C code that shows the Poisson distribution of the probability to attack Bitcoin.

bitcoin_attacker_success_probability.c

#include <math.h>
#include <stdio.h>

double AttackerSuccessProbability(double q, int z) {
   double p = 1.0 - q;
   double lambda = z * (q / p);
   double sum = 1.0;
   int i, k;
   for (k = 0; k <= z; k++)
   {
       double poisson = exp(-lambda);
       for (i = 1; i <= k; i++)
           poisson *= lambda / i;
       sum -= poisson * (1 - pow(q / p, z - k));
   }
   return sum;
}

int main() {
    double P;
    double q = 0.49;

    for (int z = 0; z <= 1000; z++ ) {
        P = AttackerSuccessProbability(q, z);
        printf("q=%f z=%d   P=%f\n", q, z, P);
    }

    return 0;
}