I don't know what the chances are, but you seem to be under the impression that you can just wait to see if you're caught, apologize, and pay some money to make things OK.
Let's say you failed to report rental income and the IRS finds out. Obviously there will be penalties but how would the proper amount of tax be calculated if they found it years later? Would you still be able to add the deductions you would have had years ago?
It may be difficult to do from a federal prison for up to 5 years, and the deductions to which you may have been entitled may be wiped out by the up to $100,000 fine and paying the government's legal bill to prosecute you, and paying your own tax defense attorney if you elect not to represent yourself:
https://www.law.cornell.edu/uscode/text/26/7201And of course you'll be a convicted federal felon, which might make it hard to get a job later.
Oh, and you may also be assessed a fraud tax penalty of up to 75 percent of what you fraudulently didn't pay:
https://www.law.cornell.edu/uscode/text/26/6663They have six years to catch you for tax fraud:
https://www.irs.gov/pub/irs-utl/tax_crimes_handbook.pdf -- page 31 of the PDF
Also, there is a whistleblower program where people who turned in tax frauds were entitled to 15% to 30% of whatever the IRS collected. I could have turned in my ex-wife at one point but chose not to because of the children. Anyone around you could be tempted to turn you in for the money:
https://www.irs.gov/compliance/whistleblower-officeFinally, if you're going to go the tax evasion / tax fraud route, you better hope that the IRS of the future doesn't check posts of yours like this (and your other thread) on message boards. If they find these posts, then it will help prove their case that it's willful and not accidental.