In the lottery you do not have 2 choices, you have millions of number combinations to choose from, so your comment about the lottery not being 0.5 probability of winning is true, but irrelevant.
My point was relevant if you did get it. The point I made was that if there are 2 different outcomes, outcome A="win the lottery" and outcome B="do not win the lottery", that doesn't mean they are equally probable. People make this assumption because when rolling a dice all outcomes are equally probable, and that's pretty much the only prob. math they've ever done. So in the Monty Hall's paradox there are 2 doors but the p to win the car is not 0.5 when you switch, even though you can either win the car or not.