This is a quote from the book "Bitcoin: A Peer-to-Peer Electronic Cash System" by Satoshi Nakamoto
.../> {
double poisson = exp(-lambda);
for (i = 1; i <= k; i++)
poisson *= lambda / i;
sum -= poisson * (1 - pow(q / p, z - k));
return sum;

Running some results, we can see the probability drop off exponentially with z.

z=0 P=1.0000000
z=1 P=0.2045873
z=2 P=0.0509779

z=3 P=0.0131722
z=4 P=0.0034552
z=5 P=0.0009137
z=6 P=0.0002428
z=7 P=0.0000647
z=8 P=0.0000173
z=9 P=0.0000046
z=10 P=0.0000012

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