a way to think about 2d6OE here vs. 2d6OE there

[Zooko]

NOTE: There was a bug resulting in inaccurate values in this table originally. Sorry to everyone whom I misled. I, too, made a lot of tactical decisions based on this incorrect table. Too bad I didn't notice the table that Saber Cherry had already posted.

Anyway, this is now updated with correct information. Read the thread to find out what the bug was.


I was recently wondering what my chance of penetrating an enemy's magic resistance is. As per this thread , the formula is:

"(11+((magic skill of mage in relevant path-magical skill level needed for spell)/2)+2d6oe). Compare to resistance value: (mr+((the targets skill in relevant path(the path of the spell being resisted))/2)+2d6oe). Pen-value > res-value = ouch."

That is:

11 + x + 2d6OE >? y + 2d6OE

Where x is your penetration bonus and y is your target's magic resistance.

Now you can subtract 2d6OE from both sides and subtract y from both sides, leaving:

11 + x - y >? 2d6OE - 2d6OE

So if your penetration bonus is 3 and your target's magic resistance is 16, then the left-hand side of the equation is -2. Let's call the left hand side of the equation your "penetration advantage".

What is the right hand side? The right hand side of the equation is given by this table. The left hand side of this table is a result that can come from 2d6OE - 2d6OE and the rightmost column is the chance that 2d6OE - 2d6OE will be less than that. Therefore, when your penetration advantage is -2, your chance of getting through the magic resistance of the target is 21%.

The same analysis should work for to-hit rolls. Your attack value is your attack skill plus your weapon attack value minus your ambidexterity penalty for multiple weapons and etc. Your target's defense skill is etc. etc. Let "your attack advantage" be your fully adjusted attack minus your target's fully adjusted defense. Now look up that number on this table and you see the chance of hitting.

You can use this table for damage. Let your "average damage" be your fully adjusted damage value minus your target's fully adjusted protection. Now look at this table and think of 0 as being that you do your average damage (14% chance), 1 is that you do one more than your average damage (12% chance) and 5 is that you do 5 more than your average damage (2% chance). The right-hand column is the chance that you'll do less than that much. That is, 43% of the time, you'll do less than your average damage, 31% of the time you'll do less than (your average minus 1) and 98% of the time you'll do less than (your average damage plus 9).

-14:  0% --  1%
-13:  1% --  1%
-12:  1% --  2%
-11:  1% --  3%
-10:  1% --  3%
 -9:  2% --  5%
 -8:  2% --  6%
 -7:  3% --  8%
 -6:  3% -- 11%
 -5:  4% -- 14%
 -4:  5% -- 18%
 -3:  6% -- 24%
 -2:  7% -- 30%
 -1:  8% -- 38%
  0:  8% -- 46%
  1:  8% -- 54%
  2:  7% -- 62%
  3:  6% -- 70%
  4:  5% -- 76%
  5:  4% -- 82%
  6:  3% -- 86%
  7:  3% -- 89%
  8:  2% -- 92%
  9:  2% -- 94%
 10:  1% -- 95%
 11:  1% -- 97%
 12:  1% -- 97%
 13:  0% -- 98%
 14:  0% -- 99%

For historical purposes: Here's the original table I posted, which was generated by incorrectly adding one open-ended die and subtracting one open-ended die instead of adding two open-ended dice and subtracting two open-ended dices.

-10:  0% --  1%
 -9:  1% --  2%
 -8:  1% --  2%
 -7:  2% --  4%
 -6:  2% --  5%
 -5:  2% --  7%
 -4:  5% -- 10%
 -3:  7% -- 14%
 -2: 10% -- 21%
 -1: 12% -- 31%
  0: 14% -- 43%
  1: 12% -- 57%
  2: 10% -- 69%
  3:  7% -- 79%
  4:  5% -- 86%
  5:  2% -- 90%
  6:  2% -- 93%
  7:  2% -- 95%
  8:  1% -- 96%
  9:  1% -- 98%
 10:  0% -- 98%
 11:  0% -- 99%

I generated this table by the stupid approach of rolling thirty-two million dice and averaging the results, rather than by using actual probability theory. Here is the generator code:

http://zooko.com/tmp.py

(That file is now updated to not have the bug.)

P.S. Okay, enough wasting my time trying to make the tables lines up nicely. This BBS software and design really sucks.