Probability - How does it work?!

if you're convinced your lottery numbers are going to win but are worried about someone else also getting it you should just play them twice.

this way if you win and have to share it with someone you get a larger portion of the pot.

if you have to share with one person you get 2/3 instead of 1/2
two people you get half instead of 1/3 and so on.

Brilliant idea. I neve thought of that. Also, and this is something that I have really struggled to understand and still don't is this scenario.

You have 3 cards lying face down and on one of them is an X meaning win and you are asked to pick one card. If one of the two cards you did not choose is turned over reveals it to be blank, so you still have a chance of winning. If you are then offered the chance to swap your original choice for the other remaining card. You should swap as this increases your chance of winning. This is a headfuck and I think it is related to 'The Envelope Paradox'