[DGD] Damage Weapons and Stuff (Math and Code)

[Ben Chambers]

Does this idea sound plausible?

The damage of weapons are specified by giving the mean and the standard
deviation.  The skills and other aspects of the character can modify these.
For example, if a player is more skilled and dealing damaging blows, it
would increase the mean.  If he can do more damage, but it is riskier the
mean and standard deviation are increased.  If he is being really careful
aiming accurately, his standard deviation may be decreased but the mean may
change as well.  An example of the standard deviation code is presented
below (it is written in C++ for testing purposes, but I would obviuosly
translate it into LPC for use in a MUD):

double l[310] = { .5000, .5040, .5080, .5120, .5160, .5199, .5239, .5279,
.5319, .5359,
                  .5398, .5438, .5478, .5517, .5557, .5596, .5636, .5675,
.5714, .5753,
                  .5793, .5832, .5871, .5910, .5948, .5987, .6026, .6064,
.6103, .6141,
                  .6179, .6217, .6255, .6293, .6331, .6368, .6406, .6443,
.6480, .6517,
                  .6554, .6591, .6628, .6664, .6700, .6736, .6772, .6808,
.6844, .6879,
                  .6915, .6950, .6985, .7019, .7054, .7088, .7123, .7157,
.7190, .7224,
                  .7257, .7291, .7324, .7357, .7389, .7422, .7454, .7486,
.7517, .7549,
                  .7580, .7611, .7642, .7673, .7704, .7734, .7764, .7794,
.7823, .7852,
                  .7881, .7910, .7939, .7967, .7995, .8023, .8051, .8078,
.8106, .8133,
                  .8159, .8186, .8212, .8238, .8264, .8289, .8315, .8340,
.8365, .8389,
                  .8413, .8438, .8461, .8485, .8508, .8531, .8554, .8577,
.8599, .8621,
                  .8643, .8665, .8686, .8708, .8729, .8749, .8770, .8790,
.8810, .8830,
                  .8849, .8869, .8888, .8907, .8925, .8944, .8962, .8980,
.8997, .9015,
                  .9032, .9049, .9066, .9082, .9099, .9115, .9131, .9147,
.9162, .9177,
                  .9192, .9207, .9222, .9236, .9251, .9265, .9279, .9292,
.9306, .9319,
                  .9332, .9345, .9357, .9370, .9382, .8394, .9406, .9418,
.9429, .9441,
                  .9452, .9463, .9474, .9484, .9495, .9505, .9515, .9525,
.9535, .9545,
                  .9554, .9534, .9573, .9582, .9591, .9599, .9608, .9616,
.9625, .9633,
                  .9641, .9649, .9656, .9664, .9671, .9678, .9686, .9693,
.9699, .9706,
                  .9713, .9719, .9726, .9732, .9738, .9744, .9750, .9756,
.9761, .9767,
                  .9772, .9778, .9783, .9788, .9793, .9798, .9803, .9808,
.9812, .9817,
                  .9821, .9826, .9830, .9834, .9838, .9842, .9846, .9850,
.9854, .9857,
                  .9861, .9864, .9868, .9871, .9875, .9878, .9881, .9884,
.9887, .9890,
                  .9893, .9896, .9898, .9901, .9904, .9906, .9909, .9911,
.9913, .9916,
                  .9918, .9920, .9922, .9925, .9927, .9929, .9931, .9932,
.9934, .9936,
                  .9938, .9940, .9941, .9943, .9945, .9946, .9948, .9949,
.9951, .9952,
                  .9953, .9955, .9956, .9957, .9959, .9960, .9961, .9962,
.9963, .9964,
                  .9965, .9966, .9967, .9968, .9969, .9970, .9971, .9972,
.9973, .9974,
                  .9974, .9975, .9976, .9977, .9977, .9978, .9979, .9979,
.9980, .9981,
                  .9981, .9982, .9982, .9983, .9984, .9984, .9985, .9985,
.9986, .9986,
                  .9987, .9987, .9987, .9988, .9988, .9989, .9989, .9989,
.9990, .9990 };

int lookup(double x);

double invNorm(double x)
{
   if (x < .5)
      return -invNorm(1 - x);

   int n;
   n = lookup(x);

   return ((double)((int)(n / 10)) / 10) + ((double)(n % 10) / 100);
}

int lookup(double x)
{
   int a, b, c;
   a = 0;
   c = 309;

   while (c - a > 1)
   {
       b = (a + c) / 2;
       if (x == l[b])
          return b;
       else if (x < l[b])
          c = b;
       else
          a = b;

   }

   return (abs(x - l[a]) < abs(x - l[c]) ? a : c);
}

double damage(double mean, double stdDev)
{
 return mean + (invNorm(getRand()) * stdDev);
}

The way this works is it has a list of the area under the normal density
curve.  It uses this table to look up the inverse normal using  binary
search.  This will always be a number in the range -3 to 3 corresponding to
how many standard deviations above or below the mean the specified
probability is.  If you aren't familiar with it, the standard density curve
is one where stuff closer to the mean is more likely to occur than stuff
farther from the mean.  The random number generated by getRand is in the
range 0 to 1, with 4 digits of precision.  How would this work as far as
speed?  Does it even make sense to do something like this?  Any ideas for
improving this algorithm?



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