What I mean is, there are few enough cases so we can put them all on one piece of paper and count. That's what I did in my first comment here. There are exactly as many cases of HT and HH, hence my belief in 50% odds. That's pretty much the standard way to tackle basic probability questions.
But maybe I'm misinterpreting what they mean and there's some way to structure a bet so the odds fall to one side or the other. I just having found it yet. If we could find it and put it on paper, we'd have a clear understanding of why it works.
Plus, it'd probably be pretty counterintuitive and with a decent bankroll would be reliably profitable over the long term, in certain environments.
Your MC results are interesting, I've looked at your code and it seems straightforward. But counting all possible cases is essentially a mathematical proof, and I just can't find any mistakes in it, or figure out how it could be wrong.
But maybe I'm misinterpreting what they mean and there's some way to structure a bet so the odds fall to one side or the other. I just having found it yet. If we could find it and put it on paper, we'd have a clear understanding of why it works.
Plus, it'd probably be pretty counterintuitive and with a decent bankroll would be reliably profitable over the long term, in certain environments.
Your MC results are interesting, I've looked at your code and it seems straightforward. But counting all possible cases is essentially a mathematical proof, and I just can't find any mistakes in it, or figure out how it could be wrong.