I've been teaching a course on classical epistemology this term, so I've thought a little about knowledge.
A common judgement in the literature seems to be that knowledge is incompatible with a certain kind of luck -- the kind of luck we find in Gettier cases. This is then cashed out in terms of safety: for a belief to constitute knowledge it must be true in all nearby possible worlds.
While I share the initial judgement, the development in terms of safety doesn't look plausible to me. It has the wrong kind of structure.
For example, any true belief that concerns a modally robust subject matter is automatically safe. But such beliefs are not immune from Gettier cases. I'm sure one can find examples where, say, Newton's laws are used to predict whether two asteroids will collide, and the laws happen to give the correct answer ('no'), but they don't predict the correct trajectories; the true reason why the asteroids won't collide involves some feature of general relativity. Now if someone in the mid 19th century asked whether the asteroids will collide, and they used Newton's laws to figure out the answer, then their belief (that the asteroids won't collide) is justified and true, but it isn't knowledge. And yet it is arguably true in all nearby worlds.
One might try to get around any specific example, but I don't think that would get to the heart of the problem. As I said, it seems to me that there is a structural problem. The kind of luck involved in the intuition that knowledge is incompatible with luck just isn't a matter of objective modal closeness.
When I described the asteroid case, I said that Newton's laws "happen to give the correct answer". This doesn't mean that there are objectively close worlds at which they give the wrong answer. So what does it mean?
Let's back up a little. To get from our sensory evidence to non-trivial beliefs about the world, we have to rely on certain assumptions. Roughly speaking, we have to assume that the objects in our environment are how they perceptually appear to be, that our samples are representative, that there is a simple and unified explanation for most events in the world, and so on.
Given these assumptions, our (total sensory) evidence implies (or makes it probable that) we have hands, and that salt dissolves in water. By contrast, on the hypothesis that the assumptions are false (that is, that some relevant ones among them are false), our evidence does not make the same conclusions probable. For example, on the hypothesis that our perceptual experiences are never correlated with features of our environment, our sensory evidence does not support the claim that we have hands.
(That's all I mean by saying that we rely on the assumptions: our evidence supports our beliefs relative to the assumptions, but not relative to certain alternative assumptions. I don't mean that we consciously use the assumptions as premises, or anything like that.)
Sometimes, our assumptions lead us astray. Things aren't always the way they appear to be. Our samples are sometimes unrepresentative. Simple explanations are sometimes false. In such a situation, our evidence does not support our conclusions. If the conclusions are false, we have a justified but false belief. If the conclusions are true, we're in a Gettier case: we have a justified true belief that isn't knowledge.
Either way, conditional on the falsehood of the relevant assumption, our evidence does not support our conclusion.
Let's look at this from a third-person perspective.
Someone relies on a normally reasonable assumption to arrive at a conclusion. Unbeknown to them, the assumption is false (in their circumstances). Conditional on this fact, their evidence does not support their conclusion: the conclusion has a high epistemic probability of being false. If the conclusion is nonetheless true, we might say that this is a matter of luck. There was a high probability of a bad outcome, but the person obtained a good outcome.
I think this is relevant kind of luck. It is not objective, circumstantial luck, but a genuinely epistemic kind of luck.
(My thoughts here were assisted by a conversation with Max Goetsch.)