Probability that an Attacker hits a Defender

The table below details the probability that an attacker will hit a defender when the attacker's skill is equal to X and the defender's skill is equal to Y. Various systems are examined.

AD&D 3E: 1d20 + Attacker THAC0 > 10 + Defender AC
Note: X represents THAC0 and all other attack modifiers. Y represents Armor Class, Dex and Size modifiers, etc.

GURPS: 3d6 <= Attacker's Weapon skill. If successful, defender can avoid the hit with 3d6 <= Active Defense skill
Note: GURPS skills are not generally rated from 1 to 10, so add 5 to each X and Y to determine the actual GURPS skill level used to arrive at the probability. Note also that defensive skills tend to be lower than offensive skills in GURPS.

HERO: 3d6 <= 11 + Attacker OCV - Defender DCV
Note: HERO OCV and DCV are generally better than 2, so add 2 to each X and Y to determine the actual HERO System OCVs and DCVs used to arrive at the probability.

WEG Star Wars: Attacker rolls a number of d6 equal to his attack skill. To avoid getting hit, the defender must roll higher than this on his defensive skill.
Note: the incremental skill pips used in Star Wars (D+1, D+2) are not accounted for. X and Y are integral numbers of dice.

Others:

A system used by many Internet freeware games, opposed rolls of 2d6 + Skill.

The Bookworms and Bastards method, opposed rolls of 2d6 * Skill.

