rules questions

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Hi all, I just started playing this with my son and had some questions where the rules were unclear. So the first one is this, are you supposed to bring you hand up to 3 cards at the beginning of each round, or his draw 1 card each turn. If it is just one card, what is with the rule that if you run out of cards to draw then you lose. If everyone starts with the same number of cards in the draw pile, wouldn't the person who goes first always run out first?