When I'm in charge of hiring, a degree doesn't really factor into my decision. I can tell if you're the sort of person who enjoys programming. I'd take a high school dropout over someone with a Master's, if the high school dropout had a substantial portfolio of open source code he could show me. Assuming the guy with the Master's didn't, naturally. If they both did, I'd want to hire them both, and I'd make a damn good argument to management about it.
How many times have we witnessed this? We know how it goes down. That shitty application has two decades worth of bug fixes and business process embedded in it. Some of the business process might look like bugs or random side effects. An effort will be launched to rewrite it, and it will fail miserably, well over budget and several years late.
If the team is unfortunate enough to actually manage to create a working executable, they will find that it doesn't offer half the functionality of the old application and does not deliver the correct results half the time. So the team will start hurriedly patching code, accumulating rushed bug fix after bug fix until the entire thing is an unmaintainable quiltwork of patches and side effects. At which point the company will decide that the new application is awful and attempt to rewrite it. It's just the circle of life...
Byte your tongue.