X Y AD&D 3E GURPS HERO/Champions WEG Star Wars 2d6 + X vs 2d6 + Y 2d6 * X vs 2d6 * Y
1 1 0.550 0.084 0.625 0.417 0.444 0.444
1 2 0.500 0.078 0.500 0.093 0.336 0.088
1 3 0.450 0.069 0.375 0.012 0.239 0.025
1 4 0.400 0.058 0.259 0.001 0.159 0.008
1 5 0.350 0.046 0.162 0.000 0.097 0.002
1 6 0.300 0.035 0.093 0.000 0.054 0.000
1 7 0.250 0.024 0.046 0.000 0.027 0.000
1 8 0.200 0.015 0.019 0.000 0.012 0.000
1 9 0.150 0.009 0.005 0.000 0.004 0.000
1 10 0.100 0.004 0.005 0.000 0.001 0.000
2 1 0.600 0.147 0.741 0.838 0.556 0.877
2 2 0.550 0.136 0.625 0.444 0.444 0.444
2 3 0.500 0.120 0.500 0.152 0.336 0.204
2 4 0.450 0.101 0.375 0.036 0.239 0.088
2 5 0.400 0.081 0.259 0.006 0.159 0.050
2 6 0.350 0.061 0.162 0.001 0.097 0.025
2 7 0.300 0.042 0.093 0.000 0.054 0.016
2 8 0.250 0.026 0.046 0.000 0.027 0.008
2 9 0.200 0.015 0.019 0.000 0.012 0.005
2 10 0.150 0.008 0.005 0.000 0.004 0.002
3 1 0.650 0.235 0.838 0.973 0.664 0.962
3 2 0.600 0.217 0.741 0.779 0.556 0.764
3 3 0.550 0.192 0.625 0.454 0.444 0.444
3 4 0.500 0.162 0.500 0.192 0.336 0.276
3 5 0.450 0.130 0.375 0.061 0.239 0.161
3 6 0.400 0.097 0.259 0.015 0.159 0.088
3 7 0.350 0.067 0.162 0.003 0.097 0.063
3 8 0.300 0.042 0.093 0.000 0.054 0.042
3 9 0.250 0.024 0.046 0.000 0.027 0.025
3 10 0.200 0.012 0.019 0.000 0.012 0.021
4 1 0.700 0.340 0.907 0.997 0.761 0.987
4 2 0.650 0.314 0.838 0.939 0.664 0.877
4 3 0.600 0.278 0.741 0.743 0.556 0.697
4 4 0.550 0.234 0.625 0.460 0.444 0.444
4 5 0.500 0.188 0.500 0.220 0.336 0.322
4 6 0.450 0.141 0.375 0.083 0.239 0.204
4 7 0.400 0.097 0.259 0.025 0.159 0.143
4 8 0.350 0.061 0.162 0.006 0.097 0.088
4 9 0.300 0.035 0.093 0.001 0.054 0.073
4 10 0.250 0.017 0.046 0.000 0.027 0.050
5 1 0.750 0.454 0.954 1.000 0.841 0.995
5 2 0.700 0.419 0.907 0.988 0.761 0.940
5 3 0.650 0.370 0.838 0.909 0.664 0.821
5 4 0.600 0.313 0.741 0.718 0.556 0.657
5 5 0.550 0.250 0.625 0.464 0.444 0.444
5 6 0.500 0.188 0.500 0.242 0.336 0.349
5 7 0.450 0.130 0.375 0.104 0.239 0.250
5 8 0.400 0.081 0.259 0.037 0.159 0.179
5 9 0.350 0.046 0.162 0.011 0.097 0.130
5 10 0.300 0.023 0.093 0.003 0.054 0.088
6 1 0.800 0.567 0.981 1.000 0.903 0.999
6 2 0.750 0.524 0.954 0.998 0.841 0.962
6 3 0.700 0.463 0.907 0.975 0.761 0.877
6 4 0.650 0.391 0.838 0.884 0.664 0.764
6 5 0.600 0.313 0.741 0.700 0.556 0.633
6 6 0.550 0.234 0.625 0.467 0.444 0.444
6 7 0.500 0.162 0.500 0.260 0.336 0.367
6 8 0.450 0.101 0.375 0.122 0.239 0.276
6 9 0.400 0.058 0.259 0.048 0.159 0.204
6 10 0.350 0.029 0.162 0.016 0.097 0.161
7 1 0.850 0.672 0.995 1.000 0.946 1.000
7 2 0.800 0.621 0.981 1.000 0.903 0.979
7 3 0.750 0.549 0.954 0.995 0.841 0.927
7 4 0.700 0.463 0.907 0.962 0.761 0.843
7 5 0.650 0.370 0.838 0.862 0.664 0.731
7 6 0.600 0.278 0.741 0.685 0.556 0.610
7 7 0.550 0.192 0.625 0.469 0.444 0.444
7 8 0.500 0.120 0.500 0.274 0.336 0.390
7 9 0.450 0.069 0.375 0.137 0.239 0.303
7 10 0.400 0.034 0.259 0.059 0.159 0.236
8 1 0.900 0.760 1.000 1.000 0.973 1.000
8 2 0.850 0.702 0.995 1.000 0.946 0.987
8 3 0.800 0.621 0.981 0.999 0.903 0.950
8 4 0.750 0.524 0.954 0.990 0.841 0.877
8 5 0.700 0.419 0.907 0.948 0.761 0.806
8 6 0.650 0.314 0.838 0.844 0.664 0.697
8 7 0.600 0.217 0.741 0.673 0.556 0.587
8 8 0.550 0.136 0.625 0.471 0.444 0.444
8 9 0.500 0.078 0.500 0.286 0.336 0.413
8 10 0.450 0.039 0.375 0.152 0.239 0.322
9 1 0.950 0.823 1.000 1.000 0.988 1.000
9 2 0.900 0.760 1.000 1.000 0.973 0.992
9 3 0.850 0.672 0.995 1.000 0.946 0.962
9 4 0.800 0.567 0.981 0.998 0.903 0.918
9 5 0.750 0.454 0.954 0.983 0.841 0.857
9 6 0.700 0.340 0.907 0.934 0.761 0.764
9 7 0.650 0.235 0.838 0.828 0.664 0.678
9 8 0.600 0.147 0.741 0.664 0.556 0.572
9 9 0.550 0.084 0.625 0.473 0.444 0.444
9 10 0.500 0.042 0.500 0.297 0.336 0.428
10 1 1.000 0.865 1.000 1.000 0.996 1.000
10 2 0.950 0.799 1.000 1.000 0.988 0.995
10 3 0.900 0.706 1.000 1.000 0.973 0.975
10 4 0.850 0.596 0.995 1.000 0.946 0.940
10 5 0.800 0.477 0.981 0.995 0.903 0.877
10 6 0.750 0.358 0.954 0.976 0.841 0.821
10 7 0.700 0.247 0.907 0.922 0.761 0.750
10 8 0.650 0.155 0.838 0.814 0.664 0.657
10 9 0.600 0.088 0.741 0.655 0.556 0.563
10 10 0.550 0.044 0.625 0.474 0.444 0.444