The aim of this repository is to show the concept of Pseudo Random distribution and highlight its distinction from true randomness.
What is Pseudo Random distribution?
Pseudo Random distribution is a statistical mechanism that affects the functionality of certain probability-based items and abilities (in games like Warcraft 3 or Dota 2). The PRD increases the probability of an event occurring each time it fails to occur, but compensates by starting with a lower probability. As a result, the effects are more consistent.
The formula for calculating the probability of an effect occurring on the N-th trial after the last successful occurrence is$P(N) = C * N$ . Each time the effect could occur but doesn't, the PRD raises the probability of it happening on the next attempt by a constant$C$ . This constant, which is also the initial probability, is lower than the listed probability of the effect it represents. Once the effect takes place, the counter is reset.
-
prd.py
is a Puthon module which implements functions for generating (including calculation of constant$C$ from given probability) and analyzing pseudo-random distributions. -
PRD-Analysis.ipynb
is a Jupyter notebook that explains the concept of Pseudo Random distribution and highlights its distinction from true randomness. The notebook includes an introduction to Pseudo Random distribution, a comparison between samples from Bernoulli distribution and Pseudo Random distributions, and an analysis of the resulting samples. The notebook also includes a histogram of both samples and a demonstration of the computation of the$C$ constants.
The notebook uses the functions provided inprd.py
to generate the samples and sequences used in the analysis.
For further information on the table containing calculated C constants, please refer to the PRD-Analysis.ipynb
file.
The table presents the calculated constant 100,000
simulations of PRD. Additionally, the table provides the percent change in probability resulting from the simulations."
P | C | Experimental P | Percent change of P |
---|---|---|---|
0.01 | 0.000156 | 0.010002 | 0.018033 % |
0.02 | 0.000620 | 0.020009 | 0.046782 % |
0.03 | 0.001386 | 0.030042 | 0.140848 % |
0.04 | 0.002449 | 0.039986 | -0.035068 % |
0.05 | 0.003802 | 0.050029 | 0.057833 % |
0.06 | 0.005440 | 0.060057 | 0.095050 % |
0.07 | 0.007359 | 0.070100 | 0.143526 % |
0.08 | 0.009552 | 0.079949 | -0.063400 % |
0.09 | 0.012016 | 0.089991 | -0.010159 % |
0.10 | 0.014746 | 0.099919 | -0.080934 % |
0.11 | 0.017736 | 0.109942 | -0.052672 % |
0.12 | 0.020983 | 0.119726 | -0.228278 % |
0.13 | 0.024482 | 0.130056 | 0.043149 % |
0.14 | 0.028230 | 0.139757 | -0.173618 % |
0.15 | 0.032221 | 0.150202 | 0.134832 % |
0.16 | 0.036452 | 0.159994 | -0.004000 % |
0.17 | 0.040920 | 0.170015 | 0.008551 % |
0.18 | 0.045620 | 0.179801 | -0.110657 % |
0.19 | 0.050549 | 0.190459 | 0.241462 % |
0.20 | 0.055704 | 0.200087 | 0.043619 % |
0.21 | 0.061081 | 0.209809 | -0.091167 % |
0.22 | 0.066676 | 0.220133 | 0.060416 % |
0.23 | 0.072488 | 0.229697 | -0.131706 % |
0.24 | 0.078511 | 0.239718 | -0.117302 % |
0.25 | 0.084744 | 0.249941 | -0.023494 % |
