This blog post won't make much sense to you, if you're not a paper-and-pencil table-top role-playing-gamer. I apologize for that, but this is what I've been thinking about. I'm thinking about the use of 1d20 versus 3d6 as a resolution mechanic in the game.
Last night was the second session of a Pathfinder Adventure Path called Shattered Star. Our characters are first level with nothing better for gear than the gear we started with (which is of course crap). Our party has an arcane spell caster, an investigator, a paladin, and my fighter. No dedicated healer.
Potential spoilers ahead if you're going to play Shattered Star, but it's crazy early in the campaign, and I won't give away stuff that you have to find out on your own.
We were looking for a particular woman that the Pathfinder Venture Captain in the area asked us to find. They had some kind of business arrangement, and the Venture Captain wanted to know what happened to the woman who had disappeared. And we found a building where she might be staying. Just wanting to talk to her, we were surprised (spoilers incoming:) that the first door we went to had a couple armed guards that came out to meet us. We tried to explain that we were looking for this girl with zero violent intentions... we just wanted to talk. But they attacked us. Taking the penalties so that we could knock them out instead of killing them, we suffered damage, and just tied them up. So this was fight #1. And we spent resources on it.
(still more spoilers:) Thinking that this was weird, we went to the other door (because the first door was apparently a guard house with no doors to the inside). We opened the door to find the floor broken and missing. Below floor level was city sewage. Three goblins attacked us. This was fight #2. We spent some more resources, took a little more damage, and still just wanted to talk to this woman.
(still more spoilers:) We went into the next room to find most of its floor missing too, and three more goblins to kill. Fight #3. More resources spent. We went into the next room to find no foes, but still a missing floor with sewage at the bottom. The final room on that floor was still floor-less, and we got talked at by some sort of snake/goblin thing that claimed to be the king. It didn't attack us though, and we were still hoping to talk to this girl. At this point I thought we might be rescuing the girl or something.
(spoilers:) We climbed a ladder to a second floor, and found the woman we were looking for, but she was suited for being tied up in a padded room. She was the queen of the goblins. Two of her goblins attacked us, and she did too. This is fight #4. She did some serious damage to us. But we managed to defeat her without killing her. The snake thing came back out to take something from us, and we fought it too. Fight #5, though I'll admit it didn't sap us as much as the other fights. At this point our band of first level characters were out of spells, and the paladin and my fighter had used their only cure potions. My fighter had 4 hit points left, and the paladin had 3 hit points left. We thought we were done. But we were wrong.
(probably the last paragraph of spoilers:) We got outside the building, and some well geared woman with three well armed and armored goons comes out and says that she'll let us go if we give her a magical item that the girl we were looking for had. This magic item is something we (as the players) recognized as central to the plot of the whole adventure path, and we didn't want to give it up... so we fought...
No more spoilers: We were out of resources, low on hit points, and facing our sixth consecutive fight as level 1 characters against an equal number of level 2 characters. I'm told this is balanced... but I disagree. We fought, and then in addition to the fight being unbalanced to begin with, our dice were trying to kill us. We were rolling our 1d20 to see if we could hit our foes, and 7 out of 10 rolls were 5 or below. Hooray for the law of independent probability.
Three of our four characters ended up in the negative hit points (unconscious), and the fourth ran away with the magic item. We probably should have died. The bad guys should have just killed us, and the campaign should have been over. The one survivor could have continued I suppose. I assert this was a poorly written encounter if you consider that the characters are first level, have shit gear, and (minor spoiler:) might not find the healing potions hidden along the way through that set of fights. We did not find them.
But beyond the encounter being poorly designed, the dice really were against us. We rolled a lot of ridiculously low rolls that meant we were ineffective. We did almost nothing to the bad guys in that last fight, and it was frustrating to sit and watch as everything we tried to do failed while they whittled us down from our already pathetic state of being.
The fact that 1d20 can so thoroughly ruin an evening of what is supposed to be fun is why I'm writing this whole thing. It's a question of linear probability instead of a bell curve.
