Earlier quoted context omitted.
> If you have infinite time, then you can wait for it to take more than a few hundred iterations. To be clear, you're making this argument while also arguing "this wouldn't happen in the real world". [1] You can't have it both ways. > Also "constant time" wasn't even part of the original promise! We're not even asking for "constant time". We're literally only asking for "will finish in any bounded amount of time". Ev…
> You can't have it both ways. I addressed that in my next sentence! The whole point of making it two sentences was to split up the real world and not real world cases. Come on. > We're not even asking for "constant time". We're literally only asking for "will finish in any bounded amount of time". Even an exponential time bound would've been better than this! N is 1. Every bound is a constant bound. > if you sold so…
Your next sentence was just obviously flat-out wrong though. Not just because who says that's the case (maybe I don't have that much time?) but because it's trivial to find P(H) that makes it false for any duration of time. "A few hundred iterations" literally doesn't guarantee anything unless you make unstated assumptions about the biases your device works for.
I don't get why we're going in circles here. It seems we've hashed everything out.
> N is 1. Every bound is a constant bound.
Kind of a meaningless statement when you don't even say what your N is. I can imagine lots of N where that's not the case. But whatever you want to call it, my point entirely stands.
> They would not be entitled to a penny back because it's impossible for them to hit the failure case.
No, it is very possible. All they need to be given is a coin whose bias they don't know beforehand, whose bias is unfortunate. Or a coin whose bias they do know to be much worse than whatever you imagined a few hundred tosses would be enough for.