Strictly speaking, the chance of observing exactly 0.5 (that is, with infinite trailing zeros) is zero. Also, in practice, we generally do not care about exact results, but results within a certain margin. Accordingly, in practice, we can relax the definition of fairness and we can say that a fair coin is one with a value of  around 0.5. For example, we could say that any value in the interval [0.45, 0.55] will be, for our purposes, practically equivalent to 0.5. We call this interval a Region Of Practical Equivalence (ROPE). Once the ROPE is defined, we compare it against the Highest-Posterior Density (HPD). We can get at least three scenarios:

• The ROPE does not overlap with the HPD; we can say the coin is not fair
• The ROPE contains the entire HPD; we can say the coin is fair
• The ROPE partially overlaps with HPD; we cannot say the coin is fair or unfair

If we choose a ROPE in the interval [0, 1], we will always say we have a fair coin. Notice that we do not need to collect data to perform any type of inference. Of course, this is a trivial, unreasonable, and dishonest choice and probably nobody is going to agree with our ROPE definition. I am just mentioning it to highlight the fact that the definition of the ROPE is context-dependent; there is no auto-magic rule that will fit everyone's intentions. Decisions are inherently subjective and our mission is to take the most informed possible decisions according to our goals.

We can use the plot_posterior function to plot the posterior with the HPD interval and the ROPE. The ROPE appears as a semi-transparent thick (green) line:

az.plot_posterior(trace, rope=[0.45, .55])

Another tool we can use to help us make a decision is to compare the posterior against a reference value. We can do this using plot_posterior. As you can see, we get a vertical (orange) line and the proportion of the posterior above and below our reference value:

az.plot_posterior(trace, ref_val=0.5) 

For a more detailed discussion on the use of the ROPE you could read Chapter 12 of the great book Doing Bayesian Data Analysis by John Kruschke. This chapter also discusses how to perform hypothesis testing in a Bayesian framework and the caveats of hypothesis testing, whether in a Bayesian or non-Bayesian setting.