success odds for differing rolls

probability roll+stat diff > threshold

||  || 1d6 || 1d10 || 3d6 || 1d8 || 1d12 || 3d8 || 1d10 || 1d20 ||
|| stat diff || vs 1d6 || Vs 5 || Vs 10 || Vs 1d8 || Vs 6 || Vs 13 || vs 1d10 || Vs 10 ||
|| -11 ||  ||  ||  ||  ||  || 0.00 ||  ||  ||
|| -10 ||  ||  ||  ||  ||  || 0.002 ||  || 0.00 ||
|| -9 ||  ||  ||  ||  ||  || 0.008 || 0.00 || 0.05 ||
|| -8 ||  ||  || 0.000 ||  ||  || 0.020 || 0.01 || 0.10 ||
|| -7 ||  ||  || 0.005 || 0.00 ||  || 0.039 || 0.03 || 0.15 ||
|| -6 ||  ||  || 0.019 || 0.02 || 0.00 || 0.068 || 0.06 || 0.20 ||
|| -5 || 0.00 || 0.00 || 0.046 || 0.05 || 0.08 || 0.109 || 0.10 || 0.25 ||
|| -4 || 0.03 || 0.10 || 0.093 || 0.09 || 0.17 || 0.164 || 0.15 || 0.30 ||
|| -3 || 0.08 || 0.20 || 0.162 || 0.16 || 0.25 || 0.234 || 0.21 || 0.35 ||
|| -2 || 0.17 || 0.30 || 0.259 || 0.23 || 0.33 || 0.316 || 0.28 || 0.40 ||
|| -1 || 0.28 || 0.40 || 0.375 || 0.33 || 0.42 || 0.406 || 0.36 || 0.45 ||
|| 0 || 0.42 || 0.50 || 0.500 || 0.44 || 0.50 || 0.500 || 0.45 || 0.50 ||
|| 1 || 0.58 || 0.60 || 0.625 || 0.56 || 0.58 || 0.594 || 0.55 || 0.55 ||
|| 2 || 0.72 || 0.70 || 0.741 || 0.67 || 0.67 || 0.684 || 0.64 || 0.60 ||
|| 3 || 0.83 || 0.80 || 0.838 || 0.77 || 0.75 || 0.766 || 0.72 || 0.65 ||
|| 4 || 0.92 || 0.90 || 0.907 || 0.84 || 0.83 || 0.836 || 0.79 || 0.70 ||
|| 5 || 0.97 || 1.00 || 0.954 || 0.91 || 0.92 || 0.891 || 0.85 || 0.75 ||
|| 6 || 1.00 ||  || 0.981 || 0.95 || 1.00 || 0.932 || 0.90 || 0.80 ||
|| 7 ||  ||  || 0.995 || 0.98 ||  || 0.961 || 0.94 || 0.85 ||
|| 8 ||  ||  || 1.000 || 1.00 ||  || 0.980 || 0.97 || 0.90 ||
|| 9 ||  ||  ||  ||  ||  || 0.992 || 0.99 || 0.95 ||
|| 10 ||  ||  ||  ||  ||  || 0.998 || 1.00 || 1.00 ||
|| 11 ||  ||  ||  ||  ||  || 1.00 ||  ||  ||
||  || 2d6 || 1d10 || 3d6 || 2d8 || 1d12 || 3d8 || 2d10 || 1d20 ||
|| Std-dev || 2.42 || 2.87 || 2.96 || 3.24 || 3.45 || 3.97 || 4.06 || 5.77 ||

http://www.splitreflection.com/~cal/RP/D10/diceoptions.gif