TeX file confirming that Python code emulated correctly \pdfuniformdeviate

RNGrandomwalk.tex

\newcount\cnta
\newcount\cntb
%\newcount\cntc
%\newcount\cntd

\newcount\maxrand
\maxrand "10000000

% \the\maxrand

\input xinttools.sty

\def\testwalk#1#2#3{%
   % #1 = seed (O or 1)
   % #2 = number of repetitions
   % #3 = length of batches; must be an odd integer
   \pdfsetrandomseed #1
   \cnta 0
   \xintloop
     \edef\x{\pdfuniformdeviate \maxrand}%
     \advance\cnta 1
     \ifnum\cnta<54
   \repeat
   \cnta 0
   \def\Dzero{0}%
   \def\Done{0}%
   \xintloop {%
     \def\S{0}%
     \cntb 0
     \xintloop
       \ifodd\pdfuniformdeviate\maxrand\relax
         \edef\S{\the\numexpr\S+1}%
       \else
         \edef\S{\the\numexpr\S-1}%
       \fi
     \advance\cntb 1
     \ifnum\cntb < #3
     \repeat
   }\ifnum\S>0
       \edef\Done{\the\numexpr\Done+1}%
    \else
       \edef\Dzero{\the\numexpr\Dzero+1}%
    \fi
    \advance\cnta 1
    \ifnum\cnta < #2
    \repeat

    \noindent More 0s: \Dzero

    \noindent More 1s: \Done

    Observed probability of more 1s after #2 batches of #3 is 
    \the\dimexpr \numexpr\Done*65536/#2 sp\relax
}

\testwalk {0}{10000}{165}
    
\testwalk {1}{10000}{165}

\testwalk {0}{30000}{55}
    
\testwalk {1}{30000}{55}

\bye

PRODUCES:

Avec 10000 x 165 et 30000 x 55:

More 0s: 4655
More 1s: 5345
Observed probability of more 1s after 10000 batches of 165 is 0.5345pt
More 0s: 4603
More 1s: 5397
Observed probability of more 1s after 10000 batches of 165 is 0.5397pt
More 0s: 14932
More 1s: 15068
Observed probability of more 1s after 30000 batches of 55 is 0.50227pt
More 0s: 15079
More 1s: 14921
Observed probability of more 1s after 30000 batches of 55 is 0.49736pt

Avec 100000 x 165 et 300000 x 55:

More 0s: 46630
More 1s: 53370
Observed probability of more 1s after 100000 batches of 165 is 0.5337pt
More 0s: 46906
More 1s: 53094
Observed probability of more 1s after 100000 batches of 165 is 0.53094pt
More 0s: 149868
More 1s: 150132
Observed probability of more 1s after 300000 batches of 55 is 0.50044pt
More 0s: 150226
More 1s: 149774
Observed probability of more 1s after 300000 batches of 55 is 0.49925pt

et avec 1000000 fois 165 vs 3000000 fois 55:

More 0s: 468404
More 1s: 531596
Observed probability of more 1s after 1000000 batches of 165 is 0.5316pt
More 0s: 467180
More 1s: 532820
Observed probability of more 1s after 1000000 batches of 165 is 0.53282pt
More 0s: 1500787
More 1s: 1499213
Observed probability of more 1s after 3000000 batches of 55 is 0.49974pt
More 0s: 1498957
More 1s: 1501043
Observed probability of more 1s after 3000000 batches of 55 is 0.50035pt

sur l'iMac (2.8Ghz):
real	19m18.345s
user	19m18.240s
sys	0m0.203s