Skill Check

Success = 1 - 1 / (1 + exp(0.03 * (Attack - Defense))

where "exp" returns e raised to the power of the number that follows, the constant e equals 2.71828182845904, the base of the natural logarithm. EXP is a standard function for both Microsoft Excel and LibreOffice.

From http://www.calloffate.com/forum/forum_posts.asp?TID=191&PID=29738 :

Answer: srand - Casting spells uses a slightly different skill check curve than that used for all other skill checks. It has the same midpoint, but is steeper through the middle. So once you are over the 50/50 point, your casting gets reliable much faster than with a normal skill check curve. But conversely, under the 50/50 point your casting is much less reliable than with the normal skill check curve. I just found this out tonight, myself.

Example
Using this formula for a skill check of 500 generates the following chances of success:

You can easily generate success %s for any specific skill level using a spreadsheet by putting the skill level into cell A1, the difficulty in cell A2, and inserting the following formula into cell A3:

=1 - 1 / (1 + EXP(0.03 * (A1 - A2)))