One of the greatest criticisms to the d20 system is that it is full of extremes. Intrinsic in the d20 system is a uniform distribution of values 1-20 to which all have the same likelihood of being rolled (This probability value is 5%). This makes it just as likely to roll a natural 20, as a 10 or a 1. This for most people is not a bad thing. But if you have ever rolled badly consistently you know what it feels like to get killed due to unluckiness. These failures are often not only completely uncharacteristic to the characters’ abilities, but completely unrepresentative of the world’s physics. A uniform distribution is an unrealistic option to express a semi-realistic world. A normal distribution (or bell shaped curve) is a much better representation of reality. A normal distribution makes chance far more likely to be average then extreme, causes the world to function more predictably.
Taking 10 and 20 are game dynamics which are meant to correct this issue. Taking 10 can be done when a character has one chance but is not under any duress to do so. Taking 20 is an option which a character can take when they have nearly infinite tries available and is also not under duress. However useful taking 10 and 20 might be, it does not correct issues when a character IS under duress. It is the situations in which a character might die dependent on each role that needs to be corrected.
Situations like these are examples of this. A few of them might be an Archer that for a time can never hit the broad side of a barn for no reason, or a NPC that is extremely resistant to some PC’s spell just out of sheer luck. Another example of this would be the fighter who spends nearly all his 4 skill points a level on jump, and tries to finally use the skill and rolls a 2, killing himself where all the other characters can jump just fine. It is not that the DC to jump was hard for the fighter; it is just even though he is trained and quite good at jumping (where very few characters are) the d20 system makes extremes in success and failure so much more likely.
Now if this was just a game dynamic like any other game, it would be easier for this blatant unrealistic dynamic to exist due to its ease of use. However the nature of a roleplaying game is different. Characters understand themselves from the execution of their abilities. Also the characters understand the world by the nature of how it acts, and is interacted with. This is a huge point because d20 is so uniformly random it creates usually unwanted perceptions by the characters of effects that the DM never intended, and can not control in the future.
There are many examples of this to which I am sure most have experienced. You may be out on an adventure with your cohorts. There is some action you wish try take (You may have trained rigorously on it, or you may not). You find that you are unrealistically bad OR good at it due to d20 randomness, and it gives you a false sense of weakness or competency. This changes your perceptions of your ability, and therefore increases or decreases your likelihood to do such an action. It is easy to see why doing inappropriate actions are liable to get you killed. Your character my chalk it up to chance, but all too often it might get so extreme your character thinks they are cursed or something.
Giving a few examples of actions that warp a characters perception of themselves and their world might be climbing something to difficult for them, not tying someone up because you think you are horrible at it so you kill them because you have no choice, believing a commoner is immune to your spells because 10 of them have failed, having other cohorts think you are a terrible at hiding when you have just been wicked unlucky. These examples are limited only by your imagination and all of them are so much more likely because extremes are so much more possible then in real life.
There have been many different methods of correcting this issue. One method is to modify the nature of the dice rolled in order to emulate a d20. Rolling 2d10 is one example of this method. It creates a triangular distribution with a 1% chance at the both extremes 2 and 20; cutting 1. The sum of both 2d10s would replace the 20 roll, as well as changing critical roll chance probabilities. A second style of this method would be to use 3d6. This creates a more normally looking distribution, but clips the values 1,2,19,20 from chance.
Another method of creating a more realistic d system would be to change the very numbers on a die. This could be done by changing the values on a d50 or d30 to create repeat values making some value more common. The downside to this is you can not increase the rarity of one side. This will create a clumsy normal distribution, but it would still be more realistic then a 5% chance for every value.
Another method is to use a computer program or handheld to auto role values with whatever distribution you wish them to have. This would be easiest if every member at the table had the needed electronics at their disposable.
I have devised a few distributions that I believe might make a more realistic game.
I created so many because it is impossible to make a very close normal distribution out of a %d10’s. I find style3 to be my favorite out of all.
To explain each column:
d20 Dice Equivalent: This is the value of the die rolled from your 2d10 % roll.
Number of Chances: This is the number of chances out of a hundred of getting each value.
% Chance: This is the percentage chances of each value 1-20.
Low d100: This is the lower boundary value when finding the d20 equivalent from a d100 role.
High d100: This is the upper boundary value when finding the d20 equivalent from a d100 role.
Crit d20: Equivalent: Because I do not wish criticals to be distorted in probability due to the distortion in the d20, critical high and lows have been assigned in 5% increments; the same as the usual d20.
Low Crit: This is the low value of reaching a critical range, and usually the only value one needs to decide if there is a critical threat or not.
High Crit: This is a higher bound value for a critical range, but is not useful unless for example a 19 crit is different from a natural 20 crit.
One might ask how you use such a distribution chart at a table effectively without taking to much time deciding what your equivalent d20 value is.
One only needs 3 columns to do this, and one number normally. You print out on a piece of paper, low d100 and high d100 of the distribution of your choosing, and the equivalent d20 correspondently. You also write down at the top, your crit value. If you have a 18-20/x2 crit weapon, you would have to write down 86 as corresponding to the low crit value in the low crit table column.
Now you are off to the races. Just role d100 or 2d10 (interchangeable), and read the value on the chart. If you roll a 9, you d20 value is 5 as on style3. Want to know if you role a crit? Just role above an 86 with your 18-20/x2 crit weapon and it is an unconfirmed crit. This might seem slow at first, but try it out, you might be surprised as to how fast you get at it.
What does this do to the game?
This has a very startling effect to the game. It makes AC much more important. It makes skills more profound. It makes spells more potent or weak. Essentially it chances the very essence of the game. The power of the any value in D&D now becomes much more potent. Advantages become meaningful, where before they had a chance of having an effect in combat, they now are noticeable. It gives the DM more control over an encounter, and it gives PCs a more tangible idea of what skills and abilities do for them.
A great essay to understand what D&D was going for is here:
http://www.thealexandrian.net/creations/misc/d&d-calibrating.html
This is a telling quote:
Justin Alexander wrote: