Newtonian relativity puzzle

The term “expected value” has a specific, well-defined meaning in mathematics. It is (unfortunately I guess) not always consistent with the intuitive meaning of the term. For example, the expected value of a roll of a standard 6-sided die is 3.5, the average of all the (equally likely) possible outcomes. That may sound strange since no actual individual roll can result in an outcome of 3.5. It’s probably more intuitive to say that if you roll 100 times, the expected value of the grand total is 350, which is saying the same thing.

Huh, I actually never thought about that—perhaps because in German, the nomenclature is somewhat less ambiguous: ‘expected value’ in the statistical sense is ‘Erwartungswert’, whereas in the sense of ‘value you expect to see’ it’s ‘erwarteter Wert’. Maybe it ameliorates the confusion somewhat to use the term ‘expectation value’ in English.

Perhaps one way to get some intuition is to think about it as the value you expect to see on average—i.e. if you repeat the same experiment a sufficient number of times, it’s the average of the values you actually observed. As you can’t predict the actual value in any given circumstance, this is sort of the best you can do. It’s important if you bet for money—the expectation value will tell you how much you are to gain (or loose) in the long run from a certain sort of bet.

Yeah, “expected value” is a term of art, as explained by other posters such as @markn_1 and @Half_Man_Half_Wit. It’s often used in situations where you have the possibility of gaining or losing different amounts of money, like gambling games or business ventures. You could think of the “expected value” (or “mathematical expectation”) as the amount you would expect to gain (or lose, if negative) on average each time if you could repeat the same gamble many, many times.

What I find strange is that I am aware of, and use, “expected value” properly most of the time (I play Warhammer, so have to keep expected value of my dice rolls in mind while choosing targets), but in this specific case 60 feels like the right answer to the question.

Brains are weird.