Rolling mechanic question

[Tonio]

Re: Rolling mechanic question

 

Not necessarily failing to hit' date=' just failing to hit well enough to do any damage worth recording: I assume that most combats include all sorts of feints and even blows that we do not record. The roll just shows the net effect.[/quote']

 

I considered arguing that, but decided against it on the basis that that's what defense is for. In games which don't use defense (like, for example, D&D, unless you consider damage reduction), hits that do no damage are counted as misses, which is why armor tends to raise the equivalent of DCV in those games (AC in D&D). On the other hand, in games that DO use the defense concept (like HERO), hitting is hitting... small blows that don't do damage are blows that hit but rolled low enough to be completely stopped by defenses. Armor doesn't raise your DCV, just your defenses.

[Jaxom]

Re: Rolling mechanic question

 

The 4d6 bell curve isn't steeper' date=' it's fatter (less steep). And the 2d6 bell curve is a curve (well, as much as any dice-roll bell curves are real "curves"... they're really points in a curve, since there's 0 chance of rolling a 12.7 on 3d6). The 1d6 "bell curve" is a straight, horizontal line.[/quote']

 

Keep in mind that you are talking about a distribution. Depending on your definition, it can be wider or steeper... If you roll 2d6, you are going to roll a 7 16.7% of the time. You are going to get a 6, 7 or 8 (within 1 point of mean) 44.4% of the time. If you roll 4d6, you have twice as many numbers in your range, so your mean is 14 (only 11.26%) but odds of 12, 13, 14, 15, 16 (the same fraction of the center of your distribution) is 52.16%.

 

This is what most people mean when they say a "steeper" distribution. It will always be the case that the more dice you roll, the more likely you are to hit be "close" to the mean. Close is, of course, a relative term which is why statistics uses the standard deviation.

 

The comparison of 2d6 to 4d6 is, of course, the simple one mathematically, because your range has doubled exactly... All values, min, max, mean, mode, median are exactly doubled. That means that a difference of 1 in a 2d6 distribution is the same as a difference of 2 in the 4d6 distribution. The point being that since you are concerned about ranges, not discrete values, most of the time, the distribution is "more peaked near the mean".

 

 

This is actually why I tend to avoid the discussions about dice mechanisms... Statistically, if you are rolling three dice and combining them using addition and subtraction in any fixed combination, the distribution is the same as summing 3d6. Playing with 2 or 4 d6 is the same thing with a slightly wider or narrower distribution. Shifting to center on zero or 11 or any other arbitrary number is a linear transform and does not affect the distribution. Until you start hacking at the shape of the distribution in a more substantial way, it doesn't affect the game-play beyond a little math which I am comfortable with.

 

If you want to change the system meaningfully, change the shape of the distribution... Try exploding dice... Roll a six, roll again and add it. Or try dice pools where you have to roll a number of successes based on a target number. Or do something really wacky and start multiplying. Roll a d10 until you get a 1. Then multiply the result of each roll together.

[Jaxom]

Re: Rolling mechanic question

 

Because of the nature of the 3d6 distribution, Sean is correct that you can swap 3d6 less than or equal to 11 for 3d6 greater than or equal to 10. Since what he wants is a high-roll system, his proposal of 3d6+OCV greater than or equal to DCV plus 10 is a statistical equivalence. I dunno that it is necessarily more intuitive to me, but it does satisfy his goal.

[Cancer]

Re: Rolling mechanic question

 

... Or do something really wacky and start multiplying. Roll a d10 until you get a 1. Then multiply the result of each roll together.

 

And before you jump into thinking about that one, the result of that is a power-law distribution whose mean value is not defined. It's mentioned here.

[Maur]

Re: Rolling mechanic question

 

Exploding Dice already exist in a number of systems. D6 from WEG with the Wild Die. Shadowrun. Deadlands (original system, not the D20 version. Not sure about Reloaded). Exploding dice don't have that big of an effect on the mean, they just cause the tail of the distribution to taper out farther in one direction.

[PhilFleischmann]

Re: Rolling mechanic question

 

would you then multiple all CSLs and other modifiers by two ? or would you leave them the same ??

