Qualifying for character classes in Advanced Dungeons & Dragons

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Qualifying for character classes in Advanced Dungeons & Dragons Part 2: Multiple Attempts

In the previous article we looked at how to find the probability of qualifying for the various AD&D character classes. Here we expand on that to find the probabilities of qualifying in multiple attempts.
Given a probability $p$ of qualifying in a single attempt, the probability of qualifying exactly $r$ times in $n$ attempts has a binomial distribution: $$\frac{n!}{r!(n-r)!}\;p^r(1-p)^{n-r}.$$
The probability of qualifying at least once in $n$ attempts is therefore $$\sum_{r=1}^n\frac{n!}{r!(n-r)!}\;p^r(1-p)^{n-r}.$$
Alternatively, since the probability of failing to qualify in $n$ attempts is $(1-p)^n$, it follows that the probability of qualifying at least once is $1-(1-p)^n$.
The following table shows the results for each type of character for 1 to 8 attempts.

Unordered Ordered
Character Attempts 3d6 3/4d6 3d6 3/4d6


Cleric 1 97.140% 99.805% 61.280% 85.434%
2 99.918% 100.000% 85.008% 97.878%
3 99.998% 100.000% 94.195% 99.691%
4 100.000% 100.000% 97.752% 99.955%
5 100.000% 100.000% 99.130% 99.993%
6 100.000% 100.000% 99.663% 99.999%
7 100.000% 100.000% 99.870% 100.000%
8 100.000% 100.000% 99.949% 100.000%


Druid 1 30.868% 73.455% 2.873% 13.622%
2 52.208% 92.954% 5.663% 25.388%
3 66.961% 98.130% 8.372% 35.552%
4 77.159% 99.504% 11.004% 44.331%
5 84.210% 99.868% 13.561% 51.914%
6 89.084% 99.965% 16.044% 58.464%
7 92.454% 99.991% 18.455% 64.122%
8 94.783% 99.998% 20.798% 69.009%


Fighter 1 97.140% 99.805% 58.305% 84.033%
2 99.918% 100.000% 82.616% 97.451%
3 99.998% 100.000% 92.752% 99.593%
4 100.000% 100.000% 96.978% 99.935%
5 100.000% 100.000% 98.740% 99.990%
6 100.000% 100.000% 99.475% 99.998%
7 100.000% 100.000% 99.781% 100.000%
8 100.000% 100.000% 99.909% 100.000%


Paladin 1 3.966% 24.171% 0.094% 1.378%
2 7.774% 42.500% 0.188% 2.736%
3 11.432% 56.398% 0.282% 4.076%
4 14.944% 66.937% 0.376% 5.398%
5 18.317% 74.929% 0.470% 6.701%
6 21.556% 80.989% 0.564% 7.987%
7 24.667% 85.584% 0.658% 9.254%
8 27.655% 89.069% 0.751% 10.505%


Ranger 1 3.256% 29.351% 0.161% 2.927%
2 6.407% 50.088% 0.321% 5.768%
3 9.454% 64.738% 0.481% 8.526%
4 12.403% 75.088% 0.641% 11.204%
5 15.255% 82.400% 0.800% 13.803%
6 18.015% 87.566% 0.959% 16.326%
7 20.685% 91.215% 1.118% 18.775%
8 23.268% 93.794% 1.277% 21.152%


Magic-user 1 97.140% 99.805% 61.280% 85.434%
2 99.918% 100.000% 85.008% 97.878%
3 99.998% 100.000% 94.195% 99.691%
4 100.000% 100.000% 97.752% 99.955%
5 100.000% 100.000% 99.130% 99.993%
6 100.000% 100.000% 99.663% 99.999%
7 100.000% 100.000% 99.870% 100.000%
8 100.000% 100.000% 99.949% 100.000%


