Game effects of d666

[ajanders]

Unearthed Arcana introduces a variant rule that turns D20 into D666: instead of making saves, skill checks, and level checks on a d20, make them on 3d6.
I understand this turns a flat probability curve into a bell curve, decreasing the randomness of the game. I think this should help the PC side...and frankly, it helps me too, because I can more precisely determine what a monster is able to do: while a CR may change, I can know it much more certainly.
I believe, however, this makes flat bonuses worth a different amount depending on the skill of the character...if this makes any sense.
That is, a +2 flanking bonus is now more valuable to a character with a to hit bonus of +10 than a to hit bonus of +16...or than a character with a to hit bonus of +4.
Unfortunately, I can't figure out how to prove this, it's only an intuition based on playing with a bell curve in my head.
Furthermore, if I could prove it, I don't know if it actually matters to the way the game plays.
Can any of the mathematical wizards here help me with either of those questions?
Thanks,
aja

 

[Jack Simth]

I don't have the full math readily accessable, and am not specifically familiar with the rule, but....
You have a 1 in 216 chance of rolling an 18; if that's what you need to hit your target, you've got less than 1/2 of 1 percent.
If you need a 16, 17, or 18 to hit your target (+2 bonus, from flanking, say), you have a roughly 4.6% chance - still not significant; about the same probability as rolling a 20 on a d20. One more +1, however, brings the probability up to 9.3%; a 4.7% increase; another, and you hit 16.2% (6.9% up from previous) - one more +, and you are up to a whopping 25.9% (up 9.7% from previous); another, and you've hit 37.5% (up 11.6%); yet another, and you have peak step increase at a 50% success chance (12.5% more); after that, the steps mirror, going downhill; the next step up is to 62.5% (12.5% increase again), the next, about 74.1% (11.6% increase...); the next, 83.8% (9.7% gain); the next, 90.7% (6.9% gain); then 95.4% (4.7% gain); then 98.1% (2.7% increase); followed by 99.5% (only roll that fails is most possible extreme, at a scant 1.4% increase); a + of some value gives the most % success benefit to a character where the + puts the centers between the roll of 10 and roll of 11 succeeds; a +2 has greatest impact on a character that would otherwise succeed on a 12 or more (gains steps 10 and 11; a full 25% probability increase); a +4, on a character that would otherwise succeed on a 13 or better (gain steps 9, 10, 11, 12; 48.2% of the rolls fall in that range). Five that same +2 to a character that succeeds on a roll of 15 or better, and he gains only steps 14 and 13 (4.7%+6.9%; 11.6% gain); give that +4 to a a character that succeeds on a roll of 16 or better, and he gains 15, 14, 13, and 12 (21.3% increase)

Mind you, I'm sure I'm quite late by now, and that this is all clear as mud...

 

[Nifft]

I believe, however, this makes flat bonuses worth a different amount depending on the skill of the character...if this makes any sense.

It makes total sense. Here's how. The difference is in probability space.

The "d20" difference between 10 and 12 is 10%, just like the difference between 16 and 18 is 10%. Each "bump" in DC or AC or whatever is worth exactly 5%. This is a uniform distribution. If you had a 50% chance of hitting 10, you have a 45% chance of hitting 11. This generalizes to: If you had an X% chance of hitting A, you have an X-5% chance of hitting A+1.

On a normal ("bell") distribution, the difference is NOT flat. You can make NO general statement about X% = A+1.

So, a +2 bonus is practically worthless at the low end of the curve (if you succeed on 7 or less), and is very valuable on the high end (if you require a 13 or higher to succeed), because both high and low numbers are rare.

-- N

 

[Coredump]

Unearthed Arcana introduces a variant rule that turns D20 into D666:

I understand this turns a flat probability curve into a bell curve, decreasing the randomness of the game.

Now that your answer has been given, let me address this assertion.

This is wrong. Wrong. WRONG.

This (for 90% of rolls) does *nothing* to change the 'randomness'. At least not in the way you are thinking.

You are thinking "but it makes it more likely to roll a 10, and much less likely to roll an 18, surely that removes randomness." That is *only* true if each result has a separate meaning. But for the vast majority of DnD rolls it is yes/no succeed/fail hit/miss. Thus it is straight percentage. If you need a 14 to hit, it doesn't matter if you roll a 14, or an 18. And a 13 is the same as a 9, or a 2.
For damage, it matters, because each number on the die is a different result. Not true for attacks, saves, and most skills.

What you *are* doing is changing the game a great deal. Now, if you need a 16 to hit, you will hit 25% of the time. If you use d666, and keep the number at a 16, you will now hit <5% of the time. But you can get the same result by having to roll a 20 in d20, the bell curve has *no meaning nor effect*, it is a straight yes/no roll. Heck, plug the percent into a random number generator and have at it.

If you change the number to a 14 on D666, so it is still 25%, you will get NO DIFFERENCE from using the D20. Sure, more of your misses will be 10 than will be 4, but who cares, they are still misses.

I hope that makes sense.

 

[Stalker0]

Keep in mind this variant also widens the gap between fighters and secondary fighters a great deal.