I'd leave them the same. The idea was to increase the granularity of the results. If you just double everything, it's pretty much the same as it is now, mathematically speaking. The idea was a *possible* improvement to the game, not just to roll bigger dice for the sake of rolling bigger dice.

 

As the rules stand (assuming no other CV modifiers):

two characters with the same CV have a 62.5% chance to hit each other.

If their CV's differ by one, they have 74.1% and 50% chances to hit each other.

If their CV's differ by two, the chances are 83.8% and 37.5%.

If their CV's differ by three, it's 90.7% and 25.9%.

 

With only a 3 difference in CV, one character is about three and a half times as likely to hit the other as the other is to hit the first.

 

With 3d12, there are smaller increments between probability levels:

19 or less is 50%.

20 or less is about 56%

21- is about 62%

22- is about 69%

23- is about 75%

etc. (These aren't the exact odds, just estimates. I post the real odds when I have time.)

[PhilFleischmann]

Re: Rolling mechanic question

 

I can't see the 3d12 catching on' date=' personally: no matter how statistically satisfying people are unlikely to feel comfortable with the dice: those little cubes have a place in the gestalt cousciousness of the gamer and non-gamer communities.[/quote']

But dodecahedrons are so cool! How 'bout rhombic dodecahedrons? I've been wanting some dice manufacturer for a long time to make rhombic dodecahedral twelve-siders. They stack up nicely, and can be used as the three-dimensional analogue of the hexagon.

 

In a thread a long time ago, I talked about rhombic dodecahedrons as the "3-d Hex". Which are easier to use when dealing with 3-d movement. You never have to use the Pythagorean theorem to see how far you can go at a particular angle. You just count hexes, just like you would on a 2-d hex grid!

 

Whoops! Off topic.

[PhilFleischmann]

Re: Rolling mechanic question

 

The 4d6 bell curve isn't steeper' date=' it's fatter (less steep). And the 2d6 bell curve is a curve (well, as much as any dice-roll bell curves are real "curves"... they're really points in a curve, since there's 0 chance of rolling a 12.7 on 3d6). The 1d6 "bell curve" is a straight, horizontal line.[/quote']

I'm not sure what you mean by this. 4d6 is more likely to produce results in the middle of its relative range than 3d6, which in turn produces more middling results than 2d6, which in turn produces more middling results than 1d6. That's a general rule: the more dice, the steeper the curve.

 

And the 2d6 curve is indeed triangular: /\ The sides of the "bell curve" are not bell-shaped, but straight lines. The ways of rolling 2,3,4,5...12 are: 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1.

 

As opposed to the 3d6 curve, which is bell-shaped: 1, 3, 6, 10, 15, 21, 25, 27, 27, 25, 21, 15, 10, 6, 3, 1.

 

True, although that mucks with the chances to hit and stuff, since the average roll is lower.

No doesn't. You just change the to-hit number needed.

 

On the other hand, I feel a fatter bell curve (offered by 4d6) is a good thing. =)

I'm interested to know what you mean by "fatter" in this case. You're less likely to produce results at the extremes of the range (4-24) than you were at the extremes of 3-18 with 3d6.

 

3d12 gives you more granularity, but the same curve. Maybe more granularity is a good thing... I'm not sure it's needed at all, though. Maybe for low-powered games, where CVs are lower?

The CVs being low or high doesn't really matter so much, it's the range of variance of CVs that makes a difference. I'd say it would be more needed in a game where CVs varied greatly. With the RAW, a 9 CV only misses a 3 CV on an 18. And a 3 CV only hits an 11 CV on a 3. With 3d12, it takes a greater variance to get to those extremes.

[Netzilla]

Re: Rolling mechanic question

 

FYI, for those interested in trying the 2d6 - 2d6 die mechanic, you might want to take a look at picking up some of these. I like them for Feng Shui, myself. That way you don't have to worry about remember which color is positive and which is negative.

[Sean Waters]

Re: Rolling mechanic question

 

I considered arguing that' date=' but decided against it on the basis that that's what defense is for. In games which don't use defense (like, for example, D&D, unless you consider damage reduction), hits that do no damage are counted as misses, which is why armor tends to raise the equivalent of DCV in those games (AC in D&D). On the other hand, in games that DO use the defense concept (like HERO), hitting is hitting... small blows that don't do damage are blows that hit but rolled low enough to be completely stopped by defenses. Armor doesn't raise your DCV, just your defenses.[/quote']

 

It is an interesting philosophical point, but my view is based on the idea that even most superheroes only attack every couple of seconds, and (even taking into account the possibility of sweep or autofire atatcks) that is unrealistically slow to be anything more than a 'net effect' calculation.

