The Boring Math Post

 I've mentioned already that for Missions & Mayhem, I came up with what may not be a novel mechanic for general proficiency checks, but at least one that's fairly uncommon in my experience. Characters all start with Basic level proficiency in all areas. This is both due to action movie logic (everyone has a chance to fly that helicopter), but also for game expedience. One problem with d20 Modern (and other 3E-forward games) is the way feats and skill training can prevent you from doing things that maybe every character should at least be able to try. 

At Basic level, if you want to perform an action covered by a proficiency in combat or other tense situations (usually no or few rolls in non-tense situations), you roll 2d4. 

At Skilled level, you roll 2d6.

At Advanced level, you roll 2d8. 

Difficulties for most tasks range up the odd numbers from 5 to 13. I haven't put anything at 15 yet, but that's still a possibility. There may be one or two things on an even number (an 8, for example), but mostly I've used the odd numbers since that's what the Classic D&D Turn Undead chart uses. 

Certain situational factors may give advantage or disadvantage on rolls. For these general proficiency 2dX rolls, advantage means rolling three dice and taking the best two. Disadvantage is rolling three dice and taking the worst two. I messed around with rolling 2d6 and 2d6 but it's easier to just add one die to the roll than have people roll twice (or roll four dice in two different colors). 

Using anydice.com to calculate these, I have the following percent chances of success for the various task difficulties: 

 

Difficulty:	5	7	9	11	13	15
2d4	62.50	18.75	–	–	–	–
2d4 Advantage	82.81	39.06	–	–	–	–
2d4 Disadvantage	35.94	6.25	–	–	–	–
2d6	83.33	58.33	27.78	8.33	–	–
2d6 Advantage	94.15	80.56	52.31	19.91	–	–
2d6 Disadvantage	64.35	31.94	10.65	1.85	–	–
2d8	90.63	76.56	56.25	32.81	15.63	4.69
2d8 Advantage	97.85	91.80	79.30	58.59	33.78	11.91
2d8 Disadvantage	77.93	53.71	30.08	13.48	4.49	0.78

 

One more factor to consider is that there is a Gamble mechanic.  I came up with this as a way to add some player choice into the chase mechanic (which is best 3 of 5 contested rolls). Then I realized it also works for other 2dX checks. Why not gamble when trying to defuse a bomb, hoodwink the Prime Minister, or land a plane after the pilot passed out from eating bad fish? 

For the Gamble, players can pick one of their ability scores. They roll a d20. If they get their score or less, they get a +1 on the related general proficiency check. If they roll over, they get a -1 penalty to the check. A character can gamble on each ability score once per game session. 

This way, even if you're rolling 2d4, you've got a slight chance to get a 9 if you need it. Or a 13 if you're rolling 2d6.