It doesn’t assume time is continuous, and ‘converges to 0,5’ isn’t the mathematical answer. Each point in time at which a switch happens is after a rational time interval (\frac{1}{2^n} is rational for all n), and the rational numbers aren’t a continuum (there’s always an irrational number between any two rational numbers). That’s nitpicking of course—you presumably meant that the difference between two successive switches shrinks without lower bound. That’s true, but it’s true for time in all of our best physical theories (in fact, time is a continuum in all of our best physical theories)—the fundamental nature of the Planck time being only conjectural at this point. More to the point, the series that determines the state of the lamp after two seconds is 1 - 1 + 1 - 1 + … The limit of this isn’t 0,5—it’s divergent, so it simply has no well-defined limit.
More importantly, the point I was making is that everyone who claims there is random choice either must leave that random choice a black box, or accept the possibility of processes such as that of Thomson’s lamp. In the first case, they can’t complain about free will, because one can just similarly leave it a black box; in the latter case, they can’t complain about free will, because this sort of process is just as sufficient for free will as it is for random choice.
The same is true for anybody who believes in causality. Either, they accept that the reason for anything happening now is an infinite chain of determinations, or they accept that there’s a black-box beginning—a buck-stops-here uncaused cause and unmoved mover.
The simple truth is that science doesn’t tell us what it is that makes things happen. It tells us—as in, gives a descriptive account of—how things happen. You can think of it as a compression algorithm: any not completely random data will have a description in terms of a shorter string (initial conditions) and an algorithm to reproduce it (the laws of physics). But how that data was created—sampling each bit from a certain probability distribution, each successive bit being determined (‘caused’) by its predecessors, each bit chosen freely—is entirely inaccessible.
The simplest hypothesis in accordance with all data (the universe’s flatness, e.g.) is that it is (spatially) infinite. And most of our current best theories depend on properties of the continuum (the real numbers), such that there is an infinity of moments between any given two points in time, and an infinity of points in each spatial interval. Those theories may yet be overturned, of course, but they’re the best fit for the data we have at the moment.
I don’t think @Mijin would disagree with that, and neither do I. The same, of course, is true for chance and causality. The point is just that free will (like chance and causality) simply isn’t a scientific nor an explanatory hypothesis, so criticizing it on that account is rather like criticizing a submarine for failing to be able to fly.