Probability - How does it work?!

. . . or imagine two players rather than one, they both choose a card (one the far left card and the other the card on the far right) the host removes the rest of the cards, do they both improve their chances of finding the card marked X by swapping ?

If the two players are aware of what each other is doing then no. Either: one of them has the winning card (2/1000) but they don't know which, or: the host has already revealed the prize and they've both lost (998/1000). The presence of the other player has changed the constraints on what the host does, so this two contestant game is different from the one contestant version.

If each is unaware of the other then yes, but there is only a small chance that the host can turn over the same 998 cards to both players (if one has picked the winner with their first choice). If that happens then it will be rational for both players to switch and one will win and one will loose. If neither picked the winner on their first move then the host must show each player the other player's card as one of 998 and leave the same card unturned for both, and both players will rationally switch to that card and win.

Different states of knowledge lead to different rational conclusions. If you can cope with that then you are a Bayesian. If not then philosophers will lead you round in circles as you try to define chance and randomness.

When the player first picks a card and thinks there's a 1/1000 chance of it being the winner, the host knows differently: he either knows that it is, or knows that it isn't.