Ha! Wish I had a dollar for every tap I've broken and removed. 20+ years in Tool and Die and CNC machining will get ya good at it. lol Sadly though, every situation is different and I have not had consistent luck with extractors. A good pick to get the broken tap and chips out of the hole, some compressed air and a small sharp punch to work the tap back and forth if you can get to it. I know its not likely but if you know someone with a Bridgeport you can cut them out with a carbide endmill, takes some patience but works. In the future a good cutting oil is very important as is using the proper size drill. Dont use spiral flute taps, they are not as strong as plug/ hand taps and have less lead chamfer so they take more force to turn as well. The best taps you can have in the garage on my opinion are form taps though. Stronger than any cut tap, creates awesome threads and can be used in most metals except for cast materials. I can share with you the drill sizes needed for form taps if need be, I have a chart I made on my computer.