Illusionist 1 7.562% 35.744% 0.372% 2.915%
2 14.553% 58.712% 0.742% 5.745%
3 21.015% 73.470% 1.111% 8.492%
4 26.988% 82.953% 1.479% 11.160%
5 32.509% 89.046% 1.845% 13.749%
6 37.613% 92.962% 2.210% 16.264%
7 42.331% 95.477% 2.574% 18.704%
8 46.692% 97.094% 2.936% 21.074%


Thief 1 97.140% 99.805% 61.280% 85.434%
2 99.918% 100.000% 85.008% 97.878%
3 99.998% 100.000% 94.195% 99.691%
4 100.000% 100.000% 97.752% 99.955%
5 100.000% 100.000% 99.130% 99.993%
6 100.000% 100.000% 99.663% 99.999%
7 100.000% 100.000% 99.870% 100.000%
8 100.000% 100.000% 99.949% 100.000%


Assassin 1 58.571% 93.483% 6.395% 27.134%
2 82.837% 99.575% 12.382% 46.906%
3 92.889% 99.972% 17.985% 61.312%
4 97.054% 99.998% 23.230% 71.810%
5 98.780% 100.000% 28.140% 79.459%
6 99.494% 100.000% 32.735% 85.033%
7 99.791% 100.000% 37.037% 89.094%
8 99.913% 100.000% 41.064% 92.053%


Monk 1 7.625% 39.576% 0.372% 3.781%
2 14.669% 63.489% 0.742% 7.419%
3 21.176% 77.938% 1.111% 10.920%
4 27.186% 86.669% 1.479% 14.288%
5 32.738% 91.945% 1.845% 17.529%
6 37.867% 95.133% 2.210% 20.647%
7 42.605% 97.059% 2.574% 23.647%
8 46.981% 98.223% 2.936% 26.534%


Bard 1 0.027% 1.581% 0.002% 0.146%
2 0.053% 3.138% 0.003% 0.292%
3 0.080% 4.670% 0.005% 0.437%
4 0.106% 6.177% 0.007% 0.583%
5 0.133% 7.661% 0.009% 0.728%
6 0.159% 9.121% 0.010% 0.873%
7 0.186% 10.558% 0.012% 1.018%
8 0.213% 11.973% 0.014% 1.162%


Half-elf Cleric 1 75.236% 93.253% 58.443% 84.445%
2 93.868% 99.545% 82.730% 97.580%
3 98.481% 99.969% 92.823% 99.624%
4 99.624% 99.998% 97.018% 99.941%
5 99.907% 100.000% 98.761% 99.991%
6 99.977% 100.000% 99.485% 99.999%
7 99.994% 100.000% 99.786% 100.000%
8 99.999% 100.000% 99.911% 100.000%


Half-orc Cleric 1 92.909% 99.643% 21.788% 51.230%
2 99.497% 99.999% 38.829% 76.215%
3 99.964% 100.000% 52.157% 88.400%
4 99.997% 100.000% 62.581% 94.343%
5 100.000% 100.000% 70.734% 97.241%
6 100.000% 100.000% 77.110% 98.654%
7 100.000% 100.000% 82.098% 99.344%
8 100.000% 100.000% 85.998% 99.680%


Half-elf Druid 1 30.868% 73.455% 2.873% 13.622%
2 52.208% 92.954% 5.663% 25.388%
3 66.961% 98.130% 8.372% 35.552%
4 77.159% 99.504% 11.004% 44.331%
5 84.210% 99.868% 13.561% 51.914%
6 89.084% 99.965% 16.044% 58.464%
7 92.454% 99.991% 18.455% 64.122%
8 94.783% 99.998% 20.798% 69.009%


Dwarf Fighter 1 95.464% 99.763% 30.568% 62.123%
2 99.794% 99.999% 51.792% 85.653%
3 99.991% 100.000% 66.528% 94.566%
4 100.000% 100.000% 76.760% 97.942%
5 100.000% 100.000% 83.864% 99.220%
6 100.000% 100.000% 88.796% 99.705%
7 100.000% 100.000% 92.221% 99.888%
8 100.000% 100.000% 94.599% 99.958%