0.26 | 0.091183 | 0.259523 | -0.183642 % |
0.27 | 0.097826 | 0.269991 | -0.003410 % |
0.28 | 0.104670 | 0.280054 | 0.019284 % |
0.29 | 0.111712 | 0.289533 | -0.161100 % |
0.30 | 0.118949 | 0.300399 | 0.132876 % |
0.31 | 0.126379 | 0.309768 | -0.074764 % |
0.32 | 0.134001 | 0.320276 | 0.086154 % |
0.33 | 0.141805 | 0.330466 | 0.141209 % |
0.34 | 0.149810 | 0.339714 | -0.084029 % |
0.35 | 0.157983 | 0.349404 | -0.170409 % |
0.36 | 0.166329 | 0.360940 | 0.261241 % |
0.37 | 0.174909 | 0.369308 | -0.187139 % |
0.38 | 0.183625 | 0.379834 | -0.043721 % |
0.39 | 0.192486 | 0.390003 | 0.000880 % |
0.40 | 0.201547 | 0.400134 | 0.033611 % |
0.41 | 0.210920 | 0.410268 | 0.065413 % |
0.42 | 0.220365 | 0.420242 | 0.057673 % |
0.43 | 0.229899 | 0.429210 | -0.183642 % |
0.44 | 0.239540 | 0.439061 | -0.213503 % |
0.45 | 0.249307 | 0.450152 | 0.033861 % |
0.46 | 0.259872 | 0.460054 | 0.011641 % |
0.47 | 0.270453 | 0.469914 | -0.018347 % |
0.48 | 0.281008 | 0.480134 | 0.028008 % |
0.49 | 0.291552 | 0.490316 | 0.064542 % |
0.50 | 0.302103 | 0.500556 | 0.111123 % |
0.51 | 0.312677 | 0.509635 | -0.071639 % |
0.52 | 0.323291 | 0.519610 | -0.074984 % |
0.53 | 0.334120 | 0.529973 | -0.005170 % |
0.54 | 0.347370 | 0.540298 | 0.055210 % |
0.55 | 0.360398 | 0.549738 | -0.047727 % |
0.56 | 0.373217 | 0.559553 | -0.079776 % |
0.57 | 0.385840 | 0.569814 | -0.032709 % |
0.58 | 0.398278 | 0.579163 | -0.144331 % |
0.59 | 0.410545 | 0.587779 | -0.376457 % |
0.60 | 0.422650 | 0.600886 | 0.147618 % |
0.61 | 0.434604 | 0.609321 | -0.111246 % |
0.62 | 0.446419 | 0.621238 | 0.199618 % |
0.63 | 0.458104 | 0.630469 | 0.074495 % |
0.64 | 0.469670 | 0.640160 | 0.024966 % |
0.65 | 0.481125 | 0.649414 | -0.090169 % |
0.66 | 0.492481 | 0.661109 | 0.168022 % |
0.67 | 0.507463 | 0.670763 | 0.113849 % |
0.68 | 0.529412 | 0.681129 | 0.166075 % |
0.69 | 0.550725 | 0.689555 | -0.064448 % |
0.70 | 0.571429 | 0.698841 | -0.165526 % |
0.71 | 0.591549 | 0.709129 | -0.122629 % |
0.72 | 0.611111 | 0.720181 | 0.025126 % |
0.73 | 0.630137 | 0.730055 | 0.007521 % |
0.74 | 0.648649 | 0.740949 | 0.128284 % |
0.75 | 0.666667 | 0.748425 | -0.210058 % |
0.76 | 0.684211 | 0.760213 | 0.028088 % |
0.77 | 0.701299 | 0.769811 | -0.024534 % |
0.78 | 0.717949 | 0.780153 | 0.019604 % |
0.79 | 0.734177 | 0.789883 | -0.014788 % |
0.80 | 0.750000 | 0.800493 | 0.061638 % |
0.81 | 0.765432 | 0.810340 | 0.041968 % |
0.82 | 0.780488 | 0.819142 | -0.104670 % |
0.83 | 0.795181 | 0.830117 | 0.014052 % |
0.84 | 0.809524 | 0.840364 | 0.043379 % |
0.85 | 0.823529 | 0.850818 | 0.096192 % |
0.86 | 0.837209 | 0.858605 | -0.162216 % |
0.87 | 0.850575 | 0.870618 | 0.070980 % |
0.88 | 0.863636 | 0.879871 | -0.014638 % |
0.89 | 0.876404 | 0.890758 | 0.085112 % |
0.90 | 0.888889 | 0.899936 | -0.007099 % |
0.91 | 0.901099 | 0.911270 | 0.139524 % |
0.92 | 0.913043 | 0.918974 | -0.111516 % |
0.93 | 0.924731 | 0.930051 | 0.005470 % |
0.94 | 0.936170 | 0.940247 | 0.026307 % |
0.95 | 0.947368 | 0.949857 | -0.015048 % |
0.96 | 0.958333 | 0.959076 | -0.096227 % |
0.97 | 0.969072 | 0.969866 | -0.013788 % |
0.98 | 0.979592 | 0.980075 | 0.007661 % |
0.99 | 0.989899 | 0.989727 | -0.027612 % |