Rules Junkies: 2d10 vs d20

[Pbartender]

While in D20 it just removes one chance of being hit, in 2d10 it could remove any number of possibilities of being hit, and is impossible to predict since it depends on where it is on the bell curve.

Actually, the increase in probability for 2d10 is tricky, but not that tough if you plot it out.

For 1d20, the probability curve is a flat, horizontal line. The probability to hit any number from 1-20 is 5%, and never increases or decreases.

For 2d10, the probability curve is linear. It goes up at a 45 degree angle until it hits the maximum probability, and then goes back down at a 45 degree angle. The percentages to roll equal to or higher than for a particular DC using 2d10 go as follows...

21 - 0% (+0%)
20 - 1% (+1%)
19 - 3% (+2%)
18 - 6% (+3%)
17 - 10% (+4%)
16 - 15% (+5%)
15 - 21% (+6%)
14 - 28% (+7%)
13 - 36% (+8%)
12 - 45% (+9%)
11 - 55% (+10%)
10 - 64% (+9%)
9 - 72% (+8%)
8 - 79% (+7%)
7 - 85% (+6%)
6 - 90% (+5%)
5 - 94% (+4%)
4 - 97% (+3%)
3 - 99% (+2%)
2 - 100% (+1%)
1 - 100% (+0%)

You can see that you'll get the biggest benefit from a +1 bonus when performing a tack that has a DC in the middle range of your ability. You'll get much least benefit when performing tasks that are excessively easy or excessively difficult. That sort of model does make some sense, when you think about it.

 

[Malin Genie]

I'm not sure if you're being sarcastic or not... so I'll just assume not and maybe make an idiot out of myself.

Nope, not sarcastic, just somewhat stupefied...

Look at some of the treasure or encounter tables from the original Gygax games. All of the rare stuff is at 1 or 100. Of course, those are often weighted as well (frex, an entry might be 46-48), so as to alter the probabilities that way.

But encounter and treasure tables don't have means.

All I meant by my comment was that I was surprised that people being told the mean of a distribution would then infer that results near the mean are more likely. It could be the case (2d10 roll) or not (1d20 roll) or even the opposite (roll a d6, the result is 1 on a 1-2, 10 on a 3, 11 on a 4 and 20 on a 5-6, so the 'end results' are more likely, but the mean is the same.)

 

[AeroDm]

Looking at PBartender's chart I realized that the chance of rolling equal or higher than a 12 (45%) is the same for both 2d10 and d20. So any time that the target number is 12 or lower, the 2d10 grants more successes. In most games that I've seen challenges seem to land so that the best at any task has to roll about a 10, meaning combat would become more predictable.

As has been stated many times, critical threat ranges become more powerful than critical multipliers, but since critical damage becomes less common as well the higher numbers will be more powerful intrinsically.

 

[LightPhoenix]

But encounter and treasure tables don't have means.

But the dice you roll for them do.

All I meant by my comment was that I was surprised that people being told the mean of a distribution would then infer that results near the mean are more likely.

People surprise me both with what they don't know and what they do know on a daily basis.

 

[Angel Tarragon]

Likewise, it has always bothered me that an 8 strength character could break something that an 18 strength character failed at because of the variance of the die.

In the Players Option: Skills and Powers book, this was brought up as well. It mentions allowing characters that have a hiher score than 15 in their subability score of Muscle to allow another attempt.

By modifying this you can have reflect in the third edition rules by saying that a character with a 14 or higher in strength can make a number of attempts equal to half her stregth bonus, rounded down.

 

[AeroDm]

I actually rather like that... It is very simple and solves a lot of the issues that aren't annoying enough to be problems but still creep into play constantly.

 

[blargney the second]

I'm thinking of switching to 2d10, so I've been following this thread with a lot of interest. For those who have actually tried it, which do you prefer?

-blarg