 

In any event, although Hero combat is not the quickest on the tabletop, you look how much time it takes 'in game' to complete even a pretty huge combat: I can't remember any combat ever taking more than a minute of game time. That is ridiculously fast.

 

(Am I arguing against my own point: I don't think so - if attacks ARE a net effect calculation then my argument makes sense and if they are not, well, we are clearly don't have enough granularity between attacks and defences)

 

SO: if you slow down the hit rate you wind up with a more appropriately paced combat.

 

This has a number of effects, not least of all boosting the utility of REC and regeneration. Of course you can get round that easy enough in character build (just allow more OCV levels to be bought).

 

In addition, aiming at a 10 just feels friendlier than aiming at an 11. We want more people to play Hero, it is not good simply shouting that the maths isn't difficult. I KNOW THAT. We have to have them make that choice, and the smoother the path, the more likely they are to take it.

 

Moreover, if you DID got his way it would remove one of the best arguments for high rolling

[Sean Waters]

Re: Rolling mechanic question

 

But dodecahedrons are so cool! How 'bout rhombic dodecahedrons? I've been wanting some dice manufacturer for a long time to make rhombic dodecahedral twelve-siders. They stack up nicely, and can be used as the three-dimensional analogue of the hexagon.

 

In a thread a long time ago, I talked about rhombic dodecahedrons as the "3-d Hex". Which are easier to use when dealing with 3-d movement. You never have to use the Pythagorean theorem to see how far you can go at a particular angle. You just count hexes, just like you would on a 2-d hex grid!

 

Whoops! Off topic.

 

I'll rep you when I can for sheer unmitigated enthusiasm

[Sean Waters]

Re: Rolling mechanic question

 

FYI' date=' for those interested in trying the 2d6 - 2d6 die mechanic, you might want to take a look at picking up some of these. I like them for Feng Shui, myself. That way you don't have to worry about remember which color is positive and which is negative.

 

Another thing I've tried, if you favour greater randomness, is this:

 

I got 4 blank dice and painted them up with 0 to 5 and 0 to -5 (2 and 2).

 

You roll them and simply use the higher total, whether it is positive or negative, without subtraction:

 

So if you roll 3,2,-4, -5, the total is -9, ignoring the positive roll entirely.

 

That gives an interesting distribution: you have a (nearly) 50% chance of a positive or negative result (the nearly is because you can stil get a zero result if the totals match), and the total will have a 2d6 distribution - so extreme results are far moer likely. This works well if you relate the 'to hit' roll to damage, modifying a 'standard' damage result.

 

Personally I prefer 2d6-2d6, but that is just me.

[Guest steamteck]

Re: Rolling mechanic question

 

I have to say it again: I don't think it is a maths problem, I think that people who are familiar with most other role playing games, or even not familiar with role playing games at all intuitively think that a higher total is a better roll. I'm not sure there is any good reason to work against intuition: to do so makes the learning curve that little bit steeper, and I don't see that as a positive thing.

 

But the maths is simpler

 

 

It not simpler its just different. frankly roll under has been my favorite way since the Fantasy Trip. It just elegant to my sensibilities. Your abilities are X or less, if you roll over your capability you fail. This is just one of the unbroken things people feel they need to mess with just because IMO. To put my snob hat on for a minute, it also seems like a pandering to the lowest common denominator . "People are too dim and unadaptable to get this mechanic so lets do it like the :big boys"". Seems like this leads to logic leads to lots of systems all the same.This same argument could apply to dozens of good mechanics. if you're going to change to hit why leave skills alone. Changing that to roll over would be a pain in the neck. The Rollong mechanic is just perfect IMO.

