It's seems very common to use a 20 sided die to check the outcome of some ability or skill, at least among those that tend toward single-die results. This is as opposed to games that use many dice for a single check - those seem to use d6's a lot.

I like 20's. Each step represents about a 5% change in outcome, if you tend to assume that absolute success and absolute failure live at opposite ends of that roll (20 and 1).

But I have a different mechanic that I've used in a couple of home-brew games that I'd like to share and do procons for: 2d10.

* This provides a simple curve (triangle, really), making results of 2 or 20 pretty improbable (1 in 100 for each), and also means your players reliably roll in the 9 - 13 range nearly 50% of the time.

* It also translates into percentages pretty well and you just happen to have two tens in case you need to do any actuall % rolls in your game.

* If the number to be rolled against is 10, then you have a 55% chance of rolling higher -- you can still call that "baseline difficulty", just remember that you only have a 1 in 10 chance of getting a 17 or higher.

You can argue linear probability vs bell curve until you are blue in the face, but I'm more interested in some psychological aspects:

* Doubles make people feel good. Like they did something special.

* There are 10 sets of doubles, and statistically they occur about 1 every 10 rolls --often enough that you should see a few each game.

* What happens if you succeed your check and roll doubles? What if you fail your check and rolls doubles? People intuitively know that doubles on a success or failure would be extra good (or bad).

* If you scale the difficulty number up and down for different tasks, then the number of doubles above or below the mark also changes. The chances of a "critical result" automatically scale with difficulty in a natural way.

For example: if you have to roll a 17 or higher to succeed, then in addition to having a 10% chance of success, you have a 2% chance of critical success and an 8% chance of critical failure. If you only need to roll a 16 or higher, you now have a 15% chance of success, a 3% chance of critical success, and a 7% chance of critical failure.

* You can let players use special abilities (cards, character powers, etc) whenever they roll doubles on a success. You can even rank some of the powers with a number rating from 1 to 10, 1 being the most powerful. In other words -- a #5 power can only be used on doubles 5's (or less) when the skill check is successful. If your game allows for customization or accumulation of character powers over the course of the game -- well this allows for a very easy way to give out the goodies *and* keep the powers in check.

I used this in a game where you were allowed to auto-kill multiple weak opponents (of the same type) if you rolled doubles and hit, specifically 11 - the double #. Let me tell you how a player's eyes sparkle when they hit a group of rat-things with a double-5 and kill 6 of them in one crushing blow.

Of course this by no means needs to be relegated to only hack-and slash type games. Say you roll doubles while making an item, bargaining a trade, flying a plane, or whatever else.

The thing I like most about this system is that you, as the designer, can work an enormous amount of statistical chemistry on the game this way, and yet hide it all behind a veil of simplicity for the players. "Roll these two, add them together and beat that number." "If you get doubles on a win then good for you! If you fail, pray you don't get doubles." "There are some powers / augments / upgrades you can learn / evolve / equip. Their costs and use requirements are on the card."

Okay I've said my piece, now let me know what your favorite mechanics are, and why. *Or* critique my assessment as you see fit. Either way is good for me :)

--Patrick