2d6 Odds

I've been reading some Chainmail, so I figured I'd post the odds of getting various results on 2d6.

First, the odds of getting any given number:

odds for 7	6/36 =0.167
odds for 6 and 8	5/36 =0.139
odds for 5 and 9	4/36 =0.111
odds for 4 and 10	3/36 =0.083
odds for 3 and 11	2/36 =0.056
odds for 2 and 12	1/36 =0.028

These are the odds of hitting the TN or higher:

12: 1/36 = 0.028
11: 3/36 = 0.083
10: 6/36 = 0.167
9: 10/36 = 0.278
8: 15/36 = 0.417
7: 21/36 = 0.583
6: 26/36 = 0.722
5: 30/36 = 0.833
4: 33/36 = 0.917
3: 35/36 = 0.972
2: 36/36 = 1.000

Note that a +1 or 2 modifier gives relatively low benefits at the extreme ends of the scale. In the center of the scale though, small modifiers have large effects.

This can create a snowball effect very quickly, where one failed check that imposes a penalty on the next one practically ensures a slide into trouble. However, the slide slows down at some point when you reach the other tail end of the curve.

ADDENDUM:

Here's a look at a common LBB check, the morale roll. These TNs parallel many other OD&D 2d6 checks so the odds should be similar.

The modifiers for morale are given as:
BLESS: +1
LOYALTY: Up to +/- 2
CHARISMA affects loyalty base checks (again, mostly at +/-2, although some folks will have +4 with an 18) AND morale checks, so its possibly a double whammy.
So our total modifier is -4 to +5 (theoretically +7 with an 18 CHA).

Morale/Reaction Checks
2 Attempts to attack
3-5 Hostile reaction
6-8 Uncertain
9-11 Accepts offer
12 Enthusiast, Loyalty +3

Random Actions by Monsters
2-5: Negative Reaction
6-8: Uncertain Reaction
9-12: Positive Reaction

Cleric Turn Undead
7: Minor Turn
9: Major Turn
11: Best Turn