[Tonio]

Re: Rolling mechanic question

 

There's a reason why most/all of the "big boys" do it the same way. It makes more sense; it's more intuitive. Now, experience can trump intuitiveness... so rolling over would be awkward for longtime HERO players, but that doesn't make it a worse technique than rolling under. Consider, for example, how all (most?) applications have their menu at the top (File, Edit, etc.). This is widely accepted as being more intuitive than having it at either side, or the bottom. But Windows continues to put the taskbar (i.e. the Windows "menu bar") at the bottom. Not because it's better, but because Windows users are used to it. Mac users have always had all their menu bars (OS and application) at the top, and they're used to that.

 

Notice how, when rolling, bigger is always better, EXCEPT when rolling skills/to-hit. Damage, Flash effect, Entangle, Mind Control/Scan/etc effect... in all of these, high numbers are good. But when rolling to-hit, or to succeed in a skill, the reverse is desired, for no intuitive reason, especially when contrasted with, for example, Mind Control. When trying to Mind Control, you roll two sets of dice, and both are the same general concept: roll to see whether I succeed or not. Both rolls result in succeed or fail (different from rolling a, say, EB, where you roll to-hit (succeed/fail), and then damage (quantity of damage, varying effect, not succeed/fail)). But in one of those rolls, I want to roll high, the other, low. Just seems odd, if you're not used to it. =)

 

And pandering to the lowest common denominator is only a problem when you're creating problems for the greatest common factor (to extend the math analogy!). If you simply the system in such a way that it becomes boring, only so that "people [who] are too dim" can use it, then you have a problem. If you say "how much is 2+2?" rather than "solve for x: x-2 = 2"... then you're simply creating a more usable system. =)

[Guest steamteck]

Re: Rolling mechanic question

 

I see where you're coming from but the logic of being more intuitive just completely escapes me. characteristics are tailor made for roll under systems to me. X number is my level of power if it I roll equal to or under my level of ability I succeed. If that confuses people I don't understand how they can hold down a job. saying the roll over mechanic scares people off if it isn't ridiculous but true is very very sad.

To derail your windows analogy for use with multifocals, lower really IS better to see the bar more clearly. Sometimes things are different for a good reason.

Pandering to the lowest common denominator always negatively impacts the highest IMO , you just have to find a balance that works best for your audience.

[Tonio]

Re: Rolling mechanic question

 

I don't think anybody's arguing that roll under is "too complicated" or "too confusing". I'm certainly not. I'm not even arguing that it's counter-intuitive. Just that it's less intuitive than roll over, and that the fact that you (and I) are comfortable with roll under is more due to experience (getting used to) than intuitiveness. Neither system is inherently more complicated. Taken alone (that is, not considering any other rolls), neither is really more intuitive, except for a small bias towards roll over, since usually "bigger is better" in games (higher scores being better, for example, in most games).

 

My solution would be to introduce an "optional rule" to convert the system to roll over (using the same values everywhere), eventually (say, next version, or two versions after the current one?) turn the current system into the optional rule, and roll over into the standard, and after that, eliminate the current system. Not because there's anything wrong with the current one, but because they're mechanically identical and roll over is more intuitive for newcomers.

[Maur]

Re: Rolling mechanic question

 

There's a reason why most/all of the "big boys" do it the same way. It makes more sense; it's more intuitive. Now' date=' experience can trump intuitiveness... so rolling over would be awkward for longtime HERO players, but that doesn't make it a worse technique than rolling under. Consider, for example, how all (most?) applications have their menu at the top (File, Edit, etc.). This is widely accepted as being more intuitive than having it at either side, or the bottom. But Windows continues to put the taskbar (i.e. the Windows "menu bar") at the bottom. Not because it's better, but because Windows users are used to it. Mac users have always had all their menu bars (OS and application) at the top, and they're used to [i']that[/i].

 

Hmm, I guess that Dock sitting right about where the taskbar does is just a fluke then... As to why the menus sit at the top, well I don't think that is any more intuitive than the bottom or the side. It just made for a convenient place to put them that would be most likely kept visible all the time. Apple put the menubar at the top of the screen for all applications as a way to deal with the limited real estate available on that era's CRTs. Now, it doesn't make sense as it divorces the menu from the application and slows a user down if they have to mouse across a 24 or 30" LCD to get to the menu...

 

As for what is more natural, roll under or roll over, well, neither. If a larger number was always better, then why is 1st place better than 2nd?

