When you plug the card that says that once the player has won the most points, how it works in case of a tie score.
Thanks for the reply.

I'm not sure I understand the question here but if you're asking who wins in case of a tie amongst two (or more) players when the Stage II Public Objective Imperium Rex is played the base game rulebook has the answer on page 14.

"While the Primary Ability of the Imperial Strategy card is resolved, it is possible that the “Imperium Rex” objective card is drawn from the Objective Deck. When this card is drawn, the game ends immediately and a winner is declared The winner is the player who has the most victory points (the active player does not receive the 2 victory points). If there is a tie, then the greater number of resolved Objective Cards breaks the tie; if there is still a tie, then the greater number of planets, then unused Command Counters, and then the total number of Command Counters on a player's Race Sheet. If still tied, then the game ends in a draw between the tying players."

Thanks for answer.

This is correct.

In addition, if two players reach 10/14 VP at the same time, the player with the best (lowest) strategy card will win, in case that situation ever comes up.

Bowoodstock said:

It doesn't, since Objectives are claimed in order of initiative and the game ends when a player reach 9/10/14 VP

Don Kristobal said:

Or whichever amount of VP you've agreed to play until...

Initiative = strategy card if I'm not mistaken.

Bowoodstock said:

Yes, your initiative is the number on your lowest strategy card. Yes, objectives are technically ALWAYS claimed in initiative order but initiative order usually isn't relevant unless two or more players are about to claim victory on the same strategy phase.

itschowda said:

And yes, Initiative is ALSO the name of the base set Strategy Card with the (Initiative-)number 1 on it.