On Tue, Dec 26, 2023 at 4:36 PM Steve Baker <[email protected]> wrote:
That was one of the hardest parts about writing that app — I did a lot of
> research about tips and tricks, and have a few nested randomizer routines
> in there to compensate. While I have not done a statistical study with a
> significant sample set, it kicks out dice rolls that are very random, and
> the folks that I play with feel comfortable with its results. The source
> code is available and I’d be happy to highlight the key bits (some upfront
> prep early in the code and most of the randomizer functions are towards the
> back, etc).
>
Steve,
I was curious how nesting the randomizer had affected the quality of the
randomization, so I poked around at the source code for DICEBOX. While I
had a lot of fun trying to weave my way through the tightly crunched code,
in the end I wasn't able to extract just the randomizer. Could you help me
grok it? Once the routine is extracted, I think your RNG might be useful
for anyone else who wants to reuse your work.
I've already written code that can do a check of RNG uniformity via the χ²
(chi squared) test on a Model T. (See attachment). It rolls a D sided die N
times and returns a probability p that the RNG is selecting every number
equally. I just need your routine at line 10000 which takes variable D
(number of sides) as input and outputs variable R (random integer from 1 to
D, inclusive).
—b9
P.S. On the Tandy 200, DICEBOX needs a line *15 GOTO 100* or it gives an
error.
--- CUT HERE ---
0 GOTO 1000 REM RNG Tester by hackerb91 DATA 0.000, 0.000, 0.001,
0.004, 0.016, 2.706, 3.841, 5.024, 6.635, 7.8792 DATA 0.010, 0.020,
0.051, 0.103, 0.211, 4.605, 5.991, 7.378, 9.210, 10.5973 DATA 0.072,
0.115, 0.216, 0.352, 0.584, 6.251, 7.815, 9.348, 11.345, 12.8384 DATA
0.207, 0.297, 0.484, 0.711, 1.064, 7.779, 9.488, 11.143, 13.277,
14.8605 DATA 0.412, 0.554, 0.831, 1.145, 1.610, 9.236, 11.070, 12.833,
15.086, 16.7506 DATA 0.676, 0.872, 1.237, 1.635, 2.204, 10.645,
12.592, 14.449, 16.812, 18.5487 DATA 0.989, 1.239, 1.690, 2.167,
2.833, 12.017, 14.067, 16.013, 18.475, 20.2788 DATA 1.344, 1.646,
2.180, 2.733, 3.490, 13.362, 15.507, 17.535, 20.090, 21.9559 DATA
1.735, 2.088, 2.700, 3.325, 4.168, 14.684, 16.919, 19.023, 21.666,
23.58910 DATA 2.156, 2.558, 3.247, 3.940, 4.865, 15.987, 18.307,
20.483, 23.209, 25.18811 DATA 2.603, 3.053, 3.816, 4.575, 5.578,
17.275, 19.675, 21.920, 24.725, 26.75712 DATA 3.074, 3.571, 4.404,
5.226, 6.304, 18.549, 21.026, 23.337, 26.217, 28.30013 DATA 3.565,
4.107, 5.009, 5.892, 7.042, 19.812, 22.362, 24.736, 27.688, 29.81914
DATA 4.075, 4.660, 5.629, 6.571, 7.790, 21.064, 23.685, 26.119,
29.141, 31.31915 DATA 4.601, 5.229, 6.262, 7.261, 8.547, 22.307,