Elf Fighter 1 73.219% 93.089% 39.643% 73.306%
2 92.828% 99.522% 63.570% 92.874%
3 98.079% 99.967% 78.012% 98.098%
4 99.486% 99.998% 86.729% 99.492%
5 99.862% 100.000% 91.990% 99.864%
6 99.963% 100.000% 95.165% 99.964%
7 99.990% 100.000% 97.082% 99.990%
8 99.997% 100.000% 98.239% 99.997%


Gnome Fighter 1 75.222% 93.253% 48.858% 79.235%
2 93.861% 99.545% 73.845% 95.688%
3 98.479% 99.969% 86.624% 99.105%
4 99.623% 99.998% 93.159% 99.814%
5 99.907% 100.000% 96.501% 99.961%
6 99.977% 100.000% 98.211% 99.992%
7 99.994% 100.000% 99.085% 99.998%
8 99.999% 100.000% 99.532% 100.000%


Half-elf Fighter 1 94.949% 99.368% 58.035% 83.968%
2 99.745% 99.996% 82.390% 97.430%
3 99.987% 100.000% 92.610% 99.588%
4 99.999% 100.000% 96.899% 99.934%
5 100.000% 100.000% 98.699% 99.989%
6 100.000% 100.000% 99.454% 99.998%
7 100.000% 100.000% 99.771% 100.000%
8 100.000% 100.000% 99.904% 100.000%


Halfling Fighter 1 73.678% 93.193% 30.747% 63.877%
2 93.071% 99.537% 52.040% 86.951%
3 98.176% 99.968% 66.786% 95.286%
4 99.520% 99.998% 76.999% 98.297%
5 99.874% 100.000% 84.071% 99.385%
6 99.967% 100.000% 88.969% 99.778%
7 99.991% 100.000% 92.360% 99.920%
8 99.998% 100.000% 94.709% 99.971%


Half-orc Fighter 1 91.247% 99.481% 23.950% 53.550%
2 99.234% 99.997% 42.164% 78.424%
3 99.933% 100.000% 56.016% 89.978%
4 99.994% 100.000% 66.550% 95.345%
5 99.999% 100.000% 74.561% 97.838%
6 100.000% 100.000% 80.654% 98.996%
7 100.000% 100.000% 85.287% 99.533%
8 100.000% 100.000% 88.811% 99.783%


Half-elf Ranger 1 3.256% 29.351% 0.161% 2.927%
2 6.407% 50.088% 0.321% 5.768%
3 9.454% 64.738% 0.481% 8.526%
4 12.403% 75.088% 0.641% 11.204%
5 15.255% 82.400% 0.800% 13.803%
6 18.015% 87.566% 0.959% 16.326%
7 20.685% 91.215% 1.118% 18.775%
8 23.268% 93.794% 1.277% 21.152%


Elf Magic-user 1 97.089% 99.804% 51.230% 80.163%
2 99.915% 100.000% 76.214% 96.065%
3 99.998% 100.000% 88.400% 99.219%
4 100.000% 100.000% 94.342% 99.845%
5 100.000% 100.000% 97.241% 99.969%
6 100.000% 100.000% 98.654% 99.994%
7 100.000% 100.000% 99.344% 99.999%
8 100.000% 100.000% 99.680% 100.000%


Half-elf Magic-user 1 97.140% 99.805% 61.280% 85.434%
2 99.918% 100.000% 85.008% 97.878%
3 99.998% 100.000% 94.195% 99.691%
4 100.000% 100.000% 97.752% 99.955%
5 100.000% 100.000% 99.130% 99.993%
6 100.000% 100.000% 99.663% 99.999%
7 100.000% 100.000% 99.870% 100.000%
8 100.000% 100.000% 99.949% 100.000%


Gnome Illusionist 1 6.269% 33.908% 0.312% 2.749%
2 12.144% 56.319% 0.622% 5.421%
3 17.652% 71.130% 0.932% 8.021%
4 22.814% 80.920% 1.241% 10.549%
5 27.652% 87.389% 1.548% 13.008%
6 32.188% 91.665% 1.855% 15.399%
7 36.439% 94.492% 2.161% 17.724%
8 40.423% 96.359% 2.466% 19.985%


