NASA - Eta Carinae may be about to explode. But no one knows when - it may be next year, it may be one million years from now. Eta Carinae's mass - about 100 times greater than our Sun - makes it an excellent candidate for a full blown supernova. Historical records do show that about 170 years ago Eta Carinae underwent an unusual outburst that made it one of the brightest stars in the southern sky. Eta Carinae, in the Keyhole Nebula, is the only star currently thought to emit natural LASER light. This featured image brings out details in the unusual nebula that surrounds this rogue star. Diffraction spikes, caused by the telescope, are visible as bright multi-colored streaks emanating from Eta Carinae's center. Two distinct lobes of the Homunculus Nebula encompass the hot central region, while some strange radial streaks are visible in red extending toward the image right. The lobes are filled with lanes of gas and dust which absorb the blue and ultraviolet light emitted near the center. The streaks, however, remain unexplained.
A half hour while you watch is about as likely as any other half hour, I think - the chance will increase over time, but not on human lifescales.
Supernova core collapse is about a quarter of the speed of light, and Betelgeuse reaches out to about Jupiter's orbit, which is about three-quarters of a light hour away from the sun? So we'd expect the core collapse take about three hours. Might need an astrophysicist to correct me - if it's half the diameter, then the volume will have reduced eight times and the visible circle four times, so the heat should have doubled and it'll be much brighter? Might be able to get an early warning on that; telescopes will be much more sensitive than our eyes, so we'll know to drag a chair outside and keep our eyes on Orion.
I think they used to do this, but Betelgeuse has these weird periods where it changes its form rather rapidly. I would have to look into it again, but I think they decided that transition between fusion cycles isn't static (H-He -> CNO and back sort of thing)