Hypothetical situation: You are playing 5 card draw poker, with 3 draws. On the initial deal, you are dealt 3 of a kind fours. You are looking to make a full house or four of a kind. Are your odds better to improve your hand to keep 444 and card X and draw 3 times, hoping to pair card X or catch a fourth four, or to draw two cards each time, hoping to catch a fourth four or be dealt a pair or cards.

1.1.What is the probability that in keeping 444 and card X, with three draws, that the final hand would be 444XX?
2.2.What is the probability that in keeping 444 and card X, with three draws, that the final hand would be 4444X?
3.3.What is the probability that in keeping 444, with three draws, that the final hand would be 444 and any pair?
4.4.What is the probability that in keeping 444, with three draws, that the final hand would be 4444 and any given card?
5.5.Overall, which method will yield a better chance to improve, making either four 4s or a full house, 444XX?
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