The expected value of the product of two independent random variables is the product of the expected values of each; this concludes my proof that betting everything on each round is expected value maximizing in a finite game (and infinite too, if you adopt the common ways to make “infinite” precise). I’m surprised the dialogue got that far without this being brought up!
The expected value of the product of two independent random variables is the product of the expected values of each; this concludes my proof that betting everything on each round is expected value maximizing in a finite game (and infinite too, if you adopt the common ways to make “infinite” precise). I’m surprised the dialogue got that far without this being brought up!
Oh, right! I would have been able to give that proof ten years ago, but I’ve forgotten a lot since leaving university.