be sqrt(2 * 2/6) or sqrt(2/3) or about 0.8.  But also note that the 3d4 has a mean of 3 BODY, versus 2 for the d6's.  To look at it another way, consider 4d4 versus 4d6, for BODY only.  The SD for 4d4 is sqrt(4*2/4) = sqrt(2) = 1.41.  For 4d4, it's sqrt(4*2/6) = sqrt(4/3) = 1.15.

 

But the correct statement is, you're more likely to be different from the mean when you're rolling the d4's.  Above AND below.

 

The bigger factor, tho, using standard HERO BODY counting, is that you're rolling more d4's.  The SD difference won't be nearly enough to offset that you're rolling 3d4 for each 2d6, if you're equating stuns.  If you're equating mean stuns, 10d6 has a mean of 35, which would be 14d4.  The BODY means would be 10 vs. 14, the SDs would be 1.83 vs. 2.65.  The distributions overlap, but you need to be more than +2 SDs to the good, on the d6's, to hit the mean on the d4's.  In a continuous normal distribution, +/- 2 SDs from the mean covers 95% of the rolls, so > +2 SDs happens only 2.5% of the time.  10d6 is getting pretty close to a continuous normal distribution.

[Chris Goodwin]

The Espionage! RPG (first-edition spy action from Hero Games) had a section on using the funny dice.  It doesn't say anything about the costs, but maybe those could be reverse engineered?

[unclevlad]

7 minutes ago, Chris Goodwin said:

The Espionage! RPG (first-edition spy action from Hero Games) had a section on using the funny dice.  It doesn't say anything about the costs, but maybe those could be reverse engineered?

 

Based on what criterion?  If we adopt dmj's conversion for counting BODY, then the difference is probably small enough to ignore, at least initially.  But, do we use maximum STUN or mean STUN?  This is most significant if the switch is to a d4 or a d8.  Variance becomes the major concern moving up to the simplest...d12.  SD on 12d6 is sqrt(12*35/12) = basically 6.  SD on 6d12 is sqrt(6*143/12) or sqrt(71.5) or a bit under 8.5.  The mean of 6d12 is slightly lower...39 vs. 42...but that much larger SD makes 50+ damage higher.  Not a lot higher, but higher.  But so are the low, basically negligible-damage rolls.  12d6 will roll 30+ stun 98% of the time...so less than 30 STUN is awful luck.  OTOH, 6d12 will roll 30+ 86% of the time...so 29 or less is a fairly regular occurrence, at about 1 time in 7.

 

I've also been thinking about using d4's for damage.  Right now, defenses worry about the total STUN because it gets SO much higher than the BODY, on normal attacks.  This'd be less true using d4's.  Still purely conceptual, but I'm thinking 4 points per d4.  One nice thing here is, this means 1/2 dice are...2 points.  And there's no point in +1 pip.  To relate this back, with large dice like d12s, there's more incentive to offer fractional dice, and not just half dice.  This would be particularly true with e.g. AVADs or many transforms.

[Tanis Frey]

On 11/24/2024 at 10:09 PM, dmjalund said:

rolling body on different dice:

on any dice
rol1 1 -> 0 body
roll 2-5 -> 1 body
roll 6-9 -> 2 body
roll 10-13 -> 3 body
roll 14-17 -> 4 body
roll 18+ -> 5 body

I am going to use this chart to keep the body average of every die from being 1.  Many, many powers only care about body rolled.

as for costs, I am thinking about making it an advantage, as Follows:

d4 -1/4

d8 +1/4

d10 +1/2

d12 +3/4

d20 +1 1/4

Yes that is an advantage with a negative number, this allows for a player to decide to roll more dice that is balanced by a lower body average per die.

 

When my game launches I will make DC charts for the alternat dice for the powers that my players decide to take with alternate dice.

[unclevlad]

Making it an advantage has dangerous impacts because low base costs can lead to major issues.

