7598462153 comments on Two barrels problem from the Intuitive Explanation (answered) - Less Wrong
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There are a few other cases I can think of offhand where careful reading is important. Decoding poorly written instructions and this card game in particular came to mind immediately, but on reflection I think the best example in my experience would be coding, and in particular debugging. I'm by no means an expert (or necessarily a representative sample), but at least half of the bugs I spend 10+ minutes chasing around end up being caused by a minor brain-dead error in a single expression.