From BitcoinX Profitability Calculator for 1TH/s

Average generation time for a block (solo) 2 years, 131 days (can vary greatly depending on your luck)

Will you wait ~2-3 years to MAYBE get a block worth about $15,000 right now?

You'll make a lot more in a pool in that time frame.

How is that possible?

The math doesn't add up.

You'll make more in that time frame if you don't hit but less than if you hit because pool operator takes a cut.

The math does add up, because it's math that got the expected values.

Current difficulty * 2**32 / hash rate / seconds in a day = number of days expected to find a block

You can avoid fees by mining on a pool without them.