Dwarf Thief 1 94.713% 99.731% 26.858% 59.262%
2 99.720% 99.999% 46.503% 83.404%
3 99.985% 100.000% 60.871% 93.239%
4 99.999% 100.000% 71.380% 97.246%
5 100.000% 100.000% 79.067% 98.878%
6 100.000% 100.000% 84.689% 99.543%
7 100.000% 100.000% 88.802% 99.814%
8 100.000% 100.000% 91.809% 99.924%


Elf Thief 1 96.171% 99.771% 50.920% 80.558%
2 99.853% 99.999% 75.912% 96.220%
3 99.994% 100.000% 88.178% 99.265%
4 100.000% 100.000% 94.198% 99.857%
5 100.000% 100.000% 97.152% 99.972%
6 100.000% 100.000% 98.602% 99.995%
7 100.000% 100.000% 99.314% 99.999%
8 100.000% 100.000% 99.663% 100.000%


Gnome Thief 1 97.089% 99.804% 51.230% 80.163%
2 99.915% 100.000% 76.214% 96.065%
3 99.998% 100.000% 88.400% 99.219%
4 100.000% 100.000% 94.342% 99.845%
5 100.000% 100.000% 97.241% 99.969%
6 100.000% 100.000% 98.654% 99.994%
7 100.000% 100.000% 99.344% 99.999%
8 100.000% 100.000% 99.680% 100.000%


Half-elf Thief 1 97.140% 99.805% 61.280% 85.434%
2 99.918% 100.000% 85.008% 97.878%
3 99.998% 100.000% 94.195% 99.691%
4 100.000% 100.000% 97.752% 99.955%
5 100.000% 100.000% 99.130% 99.993%
6 100.000% 100.000% 99.663% 99.999%
7 100.000% 100.000% 99.870% 100.000%
8 100.000% 100.000% 99.949% 100.000%


Halfling Thief 1 96.883% 99.802% 43.225% 73.874%
2 99.903% 100.000% 67.766% 93.174%
3 99.997% 100.000% 81.699% 98.217%
4 100.000% 100.000% 89.610% 99.534%
5 100.000% 100.000% 94.101% 99.878%
6 100.000% 100.000% 96.651% 99.968%
7 100.000% 100.000% 98.098% 99.992%
8 100.000% 100.000% 98.920% 99.998%


Half-orc Thief 1 92.909% 99.643% 21.788% 51.230%
2 99.497% 99.999% 38.829% 76.215%
3 99.964% 100.000% 52.157% 88.400%
4 99.997% 100.000% 62.581% 94.343%
5 100.000% 100.000% 70.734% 97.241%
6 100.000% 100.000% 77.110% 98.654%
7 100.000% 100.000% 82.098% 99.344%
8 100.000% 100.000% 85.998% 99.680%


Dwarf Assassin 1 32.381% 79.058% 3.337% 20.044%
2 54.277% 95.614% 6.563% 36.070%
3 69.082% 99.081% 9.682% 48.884%
4 79.094% 99.808% 12.696% 59.130%
5 85.864% 99.960% 15.609% 67.322%
6 90.441% 99.992% 18.426% 73.872%
7 93.536% 99.998% 21.148% 79.109%
8 95.629% 100.000% 23.780% 83.296%


Elf Assassin 1 51.151% 88.806% 6.798% 29.827%
2 76.137% 98.747% 13.135% 50.757%
3 88.343% 99.860% 19.040% 65.445%
4 94.306% 99.984% 24.544% 75.752%
5 97.218% 99.998% 29.674% 82.984%
6 98.641% 100.000% 34.455% 88.059%
7 99.336% 100.000% 38.911% 91.621%
8 99.676% 100.000% 43.064% 94.120%


