Even if I win the lottery, it was still a negative expected dollars choice to play the lottery.
At that point in the post, I hadn’t introduced mixed states. So the only options are to choose among fully deterministic worlds. Obviously if you had the choice between “win the lottery or don’t win the lottery”, then you’d go for the first.
Later when I bring in mixed states you can model such things as “buy a lottery ticket” as the achieved state, which generally has expected disutility.
At that point in the post, I hadn’t introduced mixed states. So the only options are to choose among fully deterministic worlds. Obviously if you had the choice between “win the lottery or don’t win the lottery”, then you’d go for the first.
Later when I bring in mixed states you can model such things as “buy a lottery ticket” as the achieved state, which generally has expected disutility.