Why don't 3e and 4e use percentile dice for skills?

[Elder-Basilisk]

I do want to address the notion that +3 to skills is unimportant in 4E. That really depends on the style of DM. 4E gives tons of examples on how to use skills within combat for disarming traps and devices, avoiding hazards, disabling arcane instruments or portals, or discerning information about your environment or monsters. If you DM is giving you encounters where all you are doing is rolling attacks, then maybe he should try spicing things up a little. I think this style of encounter is where 4E shines, and skills become less useless.

Hmm, I'm of the opinion that the 4e skill system and everything remotely connected to it--especially skill challenges--is a steaming pile of garbage that needs to be shoved out the airlock as soon as possible. But putting that aside, I think you are misunderstanding my argument.

It is not that +3 to a skill doesn't matter. Rather it is that +3 to a skill is still unlikely to make a difference in a single session. (I think it is probably close to the smallest bump to a skill that will actually matter as well, but that is separate). Here's why. Every time you roll the skill that you have +3 to, there is an 85% chance that the +3 bonus makes no difference and you fail even with it or you would have succeeded without it. Before you exceed a 50% chance that the +3 bonus will be the difference between success and failure for at least one roll, you need to roll that skill five times. Now, you will sometimes use a skill five times in one session, but there are a lot of other times when you won't use any one particular skill five times in the same session. By contrast, you need to make 14 attack rolls before +1 to hit is likely to turn at least one hit that session into a miss. But, you will usually make at least 14 attack rolls per session, maybe more. That's why +1 to hit for a feat is good and +3 to a skill check for the same cost is less impressive. And it's why +2% is not likely to impress anyone--you will probably not make the same kind of roll 34 times in any session.

 

[ggroy]

you will probably not make the same kind of roll 34 times in any session.

In my present 4E game, the person playing the wizard character rolls arcana skill checks at least 15 to 20 times per game session. (Sometimes even more than 20 times).

 

[Elder-Basilisk]

In the example of blowing up the complex, that shouldn't just be a random result of the die but something that would be an event (or possibility) planned by the DM, or if the players come up with a very valid plan to do so that the DM decides to go with.

And that's the problem with excess granularity. If you are running your combat system with a d1000 and extra dice for sustain or whatever, you need for there to be a variety of outcomes between 900 and 1000, otherwise there's no point to using d1000 instead of d100 or d100 instead of d20. But once you've granted that you need an escalating scale of "even awesomer than awesome" results as you obtain rarer and rarer results, you start needing results that you (and I) think should more properly be the results of story and planning than simply rolling 1000 on d1000 followed by a 12 on 2d6. For actual gaming, I don't want the dice to be determining anything that should be rarer than a natural 20. And if there is no difference between the 96-100 results, then there's no point in carrying the extra numbers when I do addition.

 

[ggroy]

Here's why. Every time you roll the skill that you have +3 to, there is an 85% chance that the +3 bonus makes no difference and you fail even with it or you would have succeeded without it.

How exactly did you calculate this 85% chance figure?

 

[Cadfan]

He assumed that 85% of the possible outcomes will be things that would have either been a success even without the +3, or things that are a failure in spite of the +3.

In other words, if you need a 15 to succeed, and you have a base +5, you will fail on a 1 to 9 and succeed on a 10 to 20. If you take a skill focus feat that gives you a +3 to the relevant skill, you now fail on a 1 to 6, and succeed on a 7 to 20.

For values of 1 to 6, you failed on both checks. For values of 10 to 20, you succeeded on both checks. Only the 7, 8, and 9 were altered in their outcome.

Note that this reasoning only works on checks that involve a single check versus a static DC where degree of failure is irrelevant. If you care about degree of success (knowledge, certain athletics, etc), then +3 always matters. If you are making an opposed check (do these still exist?), the math is different. If you care about consistency or trustworthiness of outcomes, the way you care about your skill will cause you to want to use different math as well in interpreting the advantages of a +3.

Personally, I'm not a huge fan of the +3 feats, because I'd rather take one of the +2 or +1 feats that gives some non numerical bonus. But this is how they work.

 

[ggroy]

Before you exceed a 50% chance that the +3 bonus will be the difference between success and failure for at least one roll, you need to roll that skill five times.

How exactly did you determine this?

By contrast, you need to make 14 attack rolls before +1 to hit is likely to turn at least one hit that session into a miss.