Gnome Assassin 1 57.852% 93.361% 5.619% 25.884%
2 82.235% 99.559% 10.923% 45.069%
3 92.512% 99.971% 15.928% 59.287%
4 96.844% 99.998% 20.652% 69.826%
5 98.670% 100.000% 25.111% 77.636%
6 99.439% 100.000% 29.319% 83.425%
7 99.764% 100.000% 33.291% 87.715%
8 99.900% 100.000% 37.039% 90.895%


Half-elf Assassin 1 58.571% 93.483% 6.395% 27.134%
2 82.837% 99.575% 12.382% 46.906%
3 92.889% 99.972% 17.985% 61.312%
4 97.054% 99.998% 23.230% 71.810%
5 98.780% 100.000% 28.140% 79.459%
6 99.494% 100.000% 32.735% 85.033%
7 99.791% 100.000% 37.037% 89.094%
8 99.913% 100.000% 41.064% 92.053%


Half-orc Assassin 1 31.003% 78.002% 3.291% 19.982%
2 52.394% 95.161% 6.473% 35.971%
3 67.154% 98.935% 9.551% 48.765%
4 77.337% 99.766% 12.527% 59.003%
5 84.363% 99.948% 15.406% 67.195%
6 89.211% 99.989% 18.190% 73.750%
7 92.556% 99.998% 20.882% 78.995%
8 94.864% 99.999% 23.486% 83.193%


Half-elf Bard 1 0.027% 1.581% 0.002% 0.146%
2 0.053% 3.138% 0.003% 0.292%
3 0.080% 4.670% 0.005% 0.437%
4 0.106% 6.177% 0.007% 0.583%
5 0.133% 7.661% 0.009% 0.728%
6 0.159% 9.121% 0.010% 0.873%
7 0.186% 10.558% 0.012% 1.018%
8 0.213% 11.973% 0.014% 1.162%


Half-elf Cleric/Fighter 1 75.038% 93.249% 43.189% 75.215%
2 93.769% 99.544% 67.725% 93.857%
3 98.445% 99.969% 81.665% 98.477%
4 99.612% 99.998% 89.583% 99.623%
5 99.903% 100.000% 94.082% 99.906%
6 99.976% 100.000% 96.638% 99.977%
7 99.994% 100.000% 98.090% 99.994%
8 99.998% 100.000% 98.915% 99.999%


Half-orc Cleric/Fighter 1 69.795% 92.831% 17.741% 47.931%
2 90.877% 99.486% 32.334% 72.888%
3 97.244% 99.963% 44.339% 85.883%
4 99.168% 99.997% 54.214% 92.649%
5 99.749% 100.000% 62.336% 96.173%
6 99.924% 100.000% 69.018% 98.007%
7 99.977% 100.000% 74.515% 98.962%
8 99.993% 100.000% 79.036% 99.460%


Half-elf Cleric/Fighter/Magic-user 1 73.268% 93.152% 33.545% 68.110%
2 92.854% 99.531% 55.837% 89.830%
3 98.090% 99.968% 70.652% 96.757%
4 99.489% 99.998% 80.497% 98.966%
5 99.863% 100.000% 87.039% 99.670%
6 99.964% 100.000% 91.387% 99.895%
7 99.990% 100.000% 94.276% 99.966%
8 99.997% 100.000% 96.196% 99.989%


Half-elf Cleric/Ranger 1 3.256% 29.351% 0.161% 2.927%
2 6.407% 50.088% 0.321% 5.768%
3 9.454% 64.738% 0.481% 8.526%
4 12.403% 75.088% 0.641% 11.204%
5 15.255% 82.400% 0.800% 13.803%
6 18.015% 87.566% 0.959% 16.326%
7 20.685% 91.215% 1.118% 18.775%
8 23.268% 93.794% 1.277% 21.152%


