How to decrease the confidence of a Monte Carlo algorithm in its answer?
You can compute the probability that outcome $e$ is the unique plurality answer, when repeating the algorithm $k$ times, as follows:
$$
\sum_{\substack{a+b+c+d+e=k \\ a,b,c,d,e \geq 0 \\ e &gt; a,b,c,d}} \frac{n!}{a!b!c!d!e!} \left(\frac{1}{4}\right)^e \left(\frac{3}{16}\right)^{k-e}.
$$
This can be computed explicitly. When $k = 70$, the probability is roughly $0.502$, and this is the minimal $k$ for which the probability exceeds $1/2$.