[6gvONxR4sf7o]

>Null hypothesis: this is not the case.

>The p-value is 1/32, so the null hypothesis is rejected.

This is incomplete. You need to define a test statistic and know its distribution under your null hypothesis before you can come up with a p value. What's your test statistic here and how is it distributed?

If you define your test after seeing the data, of course you can come up with an arbitrary p value. Choosing a distribution for your null to make it fit an agenda is just like choosing a distribution for your prior after seeing your data to make it fit an agenda.

You could say your prior is a delta function around HHTHT after observing it and get arbitrary evidence, but anyone reading your paper will find it unconvincing, just like anyone reading about a test statistic like this will find it unconvincing.