Counting on numbers
Suppose, you are a maximizer of expected utility with an unbounded, aggregative utility function (and with no risk aversion and no temporal discounting). You are perfectly rational. These assumptions are very unrealistic in the case of humans but let that go for the sake of the argument. Let us further assume that for you the expected utility of (A) is 1 (the probability of keeping it, given (A), equals 1, and the utility of having it equals 1). Apart from that, I claim that I can give you things of any value for you I like with no effort or loss on my side. And I want to make you choose (B) (cf. Bostrom 2009: 445). Here is how this game is played. You start by fixing the value of '/?' (or '1/w'); I follow-up by determining the value of 'ra'. I win just in case you choose (B). What do I have to do to win? The answer is easy: I let you give me your number n and respond with a number m such that m times l/n> 1. Or, more simply: such that m>n. My winning strategy in Looks Like A Tricky Game very much looks like my winning strategy in The Very Simple Game.