But in this case the astronomer didn't expect to be lucky either way - and instead asked the public at large to fund the telescope time buy. That this worked out so well in the end was due to the enormous hype that had been building (or built deliberately) around the star in question, which is the famous KIC 8462852, of course, with its erratic dips in brightness discovered by the Kepler satellite (and citizen scientists looking at its lightcurves). Its behavior is not fully explained, but some comet debris clouds are the likely culprit - and yet this star has been firmly associated the potential 'alien megastructures' in the public mind. Without these wild speculations - not exactly supported by the scientists in question but not actively discouraged either and rehashed in the media again and again - and also an added layer of drama about historical data and a long-term brightness trend or lack thereof the crowd-funding would have hardly raised a dime.
So there, the pay-per-view telescope network will soon monitor KIC 8462852 with high cadence and enough photometric precision to catch further dimmings (some of which were so strong that no Kepler would have been needed to detect them) - if any occur in the bought time interval, of course. In the best of all worlds, the dimmings (for which amateurs with their own telescopes are on the look-out as well) will return in time and display some property not seen in the Kepler data which will lead to a viable explanation. Equally likely is that nothing happens, the money is gone and a null result remains which wouldn't constrain modelmaking much. KIC 8462852 as 'star of mystery' for the public at large is a unique case in the history of astronomy so far: whether such a let's-all-fund-my-science-pet-project approach could - and should - be applied to other astronomical problems is anything but clear. The outcome and aftermath of the observing run will certainly shape opinions eventually: both amongst astronomers and the public asked to pay.