Health Insurance a mugs game?

I'm nearly 30 and I pay $17.83 a fortnight for Health Insurance. $463 a year for Hospital and Specialist care.
Sure I can get treatment for free at any public hospital, but there are waiting times to consider.
And if I have to go to hospital, I'd like a private room and not have to listen to the person next to me crying out in agony all night in a vain attempt to be given some morphine.

So is it a good investment? If I saved that much for 20 years (conservatively) I'd have about $14,000. What are the chances of me requiring $14,000 worth of private health care in the next 20 years? That's what I'm gambling on. That what the health insurance company (Southern Cross) are gambling on too.

Southern cross is "not for profit" I guess that means every dollar they take in they pay out again. (Minus admin and CEO salaries). So excellent chances of claims being approved. But in a way my premiums pay for older people, then when I'm older, all the youngin's can subsidise me! Its the ultimate pyramid scheme, we just have to keep recruiting people to sign up for health insurance.

I keep looking at it, wondering if this is something worth continuing with, that $17.83 could be going on my mortgage. Murphy's law says as soon as I cancel my insurance I'll need it, so for now FEAR will keep me contributing to the insurance game.