Half-elf Cleric/Magic-user 1 75.042% 93.250% 45.393% 76.468%
2 93.771% 99.544% 70.180% 94.463%
3 98.445% 99.969% 83.716% 98.697%
4 99.612% 99.998% 91.108% 99.693%
5 99.903% 100.000% 95.144% 99.928%
6 99.976% 100.000% 97.348% 99.983%
7 99.994% 100.000% 98.552% 99.996%
8 99.998% 100.000% 99.209% 99.999%


Half-orc Cleric/Thief 1 79.540% 97.012% 16.139% 45.854%
2 95.814% 99.911% 29.674% 70.682%
3 99.143% 99.997% 41.024% 84.126%
4 99.825% 100.000% 50.542% 91.405%
5 99.964% 100.000% 58.524% 95.346%
6 99.993% 100.000% 65.218% 97.480%
7 99.998% 100.000% 70.832% 98.636%
8 100.000% 100.000% 75.539% 99.261%


Half-orc Cleric/Assassin 1 17.116% 59.696% 2.182% 17.127%
2 31.303% 83.756% 4.317% 31.321%
3 43.061% 93.453% 6.405% 43.084%
4 52.807% 97.361% 8.447% 52.833%
5 60.884% 98.937% 10.445% 60.911%
6 67.580% 99.571% 12.399% 67.606%
7 73.129% 99.827% 14.311% 73.154%
8 77.728% 99.930% 16.181% 77.752%


Elf Fighter/Magic-user 1 73.137% 93.087% 35.044% 69.587%
2 92.784% 99.522% 57.807% 90.750%
3 98.062% 99.967% 72.593% 97.187%
4 99.479% 99.998% 82.197% 99.144%
5 99.860% 100.000% 88.436% 99.740%
6 99.962% 100.000% 92.488% 99.921%
7 99.990% 100.000% 95.121% 99.976%
8 99.997% 100.000% 96.831% 99.993%


Half-elf Fighter/Magic-user 1 75.038% 93.249% 43.189% 75.215%
2 93.769% 99.544% 67.725% 93.857%
3 98.445% 99.969% 81.665% 98.477%
4 99.612% 99.998% 89.583% 99.623%
5 99.903% 100.000% 94.082% 99.906%
6 99.976% 100.000% 96.638% 99.977%
7 99.994% 100.000% 98.090% 99.994%
8 99.998% 100.000% 98.915% 99.999%


Gnome Fighter/Illusionist 1 6.210% 33.885% 0.242% 2.489%
2 12.034% 56.288% 0.483% 4.916%
3 17.496% 71.100% 0.724% 7.282%
4 22.619% 80.893% 0.965% 9.590%
5 27.424% 87.367% 1.204% 11.840%
6 31.931% 91.648% 1.443% 14.034%
7 36.158% 94.478% 1.682% 16.174%
8 40.122% 96.349% 1.920% 18.260%


Dwarf Fighter/Thief 1 72.650% 93.127% 22.643% 55.604%
2 92.520% 99.528% 40.159% 80.290%
3 97.954% 99.968% 53.709% 91.249%
4 99.440% 99.998% 64.190% 96.115%
5 99.847% 100.000% 72.299% 98.275%
6 99.958% 100.000% 78.571% 99.234%
7 99.989% 100.000% 83.423% 99.660%
8 99.997% 100.000% 87.177% 99.849%


Elf Fighter/Thief 1 63.313% 90.632% 34.832% 69.930%
2 86.541% 99.122% 57.531% 90.958%
3 95.062% 99.918% 72.324% 97.281%
4 98.188% 99.992% 81.964% 99.182%
5 99.335% 99.999% 88.246% 99.754%
6 99.756% 100.000% 92.340% 99.926%
7 99.911% 100.000% 95.008% 99.978%
8 99.967% 100.000% 96.747% 99.993%


Gnome Fighter/Thief 1 74.781% 93.237% 37.948% 71.751%
2 93.640% 99.543% 61.495% 92.020%
3 98.396% 99.969% 76.107% 97.746%
4 99.596% 99.998% 85.174% 99.363%
5 99.898% 100.000% 90.800% 99.820%
6 99.974% 100.000% 94.291% 99.949%
7 99.994% 100.000% 96.458% 99.986%
8 99.998% 100.000% 97.802% 99.996%


