While I wouldn't dream of posting ChatGPT content, here are some questions you could give to ChatGPT to a make this all a fair bit clearer: First, what is an e

While I wouldn't dream of posting ChatGPT content, here are some questions you could give to ChatGPT to a make this all a fair bit clearer: First, what is an expectation value, as defined in the field of statistics? Second, is there some reason an expectation value wouldn't behave like a strange attractor from dynamical systems theory and sort of wander about, rather than settle down to a precise value? Third, what's the connection (if any) between conditional probability and expectation values? For the first example, a more interesting real world-problem would be one where the total number of different outcomes (toys) is unknown - say, counting the number of species of beetle that exist on planet Earth by steadily sampling all the habitats one can find - how long would the tails be? Variations of the latter examples might be odds that vary over time in conjunction with costs-of-entry that vary over time - what's the acceptable range of odds & costs to justify playing with some expectation of at least coming out even? That's a bit more like real-world markets.