The point of that analogy was to create a situation in which someone is right 55% of the time and see how the language "prudent and cautious" feels in those circumstances.
Whether that means rolling over a certian number on a die, or rolling a specific number on a very strange weighted die is irrelevant.
Consider, instead, something like guessing whether someone has had cancer. Only 8.5% of the population has ever had it. If you can guess randomly, you'll be right about 8.5% of the time. If you can guess correctly 55% of the time, you're doing far better than random guessing.
The implicit assumption of the "probable cause" concept is that the base rate is low. I.e. only a small percentage of people have illegal contraband. If a police officer is able to guess that someone is more likely than not to have contraband (i.e. more than 50% correct), then he must be acting on some concrete clues, because he's doing far better than if he just searched people randomly.
"The problem here is that invasive searches based on no more than a government official’s hunch is precisely what the Fourth Amendment is supposed to guard against."
Due to the high alert rate, we actually have a pretty good idea of the base rate of drugs in the situations that this dog is being used in (~50-60%).
The question is whether the dog is actually providing probable cause when the dog has such a high false positive rate.
The assertion of the article is specifically that drug dogs are being used and trained by police in ways that allow them to be be used as "a probable cause generator".
"The Supreme Court originally gave its imprimatur to drug dog sniffs because when used properly, the dog’s finely tuned sense of smell can detect drugs and their absence with incredible precision. But that caveat — when used properly — is critical. If a drug dog isn’t eliminating any innocent people, if it’s validating the suspicions of the police nine out of ten times resulting in searches for which up to half or more of the suspects are innocent, then descriptors such as finely tuned and incredible precision no longer apply."
Thus the base rate that we should be judging the dog against is not the base rate in the general population, but the base rate in the dog's tested sample. We need to incentivize the cultivation of higher levels of accuracy that the dogs are capable of providing.
Now if you take the 50% of people you guessed to be positive for test, only 4.25% will be true positives, indicating 8.5% accuracy rate; if you take the 50% people you guessed to be negative for test, 45.75% will be true negatives, indicating a 91.5% accuracy rate.
But your overall accuracy rate is 50%.
edit: Seriously? A downvote for this comment?
I downvoted your comment because the argument you are attempting to make is incoherent. I'm sure that you understand what you are trying to say, but as written your comment does a poor job of expressing that point of view.
If have a procedure for guessing the number rolled on a 100 sided die, you are choosing between 100 different possible guesses. That is nothing like a dog guessing if a person has, or does have drugs (two possible guesses). Attempting to compare the accuracy rates between those two cases is major statistical error.
I thought this difference would be obvious to most readers of HN and was thus surprised to see such a simple statistical error being made. I did not think that verbose explanation would be needed once the error was pointed out.