[MUD-Dev] [DGN] The psychology of random numbers
Hans-Henrik Staerfeldt
hhs at cbs.dtu.dk
Fri Jan 23 10:23:45 New Zealand Daylight Time 2004
On Wednesday 21 January 2004 02:44, Dave Bacher wrote:
> The C PRNG can be made worse by using modulus to scale results.
> You can only properly scale results with a multiply followed by a
> divide, assuming integer math. Any other technique, particularly
> modulus, skews the results. Lets say the maximum number the LCG
> can generate is 32767. If you modulus that by 100, you'll see
> that 68 through 99 occur less frequently than 0 through 67. If
> you modulus by 1000, 768 through 999 occur less frequently, and if
> you modulus by 10000, 2868 through 10000 occur less frequently.
This is an interresting and very useful piece of knowledge! Usually,
your standard I wonder though, if use the usual C PRNG are used, how
many rolls do you have to make before you can determine this skew
with any kind of statistical significance, using the usual C PRNG's,
let alone notice this by playing the game?
So i made a little program to test some of this;
#include <stdlib.h>
#include <stdio.h>
#define size 20
#define rolls 100000000
long long int count[size];
int main() {
int i;
int d;
int e=rolls/size;
for (i=0;i<size;i++) count[i]=0;
for (i=0;i<rolls;i++) {
count[rand()%size]++;
}
for (i=0;i<size;i++) {
d=count[i]-e;
printf("%3d: %6d\t%.6f\n",i,d,100.0*d/e);
}
return 0;
}
Results were;
0: -1966 -0.039320
1: -719 -0.014380
2: 1900 0.038000
3: 2124 0.042480
4: 46 0.000920
5: 1392 0.027840
6: 3128 0.062560
7: 2637 0.052740
8: 1517 0.030340
9: -757 -0.015140
10: -1387 -0.027740
11: -3359 -0.067180
12: -1681 -0.033620
13: 2176 0.043520
14: -1346 -0.026920
15: -3723 -0.074460
16: 2109 0.042180
17: -2032 -0.040640
18: -2328 -0.046560
19: 2269 0.045380
As you can see, by rolling 100 million times on a d20 (well a d20-1,
not important), the modulus count of a given dice varies at most
0.067180% from the expected for the 11. I know, i should do this for
several seeds, but i guess someone can contradict me if my numbers
were just a fluke.
Now, such a small skew can be extremely difficult to detect if you
don't keep an extremely accurate track of all your rolls. I
seriously doubt that any player will yell 'Hey why the f*** don't I
ever roll an 11?'.
The old 'random()' gives comparable results (at most: 10: -4539
-0.090780%) Using 'lrand48()' is also comparable; (at most: 17: 5026
0.100520%)
Anyway, though a few numbers on the table might be
enlightening... :-)
--
--Hans-Henrik Stærfeldt
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