[archermoo]

Re: Rolling mechanic question

 

I see where you're coming from but the logic of being more intuitive just completely escapes me. characteristics are tailor made for roll under systems to me. X number is my level of power if it I roll equal to or under my level of ability I succeed. If that confuses people I don't understand how they can hold down a job. saying the roll over mechanic scares people off if it isn't ridiculous but true is very very sad.

To derail your windows analogy for use with multifocals, lower really IS better to see the bar more clearly. Sometimes things are different for a good reason.

Pandering to the lowest common denominator always negatively impacts the highest IMO , you just have to find a balance that works best for your audience.

 

I'm with you on this one. Neither one is more intuitive than the other. I grasped the concept that rolling as high as possible isn't always the best result when I first started playing Monopoly. Or maybe Chutes & Ladders.

 

It all comes down to expectations. The math isn't easier one way over the other. One way isn't more intuitive than the other. Either way is pretty simple to do, and the one that makes most sense to you is the one that you are used to or were expecting.

[Tonio]

Re: Rolling mechanic question

 

Hmm, I guess that Dock sitting right about where the taskbar does is just a fluke then... As to why the menus sit at the top, well I don't think that is any more intuitive than the bottom or the side. It just made for a convenient place to put them that would be most likely kept visible all the time. Apple put the menubar at the top of the screen for all applications as a way to deal with the limited real estate available on that era's CRTs. Now, it doesn't make sense as it divorces the menu from the application and slows a user down if they have to mouse across a 24 or 30" LCD to get to the menu...

 

As for what is more natural, roll under or roll over, well, neither. If a larger number was always better, then why is 1st place better than 2nd?

 

Regarding menus at the top, Windows UI vs Mac UI, etc... it was an example, not supposed to spur a debate on "which is better". I picked a bad example. =)

 

First place being better than 2nd is different, since we're talking ordinals, not cardinals... it's not exactly analogous, since there's really no 0th place (the "0th" item in a 0-based array is still the first item, it's just convenient to call it the 0th item), but you CAN roll 0 damage (well, mebbe only on BODY with normal attacks), and you can inflict 0 damage (like whenever defenses are greater than damage rolled), and with modifiers you can roll a 0 on your to-hit roll (HERO's rolling system doesn't permit this by using a special rule: 3's always hit, 18's always miss), etc.

 

In situations where we're representing an ordinal quality, it can be argued that roll under makes more sense. For example, determining who acts first. Curiously enough, HERO does this the other way around (only you're not rolling). The highest DEX acts first. If you had an "initiative" stat, it'd make sense that "lower is better", since you could just add a "st", "nd", "rd", or "th" to it to determine when you act... initiative "1" goes "1st", "2" goes "2nd", etc. I'm not suggesting lower DEXs should act first, and I'm not suggesting the current system is bad or broken. Of course higher DEXs should act first... they're quicker to act. But there's a concrete concept to determine that: quickness implies acting first. No such thing with rolling under/over. As a side note, D&D used to work that way... initiative was "roll under", or more correctly, "roll low". Made sense until you consider initiative modifiers... suddenly "pluses" were bad.

 

I guess it all boils down to general weirdness when you consider all the math involved. When you roll under, pluses to your roll are bad. You have to apply them to your roll's target (whatever you have to roller under of). That's fine, except when there's no actual target. Like say "whoever rolls best wins". In a roll under system, a plus would either have to be applied to your opponent's roll (how come my opponent, who's not interacting with me, is modifying my roll?!), or turned into minuses (but minus is bad!). No, it's not hard to understand... it's just... odd, I guess. Easy to get used to, certainly! Just odd, initially.

[archermoo]

Re: Rolling mechanic question

 

I guess it all boils down to general weirdness when you consider all the math involved. When you roll under, pluses to your roll are bad. You have to apply them to your roll's target (whatever you have to roller under of). That's fine, except when there's no actual target. Like say "whoever rolls best wins". In a roll under system, a plus would either have to be applied to your opponent's roll (how come my opponent, who's not interacting with me, is modifying my roll?!), or turned into minuses (but minus is bad!). No, it's not hard to understand... it's just... odd, I guess. Easy to get used to, certainly! Just odd, initially.

 

Or applied as a positive modifier to the number you are trying to roll under.