 

Blast 3d6 (vs. ED), Reduced Endurance (1/2 END; +1/4), Attack Versus Alternate Defense (Mental Defense; +1), d20 for damage (+1 1/4) (52 Active Points)

average 31 STUN...wildly variable, but still, will stun almost any character that lacks mental def.  And it's nominally only a 10 DCs attack

 

The mean STUN on a d20 is 10.5...or 3x a d6.  Yeah, it'll be wildly variable, but (EDIT:  3d20)  18 or less STUN is only 10% of the time.  25 or more is 75% of the time;  35 or more is 39%.  45 or more is 10%.

 

Blast 5d6 (vs. ED), Reduced Endurance (1/2 END; +1/4), d20 for damage (+1 1/4) (62 Active Points)

52 STUN on average.

 

Blast 6d6 (vs. ED), Reduced Endurance (1/2 END; +1/4), d12 for damage (+3/4) (60 Active Points)

Not as bad...39 average, but I'm getting just about a 12DC attack with almost no-cost reduced END.  

 

Blast 7d6 (vs. ED), Reduced Endurance (1/2 END; +1/4), d10 for damage (+1/2) (61 Active Points)

38.5 average...11 DCs.  Still got the reduced END cooked in.

 

But I can go back to the AVAD cases...4d10 AVAD is still cheap.

 

The d20 cost is MUCH too low, that's clear...but you also have to watch out for the combination aspects.  Look at Blast (AVAD vs. Mental Def) versus Mental Attack...when both are Autofire with reduced END.  The Blast is MUCH cheaper.  This'll be similar with the smaller die sizes like the d10s and d12s.

 

With the d4's...it can't be worth it at only -1/4.  Average BODY drops 25%;  average STUN drops 30%.  You're only getting a 20% cost break.

 

d8's:  average STUN increases by almost 30%, for a 25% cost increase.  8d8 would be the same as 10d6;  36 STUN vs. 35.  But it's also worth noting that 8d8 has a higher maximum...64 vs. 60.  And for reference...40 STUN on 9d9 is 30%, whereas it's only 20% on 10d6.  At 45 STUN, it's 10% versus 4%.  And that's not considering the cost with more advantages, like the 4d8 AVAD (45 points) vs 5d6 AVAD (50 points).

 

 

EDIT:  this is, I'll freely admit, seriously abusive.  The point, tho, is to illustrate how low base costs with VERY high advantage levels is still insanely cheap.

 

Blast 2d6 (vs. ED), Attack Versus Alternate Defense (Mental Defense; All Or Nothing; +1/2), d12 for damage (+3/4), Reduced Endurance (0 END; +1), Autofire (5 shots; +1/2), Non-Standard Attack Power (+1) (47 Active Points)

 

Each round that hits would be 13 STUN.  Sure, it won't stun anyone as each is separate from that perspective, but with some levels in OCV to get 2 or 3 rounds hitting each time?  This'll take down someone with no Mental Def REAL fast.  The additional costs for highly effective autofire and reduced END on autofire are even in there...and it's still cheap.  I'm not saying this attack wouldn't have serious utility limits, mind...it's more of an illustration of the issue.

 

 

 

[LoneWolf]

You are looking at the averages but are not taking into account the bell curve.  While 1d20 and 3d6 have the same average the odds of getting a roll significantly higher or lower than average is way different.   The odds of rolling 18 on 3d6 are about .46%.  The chance of rolling 18 or higher on 1d20 is 15%.   The flip side is that your chance of rolling 3 is the same.   

 

This is going to create a situation similar to Killing attacks under 5th edition or lower.  It will lead to any character being able to be taken out with a lucky roll.  With a 12d6 attack your chances of rolling 72 0.0000000214%, the odds of rolling 72 or higher on 5d20 are 0.0003%.  That is at the extreme range but shows the difference.  A better example would be the chance of each method rolling higher than 50.  Under the 12d6 the odds of rolling higher than 50 are about 10.3%, with 5d20 the chances of rolling higher than 50 are 58.9%.  Using the proposed rule the 12d6 attack costs 60 active points where the 5d20 costs 56 points.  

