fair die or not, from 3D printer I made a 3D printed die today, but depending on the heat applied, it may or may not be a "fair" die (i.e. have an equal chance of landing on each face).
I have just tried rolling it 150 times.  The frequency results came out to:
$$ \begin{array}{c|c} \hline
1's &  21 \\
\hline
 2's & 30 \\ 
\hline
3's & 23 \\
\hline
4's & 31 \\
\hline
5's & 21 \\ 
\hline
6's & 24 \\ 
\hline
\end{array} $$
How would I calculate the chance that this die is fair?
 A: Goodness-of-fit test. Computation in R. Results agree with Comment by @Peter.
 obs = c(21, 30, 23, 31, 21, 24)
 chisq.test(obs)

    Chi-squared test for given probabilities

 data:  obs 
 X-squared = 3.92, df = 5, p-value = 0.561

If observed counts are $X_i$ and expected counts are $E = 150/6 = 25,$
Then the chi-squared goodness-of-fit statistic is
$Q = \sum_{i=1}^6 (X_i - E)^2/E,$ which is approximately
distributed as $Chisq(DF = 5).$ The critical value for a
test at level 5% is 11.07. We fail to reject the null hypothesis
that all six faces are equally likely because $Q = 3.92 < 11.07.$
Power. However, I'm wondering if 150 rolls is enough. Suppose your
die is markedly biased so that faces 1, 2, and 3 each have probability 5/36 and faces 4, 5, and 6 each have probability 7/36. Then the following
simulation shows that only about 27 in 100 tests with 150 rolls
would reject the hypothesis of fairness. That is, the power of
the goodness-of-fit test against this particular degree of bias
is about 27%. More modestly biased dice would fail the test at an even lower rate.
 m = 10^5;  q = numeric(m); E = 150/6
 for(i in 1:m) {
   faces = sample(1:6, 150, repl=T, prob=c(5,5,5,7,7,7)/36)
   x = table(faces);  q[i]=sum((x-E)^2/E)}
 mean(q > qchisq(.96, 5))
 ## 0.2702

The histogram shows values of $Q$ for 100,000 tests, each using 150 rolls of such a biased die. The vertical line is the critical value for a test at level 5%. The curve is the density of $Chisq(5)$.

Prompted by a comment, I ran a slight modification of the R code that shows
89% power for the same biased die as above, but using 600 rolls for the test. The corresponding graph is shown below.
Note: I have posted a Bayesian analysis of the data for face 1
separately.