 

And how is minus bad when you are trying to roll low?

[Tonio]

Re: Rolling mechanic question

 

I'm with you on this one. Neither one is more intuitive than the other. I grasped the concept that rolling as high as possible isn't always the best result when I first started playing Monopoly. Or maybe Chutes & Ladders.

 

It all comes down to expectations. The math isn't easier one way over the other. One way isn't more intuitive than the other. Either way is pretty simple to do, and the one that makes most sense to you is the one that you are used to or were expecting.

 

Well, in both Monopoly and Chutes & Ladders, rolling high is best in general, it's just that there are complications. In C&L, you wanna roll high... but not land on a chute, and if possible, land on a ladder. In Monopoly it's the same thing, since passing through Go gives you free money, only you want to land on some unbought properties so you can buy 'em, too. Even in Trivial Pursuit, where there's no "goal" space to reach, you still want to generally roll high, to reach the next pie-awarding space fastest (until you're close enough to land with one roll, then you want an exact roll, not a low one). And yes, there are games (those three are great examples) where rolling high is not always best... but they are exceptions to the rule (some more than others... Trivial Pursuit is probably the biggest exception of the three, Chutes and Ladders the smallest).

[archermoo]

Re: Rolling mechanic question

 

Well' date=' in both Monopoly and Chutes & Ladders, rolling high is best in general, it's just that there are complications. In C&L, you wanna roll high... but not land on a chute, and if possible, land on a ladder. In Monopoly it's the same thing, since passing through Go gives you free money, only you want to land on some unbought properties so you can buy 'em, too. Even in Trivial Pursuit, where there's no "goal" space to reach, you still want to generally roll high, to reach the next pie-awarding space fastest (until you're close enough to land with one roll, then you want an exact roll, not a low one). And yes, there are games (those three are great examples) where rolling high is not always best... but they are exceptions to the rule (some more than others... Trivial Pursuit is probably the biggest exception of the three, Chutes and Ladders the smallest).[/quote']

 

But all three quite handily shoot down the "highestest is always bestest" idea. I guess it is too bad that not many people played any of those because their dice rolling mechanic is so complicated...

[Tonio]

Re: Rolling mechanic question

 

Or applied as a positive modifier to the number you are trying to roll under.

 

That's what I meant by "whatever you have to roller under of". =)

Then I pointed out a case where there might not be a target roll (i.e. the number you are trying to roll under).

 

And how is minus bad when you are trying to roll low?

 

I didn't mean mathematically, I meant psychologically, intuitively, emotively, something along those lines. =)

[Tonio]

Re: Rolling mechanic question

 

But all three quite handily shoot down the "highestest is always bestest" idea. I guess it is too bad that not many people played any of those because their dice rolling mechanic is so complicated...

 

Sarcasm notwithstanding, the idea isn't "shot down". The idea isn't that rolling high is categorically and under all circumstances better than rolling low. It's that intuitively rolling high is presumed to be better than rolling low. Some systems use counter- or non-intuitive systems, and that's not a big problem. Most of the time it's easy to get used to (like HERO's system). Some systems use roll-high but add in complexities [oh, I see now... earlier I said "complications" when I meant "complexities"... my bad!], like most (all?) board games.

 

Just because you can drive drunk and not crash your car doesn't mean driving while drunk is a good idea. Just like there being games that use roll-low for success and work doesn't mean rolling low for success is a better idea. It might be a better idea for that particular game, it might be a worse idea balanced by superior mechanics in other areas, it might be a worse idea that's not worse enough to warrant a change (sure, you can scrap your 3-month-old video card to buy a brand-spanking new one, which is slightly faster... but it's not worth it).

[archermoo]

Re: Rolling mechanic question

 

I didn't mean mathematically, I meant psychologically, intuitively, emotively, something along those lines. =)

 

Same question remains. Psychologically, intuitively and emotively, when I am trying to roll low minuses to my roll are good things, and pluses to my roll are bad things. And on the flip side, minuses to the number I'm trying to roll under are bad, and pluses to the number I'm trying to roll under are good.

 

I've never understood why people feel the need to convince others that the way of doing things that they subjectively prefer, or that subjectively makes more sense to them, must also be objectively better. It is a matter of what you are used to and what you expect. Nothing more.