> Or in other words if your range for random numbers is similar to the opponents range. There's no such animal as "the opponent's range" here. The problem does

> Or in other words if your range for random numbers is similar to the opponents range. There's no such animal as "the opponent's range" here. The problem doesn't specify that the opponent chooses their numbers from a range, or anything else - all that's given is that there are two numbers and we know nothing about them. And if that's the case then it follows that any random number we choose might be between them, in which case our strategy beats chance. Note that nobody's claiming our choice is likely to be between the opponent's choices, just that the possibility hasn't ruled out. None of this makes any assumptions about their numbers. If you're hung up on the possibility that the opponent chooses numbers so as to counter this strategy, the author points out elsewhere that if you pick a number from an unbounded range (like a normal distribution) then you'll have a nonzero (though vanishingly small) chance of falling between any two numbers the opponent chooses.