How exactly did you determine this?

What are your starting assumptions that went into these calculations?

 

[Cadfan]

ggroy- for the first one, he took his 85% chance that the +3 won't matter, then calculated the chance that an event that's 85% likely will happen X times in a row, and ran it until he got to about 50%.

The sequence is, .85, .723, .614, .522, .444. At this point it is 44.4% likely that no roll will have been turned into a success from a miss by the addition of +3, and 55.6% likely that one will have.

For the second, with the attack rolls, he did the same thing with a 95% chance that your attack roll's success or failure is unchanged by the addition of a +1. The sequence is,

.95, .9025, .857, .815, .774, .735, .698, .663, .630, .599, .569, .540, .513, .488

And that's the 14th item on the list where the chance of never getting a miss changed to a hit drops below 50%.

 

[ggroy]

He assumed that 85% of the possible outcomes will be things that would have either been a success even without the +3, or things that are a failure in spite of the +3.

In other words, if you need a 15 to succeed, and you have a base +5, you will fail on a 1 to 9 and succeed on a 10 to 20. If you take a skill focus feat that gives you a +3 to the relevant skill, you now fail on a 1 to 6, and succeed on a 7 to 20.

For a skill check with a DC of 30 and a character with a base +5, the fail is on 1 to 20. With a skill focus feat that gives a +3 to the relevant skill, the fail is still on 1 to 20. Essentially 100% of all possible outcomes will be the same regardless of the +3.

 

[ggroy]

ggroy- for the first one, he took his 85% chance that the +3 won't matter, then calculated the chance that an event that's 85% likely will happen X times in a row, and ran it until he got to about 50%.

The sequence is, .85, .723, .614, .522, .444. At this point it is 44.4% likely that no roll will have been turned into a success from a miss by the addition of +3, and 55.6% likely that one will have.

For the second, with the attack rolls, he did the same thing with a 95% chance that your attack roll's success or failure is unchanged by the addition of a +1. The sequence is,

.95, .9025, .857, .815, .774, .735, .698, .663, .630, .599, .569, .540, .513, .488

And that's the 14th item on the list where the chance of never getting a miss changed to a hit drops below 50%.

This can actually be made more precise. The actual probability distribution is the geometric distribution.

Geometric distribution - Wikipedia, the free encyclopedia

Essentially what you're looking for is the number of times something doesn't happen (with probability 1-p), until it actually happens (with probability p). The average number of times something doesn't happen until it actually happens, is exactly 1/p with variance (1-p)/p^2.

For the first example above, p=0.15. The average number of rolls until the +3 matters is 6.67 rolls.

For the second example above, p=0.05. The average number of rolls until the +1 matters is 20 rolls.

 

[ggroy]

ggroy- for the first one, he took his 85% chance that the +3 won't matter, then calculated the chance that an event that's 85% likely will happen X times in a row, and ran it until he got to about 50%.

The sequence is, .85, .723, .614, .522, .444. At this point it is 44.4% likely that no roll will have been turned into a success from a miss by the addition of +3, and 55.6% likely that one will have.

Technically the figures in that sequence should be multiplied by 0.15, in order to satisfy the probability theory axiom that the probabilities of all exhaustive possible outcomes add up to 1.

.1275, .1084, .0921, .0783, etc ...

For the second, with the attack rolls, he did the same thing with a 95% chance that your attack roll's success or failure is unchanged by the addition of a +1. The sequence is,

.95, .9025, .857, .815, .774, .735, .698, .663, .630, .599, .569, .540, .513, .488

And that's the 14th item on the list where the chance of never getting a miss changed to a hit drops below 50%.

Same story here, where the figures in that sequence should be multiplied by 0.05.

.0475, .04513, .04287, .04073, etc ...

In general, these examples satisfy the probabilities P(k) = p(1-p)^(k-1), where k=1, 2, 3, .... to infinity. If you sum up P(k) from k=1 to infinity, you will get exactly 1. (Hint: Use the infinite geometric series 1 + x + x^2 + x^3 + ... = 1/(1-x), where |x| < 1 ).

To get the mean (average) expectation value of the probability distribution, you sum up k*P(k) from k=1 to infinity which should give you 1/p. (Hint: Use the infinite series 1 + 2x + 3x^2 + 4x^3 + ... = 1/(1-x)^2, where |x| < 1 ).