This is very suitable for Hypothesis Testing, and there already exists a framework for Testing Difference in Proportions. First, we formulate our hypotheses:
$$H = \begin{cases}
H_0: P_c=P_h \\
H_A: P_c\neq P_h
\end{cases}
$$
($P_c, P_h$ are computer and human proportions respectively.) This is two-tailed test for the equality of the two proportions. There is also a one-tailed test for testing if one is greater than the other or else. I think, for a fair game, you should test for equivalence. But, if you keep getting $P_c > P_h$, you can also consider having a one-tailed test.
First of all, you compute a pooled sample proportion, and standard error, using your reported computer/human proportions/# of throws:
$$p_{pool}=\frac{p_cn_c+p_hn_h}{n_c+n_h}$$
$$S=\sqrt{p_{pool}(1-p_{pool}) \left( \frac{1}{n_c}+\frac{1}{n_h} \right)}$$
Then, calculate your test statistic:
$z_{cal}=\frac{p_c-p_h}{S}$
Finally, you check if this value is outside your significance level thresholds. A common significance level would be $\alpha=0.05$, which correspond to range $[-1.96,1.96]$ according to standard normal table, i.e. if your calculated value is outside this range, then it means your have high chance of having biased dice throws.
For single value evaluation, i.e. questions like "is it normal to have 0.15 ?" etc; we employ a very similar technique:
$$\sigma=\sqrt{\frac{p_{true}(1-p_{true})}{n}}, z_{cal}=\frac{p_{true}-p_{observed}}{\sigma}$$, And similarly compare this calculated $z$ value with $\alpha$ significance level thresholds. For example, for $n = 50000, p_{observed}=0.15, p_{true}=0.166$ would have $z_{cal}\approx 9.62$, which is very unusual.