You begin to see why this is a subtle problem, and why I think it catches so many people. Naive statistics, and perhaps "intuitive" statistics, say it's no diff

You begin to see why this is a subtle problem, and why I think it catches so many people. Naive statistics, and perhaps "intuitive" statistics, say it's no different. In reality it's hugely different. It is generally preferable in reality to take the second choice because additional realities intervene to give you time to deal with the problem, allowing the existence of fairly highly-reliable systems, whereas those same additional realities mean that in practice, you will lose data with some frequency if you select the uniformly random result. Sometimes the better systems still catastrophically lose data, that is indeed inevitable as you point out, but what it takes to knock out that system would have result in lost data in the bad uniformly-random system, too, so in practice it's not much of a tradeoff.