Stretching the d20

The d20 is granular enough for me.

Each number in the d20 represents a 5% chance.

I really don't feel the need to distinguish "stealth 46%" from "stealth 48%", for example.

I could even use smaller dice, but I play D&Dish games and I like the d20.

However, there are a few situations in which the d20 is not enough: when you want to assign chances that are extremely high (over 95%) or low (below 5%) instead of saying "automatic success/failure".

Now, you might say you don't really need that; some situations are just impossible.

But D&D/AD&D has many such cases - thief skills (and system shock) going to 99%, 1% of low-Strength folks bending bars, and optional rules to allow someone with THAC0 20 to hit negative AC.

In other words, the d20 is only insufficient in extreme cases; I'd be happy to use it in every other circumstance (which is about 90% of the time).

Like Moldvay says, "there is always a chance". Before this section, he mentions another example: "Looking down into the chasm, your character can estimate that he has a 98% chance of dying, no saving throw, if he jumps."

I can imagine many other circumstances where 1% chances would be better than either 0 or 5%. 

For example, if you want fumbles in your game, it is ludicrous that you fail ridiculously 5% of the time, especially if you're a experienced fighter. 

Even for spell mishaps, 5% chance is just too much. A powerful mage casts several spells a day and shouldn't be dealing with fumbles every other day. 

I also love critical hits; 5% of the time seems fine for having "maximum damage", for example, but I'd love having the occasional "super crit" with double or triple damage (or maybe permanent damage, etc.)

There are several ways to "stretch" the d20 at the edges if you want more than 20 possibilities. I've discussed a d100 conversion in the last post, now I'll present an alternative:

Whenever you roll a natural 20, you can try again with a +10 bonus, picking the best result.

Conversely, a natural 1 forces you to roll again with a -10 penalty and pick the worst result.

This way, a d20 can easily generate results form -10 to 30, and beyond (you'd need several 20s in a row, but you get get to 100 once every 500 billion rolls...).

This would give you a small chance to hit even -10 AC.

If using crits, you could easy say that a margin of 30, for example, will give you triple maximum damage. Awesome, but rare.

Notice this can work for ANY kind of dice. 

For example, I hate the idea that you add your Charisma bonus to a reaction roll, making an "immediate attack" impossible (although this is not how I use the table). 

But you could re-roll a natural 1 or 6 with a -3/+3 bonus, which will allow an immediate attack by anyone, if rarely.

This also allows you to assign bonuses and penalties to enemies' reactions without taking some possibilities out of the picture.

This is similar to "exploding dice", but for me it has the advantage of not taking any result off the table. Rolling a 21 is possible, but less likely than rolling 20. Rolling a 22 is even less likely, and so on.

Note: there is a 70% off Frog God sale going on. If you like HUGE lists of monsters, I can recommend Monstrosities. Tome of Horrors Complete also looks interesting. Let me know if there are other products you recommend - I might get something for myself for Christmas! (affiliate links).