Linear Probability: the d20 system
Skill at striking a foe in combat in the d20 system (and Pathfinder in specific for my example) means having a static number as a modifier that you add to a roll with one twenty-sided die. My fighter with his bow against those foes last night was rolling 1d20+7. I'm pretty sure the thugs had an armor class of 18, and the female foe had an AC of 14. So against the thugs, my character would have to roll 11 or higher to hit them... exactly 50% of the possible values on the die. A 50% chance. And because the rolls have no effect on each other, it is just as possible for me roll ten 5's in a row as it is to roll an 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. There's no tendency on a single die. Any value is just as likely as the others, every time you roll.
To me, this is awful. Some weak mook NPC with a +1 to hit, compared to our paladin who has a +4 to hit has most of the decision about whether they actually hit made by the d20. The number of times each of them hits over the course of ten rounds might just as easily be that the mook hit all ten times, and the paladin hit zero times. The d20 controls it completely, where the modifier has so little effect on it that it barely matters.
And the way the system is designed, the defenses increase at the same rate as the hit modifier, so it REALLY doesn't matter. It's all about the stupid damnable d20. I hate it.
Bell Curve: using 3d6 in GURPS
Rolling 3 six-sided dice means a total number of possible combinations of 216. 54 of those combinations add up to either 10 or 11. A little over 48% of the possible combinations are represented by 9 to 12 which is four of the possible results out of sixteen (the numbers 3 to 18). So 25% of the results occur 50% of the time. This is the bell curve. Most of the time you roll 3d6, you'll have a result near the middle of the possible results. Rolling a 3 can only happen with exactly one of the 216 possible combinations, giving it a 0.46% chance of happening. Reaching one of the extremes is very unlikely. It happens... but not often.
So what does this mean? In GURPS you have skills that have a number, and your goal is to roll less than or equal to that number to succeed. So if you got yourself a skill of 12 with a sword (above the average of 10), you would have a ~74% chance of succeeding when you roll those 3d6. And because of the bell curve (the tendency to have a result closer to the middle), skill makes much more of a difference than the die does. If you increase your skill to 15 for example (3 points higher than the 12, just like the +4 in Pathfinder was three points higher than the +1), your chance of success goes up to a little over 95%.
Comparison
Pathfinder...
Attack Mod +7 versus an armor class of 13 means that a roll of 6 or better would succeed. So this would mean a 75% chance of success.
GURPS...
Skill 12 means a 74% chance of success.
In the session last night of Pathfinder, my archer with a +7 attack mod (which is huge for a first level character) rolled high enough to hit once out of four shots in that final fight. A 25% success rate for something that was supposed to be closer to 75% (one of the shots was against the more armored foes, which would have been the 50% chance).
That one example shows that in real life it's possible with a non-bell-curved single die to deviate in a huge way from the original probability. And this character that I designed so intently to have a huge attack modifier was subject to the die, and it didn't matter how much skill he had at firing a bow.
I can say with confidence that the person with a skill of 12 in GURPS rolling 3d6 four times would have been more likely to actually roll close to the predicted probability. Because the bell curve has a tendency toward the middle results. The likelihood is that the skill 12 person would have hit 3 of the 4 shots instead of 1.
The bell curve makes it more predictable. So instead of the easy possibility of a foe with a +1 attack modifier doing better than the character with a +4 attack modifier, skill actually matters when you use a system with a bell curve. The person with a skill of 15 in GURPS in about 20% more likely to hit than the person with the 12. And the die rolls will come close to that. Spending character resources to improve a skill in GURPS has a more reliable benefit, and the system isn't built so that attack modifiers and defenses progress at the same rate.
Conclusion
The d20 system of resolution in games sucks. It is more likely to lead to nights of frustration playing a game... which is supposed to be a fun fantasy escape from reality for a little while. Why choose that kind of randomness?
Incomplete Idea
Just use 3d6 instead of 1d20 if you're going to play a d20 game. Rolling a 3 is an auto-fail or critical-fail, and rolling an 18 is auto-success or critical success. If Pathfinder is balanced such that middle-value rolls should succeed, then it doesn't matter that we can't get a result of 19 or 20.
With a Paladin attacking with a +4 mod, his rolls would likely have ranged from 13 to 16... which is a tiny bit low compared to the ACs that our foes had... which makes me think Armor Class would need to be tweaked. Or perhaps the replacement for 1d20 would be 3d6+2? Hmm.
Well... like I said: incomplete idea.
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