 

The chance of a really low roll in theory balances out the chance of an extremely high roll, but in reality, that is not the case.  Because the fact that in Hero characters defenses reduce the amount of damage they take it means any attack below the characters defense does nothing.  It does not matter how much below the defense the attack is.   If a character has 20 defense, it does not matter if the damage is 20 or 1 point.  Both the 20 stun and the 1 stun attack are completely negated.  But the more damage that gets through the greater the chance the character suffers a major negative effect.   Getting an extra 10 stun through greatly increases the chance of stunning or knocking out an opponent.  

 

This idea is a bad idea because it increases the maximum amount of damage an attack can do and also increases the odds of an extremely high damage attack.  Combining those two factors creates a situation where any character can be taken out by a lucky shot.  
 

[unclevlad]

I did note the variability.  Also note those sample powers, where that 5d20 vs. ED did 52 STUN *average*.  I don't need to challenge extra-high rolls when this average is so incredibly ridiculous.

 

Part of it, also, is that 9d6 maxes at 54;  3d20, with the same average, maxes out at 60.  (I edited the earlier post to note that the numbers there were for 3d20).  "Just below max" is generally MUCH!!! easier than "max".  

 

5 hours ago, LoneWolf said:

With a 12d6 attack your chances of rolling 72 0.0000000214%, the odds of rolling 72 or higher on 5d20 are 0.0003%.

 

I see...you're roughly measuring by cost.  Yeah, I already noted it's WAY too low.  That said, 12d6 rolling 72...perfect sixes is 4.6 *  10^-8 percent.  5d20 rolling 72?  It's 7%.  Not sure where you're getting the numbers, but they're wrong, sorry.  (To be sure, you're *under* selling the issue.)

 

 

 

 

 

[LoneWolf]

My point is that with d6 you get a fairly predictable outcome but still allow for some variant.   If you are using critical hits you can achieve some pretty impressive damage, but it is still rare.  This makes it easy to balance the powers.   When you start adding other dice balancing the cost becomes a lot more difficult if not impossible.  If you use critical hits with variant dice it gets even worse.   The only reason I could see using something like this would be if the GM wants a very lethal system where any character can be taken out by anyone else.   

I used Copilot for the odds, but it apparently has some bugs.  
 

[unclevlad]

So we have another thing to criticize AI about?  Even a cursory look would say that 72 on 5d20 can't be down in the teeny, tiny percentages...the mean's 52, so 72 isn't *that* much over the mean, and it's well below the max.  Rolling 90 is about 0.1%.  (OK, cursory for people with decent exposure to probability or statistics.)

 

I use anydice.com these days, when we're just talking total pips.  The stats, like mean or SD, I know what the formulas are.  For trickier/combined numbers, the Java code isn't hard.  12d6 only has 2 billion cases...and a recursive solution only has a fraction of the counts.  OR, sometimes, I'll do Monte Carlo when the solution space is too big, but using a statistically good random number generator...and lots of trials.  Again, reasonably modern computer...it doesn't take long at all.

 

 

[Crusher Bob]

On 11/24/2024 at 9:48 PM, unclevlad said:

OK, so that's the starting point, but talking about point costs, we run into the hassle that costs are almost always in integer points.  

 

 

 

You can just make the cost of different dice decimal, and round to an integer at the end, just like powers with modifiers.

 

So, for example, a d10 has the average result of 5.5, so a d10 blast would cost 5.5/3.5 * 5 = 7.86 points

 

So a 50 point limit power would be 10d6 for 50 points, or 6d10 for 47.16 -> 47 points.  The 6d10 power does 2 points of damage less on average than the d6 power, so should cost around 2 to 3 points less, which it does.

