Your still stuck with: You observed X/Y. How accurate is your count. How accurate is your estimate of accuracy. How accurate is your estimate of accuracy of your accuracy estimate. ... recursive infinity.

Did you account for the possibility you're dreaming, or in a simulation? Or in a simulation of a simulation and so on? Yes, that's the curse of real numbers. In practice you set a limit of precision required, and a threshold of evidence you need to tell you that the precision should be more precise. You can get quite far with Newtonian physics without considering the corrections of general relativity, you can get quite far in engineering by assuming linearity by only expanding the Taylor transform of a non-linear expression by a bit instead of infinitely, and you can do a lot by assuming probabilistic independence of your card counting from what's going on on Pluto right now.

It is going to take me more than a few minutes to parse this. However, I am relatively certain there is a lot of sarcasm in this snippet and I like it.