Depending on what level characters they are, a fighter have a +3 to attack over a rogue let's say. So static 15%. But as the numbers above showed, depending on what AC is required to hit, that can make a HUGE amount of difference in percentage to hit.

A good compromise is the 2d10 method. It still gives you a bell curve, but not as much of one.

 

[CyberSpyder]

I hope that makes sense.

Any change that makes the game more predictable makes it less random.

Switching to a 3d6 system instead of d20 makes the game more predictable, insofar as you can say with a great deal of certainty whether you will hit or miss on a given roll. Therefore, it makes it less random.

If this is insufficient demonstration, simply take the extreme case of rolling '10d1;' that is to say, narrowing the bell curve to an infinitely thin spike at the midpoint. In this case, you can rationally say that the game has zero randomness. Your stats are of utmost importance, and you will be able to definitively state before a 'roll' whether you hit or not.

Alternately, move things in the other direction - if the die roll is instead a "d100-40," there is significantly greater randomness, and the importance of personal stats recedes; you won't be able to predict a hit or a miss with much better than 50% accuracy.

That's all I got.

 

[Aust Diamondew]

Consider using 2d10 instead of 3d6 if you want slightly more 'randomness'.

 

[Coredump]

Switching to a 3d6 system instead of d20 makes the game more predictable, insofar as you can say with a great deal of certainty whether you will hit or miss on a given roll. Therefore, it makes it less random.

But it does *not* let you have any more certainty than using a D20. For any roll, D20, 2D10, D666, there is a straight percentage of hitting or missing. It does *not* matter which method you use to determine that percentage. Heck use D100, and get the *exact* same uncertainty. (or certainty)

Under the current rules, if you need to roll a 16 to hit, you have a straight 25% chance to hit. It does not matter if you use D20, D100, D4, D8, D12, D30, even D666 can be used. (with a very slight adjustment.) It is simply a straight percentage roll. The 'curve', or lack thereof, plays NO part.

Now lets look at useing D666. And you need to roll a 15. You say that the D666 makes it 'less random'. Untrue, it is *still* just a straight percentage, this time you will hit 9.25% of the time. But there is not less uncertainty than if you rolled a D20 and said you needed a 19.


The 'bell curve' *only* becomes important for rolls that are not yes/no. For instance, if the roll determines how long something lasts, or how effective it is, or how long it takes. *Then* it matters. For making saves, attacking, etc. It just doesn't matter


Now, it does have the effect that it makes hard things *really* hard, and easy things *really* easy. But that is not the same as removing uncertainty.

 

[General Barron]

But it does *not* let you have any more certainty than using a D20. For any roll, D20, 2D10, D666, there is a straight percentage of hitting or missing. It does *not* matter which method you use to determine that percentage. Heck use D100, and get the *exact* same uncertainty. (or certainty)

.....

The 'bell curve' *only* becomes important for rolls that are not yes/no. For instance, if the roll determines how long something lasts, or how effective it is, or how long it takes. *Then* it matters. For making saves, attacking, etc. It just doesn't matter.

Umm..... no. I understand what you seem to be saying: that for any given pass/fail dice roll, there is a certain percentage chance whether it will pass or fail. However, by "certainty" and "predictablity", others are referring to how "certain" you can be when you make a prediction like "I am going to hit this next attack".

If your % chance to make that attack lies somewhere around the 50% range, then you can't make such a statement with any more than 50% accuracy (which can hardly be considered 'accurate', when there are only 2 possiblities). However, if you have a very high or very low percentage chance to hit (say, 5% or 95%), then you CAN make such an assertion with reasonable accuracy (95% accuracy in the above example).

When rolling a 1d20, the probablity of getting any number from 1-20 is 5%. So if you say, "I'm going to roll a 10", and you roll a d20, you only have a 5% chance of being correct. However, if you, say, roll 3d6, your probability of getting a 10 is higher (12.5%).

This 'bell curve' effect that everyone is talking about means that you are much more likely to get numbers close to the middle of the die roll's possible result range then you are to get numbers on the edges. The mean result from many rolls will remain the same (should be 10.5 for 1d20), however, the chance of rolling that mean on any given die roll varies depending on how many dice you are rolling.

If the probability of getting this mean result were 100%, then the game could be considered "more predictable", and you would have "more certainty" when you made predictions like "I am going to hit". With 1d20, (mean result of many rolls == 10.5), your chance of rolling this mean is basically 10% (either a 10 or 11). With 3d6, the mean result of many rolls is also 10.5, however, the chance of rolling a 10 or 11 is 25%. Basically, you are more likely to get rolls in the 8-13 range with 3d6 than you are with 1d20, making things "more predictable", since the dice rolls are more likely to fall within a smaller range.

I'd try to explain more, but hopefully you'll understand what we mean by "more predictable", and instead we can continue to discuss exactly what this would mean to the game.

 

[Hodgie]

To support General Barron here:

Because you roll the d20 (or d666) so often, this will provide less randomness for the game. Granted each roll now just has different percentages of success, but over an entire combat you can be expected to average to 10.5 with more accuracy than a d20.