Half-elf Fighter/Thief 1 75.038% 93.249% 43.189% 75.215%
2 93.769% 99.544% 67.725% 93.857%
3 98.445% 99.969% 81.665% 98.477%
4 99.612% 99.998% 89.583% 99.623%
5 99.903% 100.000% 94.082% 99.906%
6 99.976% 100.000% 96.638% 99.977%
7 99.994% 100.000% 98.090% 99.994%
8 99.998% 100.000% 98.915% 99.999%


Halfling Fighter/Thief 1 73.575% 93.189% 28.394% 61.950%
2 93.017% 99.536% 48.726% 85.522%
3 98.155% 99.968% 63.284% 94.491%
4 99.512% 99.998% 73.709% 97.904%
5 99.871% 100.000% 81.174% 99.202%
6 99.966% 100.000% 86.520% 99.697%
7 99.991% 100.000% 90.347% 99.885%
8 99.998% 100.000% 93.088% 99.956%


Half-orc Fighter/Thief 1 69.795% 92.831% 17.741% 47.931%
2 90.877% 99.486% 32.334% 72.888%
3 97.244% 99.963% 44.339% 85.883%
4 99.168% 99.997% 54.214% 92.649%
5 99.749% 100.000% 62.336% 96.173%
6 99.924% 100.000% 69.018% 98.007%
7 99.977% 100.000% 74.515% 98.962%
8 99.993% 100.000% 79.036% 99.460%


Elf Fighter/Magic-user/Thief 1 63.286% 90.631% 30.791% 66.382%
2 86.521% 99.122% 52.101% 88.698%
3 95.051% 99.918% 66.849% 96.201%
4 98.183% 99.992% 77.057% 98.723%
5 99.333% 99.999% 84.121% 99.571%
6 99.755% 100.000% 89.010% 99.856%
7 99.910% 100.000% 92.394% 99.951%
8 99.967% 100.000% 94.736% 99.984%


Half-elf Fighter/Magic-user/Thief 1 73.268% 93.152% 33.545% 68.110%
2 92.854% 99.531% 55.837% 89.830%
3 98.090% 99.968% 70.652% 96.757%
4 99.489% 99.998% 80.497% 98.966%
5 99.863% 100.000% 87.039% 99.670%
6 99.964% 100.000% 91.387% 99.895%
7 99.990% 100.000% 94.276% 99.966%
8 99.997% 100.000% 96.196% 99.989%


Elf Magic-user/Thief 1 74.924% 93.240% 42.928% 75.586%
2 93.712% 99.543% 67.428% 94.039%
3 98.423% 99.969% 81.411% 98.545%
4 99.605% 99.998% 89.391% 99.645%
5 99.901% 100.000% 93.945% 99.913%
6 99.975% 100.000% 96.544% 99.979%
7 99.994% 100.000% 98.028% 99.995%
8 99.998% 100.000% 98.874% 99.999%


Half-elf Magic-user/Thief 1 75.042% 93.250% 45.393% 76.468%
2 93.771% 99.544% 70.180% 94.463%
3 98.445% 99.969% 83.716% 98.697%
4 99.612% 99.998% 91.108% 99.693%
5 99.903% 100.000% 95.144% 99.928%
6 99.976% 100.000% 97.348% 99.983%
7 99.994% 100.000% 98.552% 99.996%
8 99.998% 100.000% 99.209% 99.999%


Gnome Illusionist/Thief 1 6.269% 33.908% 0.312% 2.749%
2 12.144% 56.319% 0.622% 5.421%
3 17.652% 71.130% 0.932% 8.021%
4 22.814% 80.920% 1.241% 10.549%
5 27.652% 87.389% 1.548% 13.008%
6 32.188% 91.665% 1.855% 15.399%
7 36.439% 94.492% 2.161% 17.724%
8 40.423% 96.359% 2.466% 19.985%