Variability in Dice Mechanics

I just read about an interesting technique for RPG dice rolls. Instead of manipulating difficulty, instead, manipulate variability.

For example, take a task in a standard D20 system. Generally, if performing that task under stressful conditions, the DM will either increase the target number (TN) or apply a penalty to the player's roll (mechanically, the same thing). This can have a chilling effect -- if the player judges the odds of success to be too small, they will probably not try at all for fear of failure.

For example, say a D20 character is +5 and is attempting a TN 14 task. They have a 60% chance of success -- not bad! Say conditions are terrible and the DM imposes a -5 penalty (or raises the TN to 19). The odds of success have decreased to 35%. If the penalty for failure is significant, most players won't even make the attempt.

What if instead, we could adjust the variability of the attempt?

I see three ways to do this.

1) The FUDGE system uses special dice labeled +1, 0, and -1. By adjusting the number of dice in the FUDGE pool added to the base roll, you adjust how variable it will be.
2) You can have a "good" die and a "bad" die (both the same kind of die). Roll both and retain only the lowest die. If you retained the good die, add it to the base roll. If you retained the bad die, subtract it from the base roll. By using a large die such as a D20, you create a highly random, variable result. If you use a small pair of dice like a D4 or D6, you have reduced the variability. The advantage of this method is that you retain the original possible range of results.
3) You should be able to add a fixed modifier and reduce the die size. For example, you could have 1d20+MOD vs. a TN. Or, you could have 1d12+4+MOD vs. the same TN. In the first case, the Minimum is 1+MOD, the maximum is 20+MOD, and the average is 10.5+MOD. In the second case, the minimum is 5+MOD, the maximum is 16+MOD, and the average remains 10.5+MOD. You've just moved the tail ends of the distribution closer to the center.

Usually, the players have the upper hand. After all, if they didn't, then most heroes would be short lived indeed! Thus, they are interested in reducing variability. The underdog is usually interested in increasing variability. Only through higher variability does the underdog have any chance of winning.

For example, take a poorly skilled character trying to hit a difficult TN (it could be a kobold trying to hit a high level fighter's AC). They may need a base roll of 18, 19, or 20 in order to actually succeed. If they use the lower-variability D12 method, then they CANNOT succeed. That lowly skilled individual wants the scenario to be as variable as possible!

Here's another example. A common D20 rule is allowing someone to "take 10." This is the ultimate in reducing variability; you're basically rolling 1d0+10. Most novices are not interested because they can't succeed. However, an expert is usually perfectly happy to take 10 -- they know that they will likely succeed and that variation just gives them a chance to fail.

If your dice mechanic allows the DM to adjust variability instead of difficulty, it gives them an interesting tool. In our original scenario, say the DM increased the variability due to difficult circumstances. A novice still has similar odds for success, and indeed, may even benefit from the increase in variability. But the expert is no longer facing a sure thing. This "levels" the playing field, which is handy for challenges that the entire party is expected to meet.