24.996, 27.488, 30.578, 32.80116 DATA 5.142, 5.812, 6.908, 7.962,
9.312, 23.542, 26.296, 28.845, 32.000, 34.26717 DATA 5.697, 6.408,
7.564, 8.672, 10.085, 24.769, 27.587, 30.191, 33.409, 35.71818 DATA
6.265, 7.015, 8.231, 9.390, 10.865, 25.989, 28.869, 31.526, 34.805,
37.15619 DATA 6.844, 7.633, 8.907, 10.117, 11.651, 27.204, 30.144,
32.852, 36.191, 38.58220 DATA 7.434, 8.260, 9.591, 10.851, 12.443,
28.412, 31.410, 34.170, 37.566, 39.99721 DATA 8.034, 8.897, 10.283,
11.591, 13.240, 29.615, 32.671, 35.479, 38.932, 41.40122 DATA 8.643,
9.542, 10.982, 12.338, 14.041, 30.813, 33.924, 36.781, 40.289,
42.79623 DATA 9.260, 10.196, 11.689, 13.091, 14.848, 32.007, 35.172,
38.076, 41.638, 44.18124 DATA 9.886, 10.856, 12.401, 13.848, 15.659,
33.196, 36.415, 39.364, 42.980, 45.55925 DATA 10.520, 11.524, 13.120,
14.611, 16.473, 34.382, 37.652, 40.646, 44.314, 46.92826 DATA 11.160,
12.198, 13.844, 15.379, 17.292, 35.563, 38.885, 41.923, 45.642,
48.29027 DATA 11.808, 12.879, 14.573, 16.151, 18.114, 36.741, 40.113,
43.195, 46.963, 49.64528 DATA 12.461, 13.565, 15.308, 16.928, 18.939,
37.916, 41.337, 44.461, 48.278, 50.99329 DATA 13.121, 14.256, 16.047,
17.708, 19.768, 39.087, 42.557, 45.722, 49.588, 52.33630 DATA 13.787,
14.953, 16.791, 18.493, 20.599, 40.256, 43.773, 46.979, 50.892,
53.67240 DATA 20.707, 22.164, 24.433, 26.509, 29.051, 51.805, 55.758,
59.342, 63.691, 66.76650 DATA 27.991, 29.707, 32.357, 34.764, 37.689,
63.167, 67.505, 71.420, 76.154, 79.49060 DATA 35.534, 37.485, 40.482,
43.188, 46.459, 74.397, 79.082, 83.298, 88.379, 91.95270 DATA 43.275,
45.442, 48.758, 51.739, 55.329, 85.527, 90.531, 95.023, 100.425,
104.21580 DATA 51.172, 53.540, 57.153, 60.391, 64.278, 96.578,
101.879, 106.629, 112.329, 116.32190 DATA 59.196, 61.754, 65.647,
69.126, 73.291, 107.565, 113.145, 118.136, 124.116, 128.299100 DATA
67.328, 70.065, 74.222, 77.929, 82.358, 118.498, 124.342, 129.561,
135.807, 140.169110 REM Calculate p from df and X2120 IF DF<1 THEN
DF=1: PRINT "Using df =" DF130 IF DF>100 THEN
DF=100: PRINT "Using df =" DF140 IF DF>30 AND
(DF MOD 10) > 0 THEN DF=DF\10: PRINT "Using df =" DF150 ' Select
a DATA line to read from151 IF DF=1 THEN RESTORE 1152 IF DF=2 THEN
RESTORE 2153 IF DF=3 THEN RESTORE 3154 IF DF=4 THEN RESTORE 4155 IF
DF=5 THEN RESTORE 5156 IF DF=6 THEN RESTORE 6157 IF DF=7 THEN RESTORE
7158 IF DF=8 THEN RESTORE 8159 IF DF=9 THEN RESTORE 9160 IF DF=10 THEN
RESTORE 10161 IF DF=11 THEN RESTORE 11162 IF DF=12 THEN RESTORE 12163
IF DF=13 THEN RESTORE 13164 IF DF=14 THEN RESTORE 14165 IF DF=15 THEN
RESTORE 15166 IF DF=16 THEN RESTORE 16167 IF DF=17 THEN RESTORE 17168
IF DF=18 THEN RESTORE 18169 IF DF=19 THEN RESTORE 19170 IF DF=20 THEN
