Luigi's games involve gambling. Your high score is the highest number of coins you have.
[edit]Picture Poker This is the easiest minigame to play. You can't lose! The game uses a 30-card deck. There are six ranks of cards, with five cards per rank:
Cloud (lowest) Mushroom Flower Luigi Mario Star (highest) You are dealt five cards, and Luigi is dealt five cards. You choose which five cards to discard (clicking on a card indicates you wish to discard it, not keep it). Then optionally bet more coins, then discard (or hold all your cards). Luigi will also discard. If your hand beats Luigi's, you are paid according to the following table:
Hand Example Multipler Pair Star Star Luigi Flower Cloud 2 Two pair Mario Mario Luigi Luigi Mushroom 3 Three of a kind Flower Flower Flower Star Cloud 4 Full house Luigi Luigi Luigi Mario Mario 6 Four of a kind Mushroom Mushroom Mushroom Mushroom Cloud 8 Five of a kind Star Star Star Star Star 16
Note that the table does not include your original wager. For example, if you bet five coins and win with two pair, your net profit is ten coins, not fifteen.
Probably the best strategy to use for discarding is the obvious one: keep all cards that fit into one of the above hands and throw away all other cards. Or to put it another way, throw away any card that appears only once in your hand. This is the same strategy Luigi uses, therefore it gives you a 50% chance to win (not counting the 0.6% chance of a draw). It automatically gives you an advantage of over 100%, meaning on average you will win a little over one coin per coin wagered. Wow! Casinos can only dream of getting an advantage this huge. :)
If you have at least a pair before the draw, always bet the maximum five coins. Otherwise, stay at the minimum bet. This will increase your edge even further than just betting five coins every time, but not by much, since you rarely get dealt junk hands.