&gt;Ok, so you&#x27;re thinking about a random variable which converges to some value when the null hypothesis is true. This is fine, but it has nothing to do whatsoever with p-values.<p>Well, the variable itself doesn&#x27;t, just the observed value of P(X|H). X can be any random variable, but typically it will need to be transformed to have a normal distribution about 0 with a standard deviation of 1 (since this is what the typical null-hypothesis predicts).<p>To effectively use p-value analysis, it is typically assumed that your null-hypothesis predicts that your observations will be normally distributed with a mean of 0 and a standard deviation of 1. The total count of heads observed will not be distributed that way. Neither will the probability of a particular sequence (what your example seemed to be calculating). I say your null hypothesis is not well-defined because the term &#x27;fair&#x27; remains undefined (though we could guess at the meaning) and in fact makes no predictions about the world. You need to apply transformations to your random variable so that it will appear normally distributed about 0 with a standard deviation of 1 if the hypothesis is true.<p>&gt;Let me say that your notation is not very appropriate. It makes no sense to say that P(X|H) converges to 1.<p>My notation is perfectly appropriate. X is a random variable and a random variable is the only thing that can go there (if you are doing p-value analysis). X is not assumed to be uniform or simple (although it certainly could be). P(T&gt;T(X)|H) can be replaced with P(Y|H) every time (Y = T&gt;T(X)).<p>&gt;As I said, you&#x27;re free to prefer your converging statistics and your well-defined null hypothesis. But you should be aware that people are talking about something completely different when discussing things like the 1e-7 p-value in the Higgs boson discovery or the reproducibility of statistically significant results.<p>I&#x27;m glad that we finally agree on this (although I dispute that anyone working on the Higgs boson discovery disagrees with me). One of my first claims was that others may not be calculating true p-values, but may calculate something and call it &#x27;p-value&#x27; and then think that it means something it does not. In fact, this entire topic even links to an article in a prominent publisher claiming the same.<p>Do you think it is purely coincidental that the figures I showed you from the Higgs experiment show the lines converging towards only two different numbers: 1 and 0?<p>Edit: You&#x27;ll have to give me some time on your edit. It&#x27;s not something I typically calculate and I have other business to attend to today.