> You can see it was a gamble by considering if Light had been outside Kanto; since he would not see it live, he would not have reacted, and all L would learn is that his suspect was in that other 2/3 of the population, for a gain of only ~0.3 bits.
My understanding of L's plan (based on what he said in the broadcast) was that he intended to do several live broadcasts, one in each region, until he was caught. Lind L. Taylor was a death row criminal being offered a deal to survive, and would've gone along with doing several broadcasts. Additionally, even if they didn't do it live and simply recorded it there's no way that Light would've known it wasn't live and he would've acted in the same manner (and since Lind was in L's custody, L would've known if he died even if Light didn't).
At the time Death Note was written, mass internet communication wasn't as prevalent and so you wouldn't expect people to find out about events like the broadcast for at least a few hours (long enough to do broadcasts in each region). L probably hoped that Kira was in a less populated city since it would cut down on more bits of entropy (and I'd argue it would've been a better idea to start broadcasting to smaller cities first -- since it's more likely an event like this in a big city would be quickly broadcast to the rest of Japan).