The point was to check whether this is a fair restatement of the problem, by attempting to up the stakes a bit. For example, if you believe that, quite obviously, the odds against heads are a billion to one, then the one-third-er position in the original problem should be equally obvious, unless I have failed at my mission.

Thank you for the suggestion! I have added a one-paragraph summary at the start. I hope this improves things a bit.