Very interesting! But I have to read up on the Appendix A4 I think to fully appreciate it...I will come back if I change my mind after it! :-)

My own, current, thoughts are like this: I would bet on the ball being white up to some ratio...if my bet was $1 and I could win $100 I would do it for instance. The probability is simply the border case where ratio between losing and winning is such that I might as well bet or not do it. Betting $50 I would certainly not do. So I would estimate the probability to be somewhere between 1 and 50%...and somewhere there is one and only one border case in between, but my human brain has difficulty thinking in such terms...

The same thing goes for the coin-flip, there is some ratio where it is rational to bet or not to.