 

As for the variability, you can check the tables in anydice, but as an example:

A 10d6 power stuns a 20 DEF 20 CON (output 10d6 - 20, result is at least 20) hero around 20.5% of the time

and a 6d10 power (output 6d10 - 20, result is at least 20) stuns the same hero around 18.22 % of the time

 

------------------------

The cost of per die of a power that would normally be 5 points would be:

(For comparison)

d6 (3.5 average) -> 5 points (10d6 -> 50 points, average 35, stuns 20.5%)

9d6 -> 45 points, average 31.5, stuns 5.96%)

 

d20 (10.5 average) -> 15 points (3d20 -> 45 points, average 31.5, stuns 22.1%)

d12 (6.5 average) -> 9.29 points (5d12 -> 46.45 -> 46 points, average 32.5, stuns 18.77%)

d10 (5.5 average) -> 7.86 points (6d10 -> 47.16 -> 47 points, average 33, stuns 18.22%)

d8 (4.5 average) -> 6.43 points (7d8 -> 45.01 -> 45 points, average 31.5, stuns 9.54%)

d4 (2.5 average) -> 3.57 points (14d5 -> 49.98 -> 50 points, average 35, stuns 14.23 %)

 

So there is some advantage in the larger die, due to higher variability but would require doing more math on the actual campaign averages to check how much that amounted to.  (isn't average defense 'supposed' to be 25 instead of 20?)

 

Edited 20 hours ago by Crusher Bob

[unclevlad]

Sure, if you want to require a calculator or spreadsheet to implement this.

 

Back to the basic point, tho.  What is this complexity adding?

 

Nothing.

[Crusher Bob]

I could see moving to different base dice to reduce the amount of dice rolled, and to increase the variability of results some.  Tabulating the results of 6d10 or 5d12 at the table [b]may[/b] be easier than 10d6.

[unclevlad]

We discussed the impact on variability extensively earlier.

 

If dmjalund's BODY-counting method is used, which I'd advocate...well, now, any saving from counting 5d12 vs. 10d6 is likely minimal.  With a little practice, I think most of us can count d6 BODY at a glance.  But with dmjalund's approach, I think that'd take a while, if I got to that point at all.  (Especially if 2 or 3 non-d6's get used.)  If I have to count the BODY, then the STUN?  Not much time savings there.  VERY true with d20s...and as we noted, the variance with d20s is HUGE.  (And the granularity is awful.)

 

Also note that the argument about quick counting doesn't apply to d4's...especially the 'older' style:

 

Didn't like counting these in D&D.  MUCH prefer the style where the numbers are at the points.

[LoneWolf]

Adding up d6 is not that hard.  You simply group by 10 count the groups and add the remainder.  For body you match the 1 and 6 and if then add or subtract the remainder from the number of dice rolled.  So, if you are rolling 12d6 and have two more 6’s than ones that comes up to 14 BODY.   Adding up dice higher than 6 will be harder especially those higher than 10.   Adding lower number in your head is easier than adding higher value numbers.   

 

Adding or removing DC is also going to be a lot more difficult.  There is a chart in the book for adding DC that is based on d6.  Now each power will have to be figured out separately by reverse engineering the power. HKA’s and HTH attacks are going to be a pain to deal with.  If the game is using 6E rules damage negation becomes way too complicated.  

 

This complicates every aspect of the game with no real benefit except using different sided dice.  It changes the balance of the game and is going to slow down things a lot. 
 

[unclevlad]

Yeah, I was just about to make the same point about adding DCs.  Note that it can also count to ranged attacks, too...either ranged martial attacks, or from skill levels, or some other form.  Doesn't Weaponmaster have some ranged options?  Oh, and of course, pushing a Blast is built in.  And figure out the fractional tweaks...like, if the attack's using d20's, and I've got +1 DC with it...what does that add to the attack?  What if it's using d8's?  

 

And LW didn't even mention what'd happen with *advantaged* non-d6 attacks.  ARGH!!!!!!  It can be bad enough with d6's...my favorite example is "the power to heal is the power to harm."  2 HAs based on Power Def...one does BODY.  I'm gonna *try* to arrange the bonus damage to be 6 DCs, much of the time...because that's +3d6 or +2d6, assuming they're both AVAD as opposed to NND.  Or I tend to note the net DCs of the attack, then add the DCs from the bonus, and convert back...with notes on the sheet.  

 

We'd now need to figure out the net cost per die, based on the die size and the level of advantage.