RESTORE 20171 IF DF=21 THEN RESTORE 21172 IF DF=22 THEN RESTORE 22173
IF DF=23 THEN RESTORE 23174 IF DF=24 THEN RESTORE 24175 IF DF=25 THEN
RESTORE 25176 IF DF=26 THEN RESTORE 26177 IF DF=27 THEN RESTORE 27178
IF DF=28 THEN RESTORE 28179 IF DF=29 THEN RESTORE 29180 IF DF=30 THEN
RESTORE 30181 IF DF=40 THEN RESTORE 40182 IF DF=50 THEN RESTORE 50183
IF DF=60 THEN RESTORE 60184 IF DF=70 THEN RESTORE 70185 IF DF=80 THEN
RESTORE 80186 IF DF=90 THEN RESTORE 90187 IF DF=100 THEN RESTORE
100210 REM p value for columns in data220 A(0)=1230 A(1)=.995:
A(2)=.990: A(3)=.975240 A(4)=.950: A(5)=.900: A(6)=.100250 A(7)=.050:
A(8)=.025: A(9)=.010260 A(10)=.005300 REM X2 is chi square, M is
alpha310 FOR T=1 TO 10320 READ M330 IF X2 > M THEN NEXT350 P=A(T-1)390
RETURN990 REM By hackerb9 February 2024.999 '1000 REM Chi Squared
statistic to 1001 REM check for uniformity of RNG.1002
' Note: This does NOT check for1003 ' independence. For that, use1004
' autocorrelation, gap, poker1005 ' or other "diehard" tests.1010
ES$=CHR$(27) 'Screen Esc sequences1020 PRINT ES$"U"; ' Turn off
labels1030 CLS1038 ' d is number of histogram bins1039 ' or,
equivalently, sides of a die.1040 D=61050 DIM X(D)1059 ' n is number
of times to roll.1060 N=1001069 ' is the count expected in a bin1070
E=N/D1099 '1100 REM Roll dice and show histogram bins.1120
PRINT"Rolling a";D;"sided die";N;"times";1130 FOR I=1 TO N1140
GOSUB 10000 ' R = random(D)1150 X(R)=X(R)+11160 TT=(R-1)*4:
GOSUB 15501170 PRINT X(R);1180 NEXT I1190 TT=D*4:GOSUB 1550:
PRINT1199 '1200 REM Calculate chi square statistic1201 ' Chi-Square =
sum{(x(i)-E)^2 / E}1210 FOR I=1 TO D: IF X(I)<5 THEN PRINT "Results
may be inaccurate due to insufficient trials (n ="N", d ="D")":
ELSE NEXT1230 X2=0: DF=-11240 FOR I=1 TO D1250 X2 = X2 + ( (X(I) -
E)^2 / E)1260 IF X(I) > 0 THEN DF=DF+11270 NEXT I1280 PRINT "Chi
square is";X21290 PRINT "Degrees of Freedom is";df1299 '1300 REM Set p
(percentage points) by 1301 REM looking up x2 (chi square)1302 REM at
df (degree of freedom) in1303 REM the chisq distribution table.1310
GOSUB 1101399 '1400 REM Interpret result 1410 PRINT "p =" P*100
"%"1420 PRINT"This Random Number Generator"1430 IF P>0.95 THEN PRINT
"is too regular. (BAD)": END1440 IF P<0.05 THEN PRINT "is not
uniformly distributed. (BAD)": END1450 PRINT "seems uniformly
distributed."1460 END1499 '1500 'Move cursor to Row AA and Col BB1510
PRINT ES$"Y"CHR$(32+AA)CHR$(32+BB);1520 RETURN1550 REM Move cursor to
position TT1560 AA=TT\40+1:BB=TT MOD 40:GOSUB 15001570 RETURN9999
'10000 REM RANDOM NUMBER GENERATOR 10001 ' Input D, integer10002 '
Output R, integer10003 ' 1..D, inclusive10010
R=INT(D*RND(1))+110090 RETURN
x2.ba
Description: Binary data
