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Tips lostcities
If you have handshake cards at the beginning and even one card in that suit, play the handshake and hope to draw more in the suit. To score well in this game you must invest substantially in a venture, without knowing in advance that you will draw the right cards in the right order. It is better to have some suits that take a loss (which you try to minimize) so that you can focus on making other suits pay off.
There is no need to attempt all 5 expeditions; usually 4 is sufficient (and it's likely one will score poorly or negatively).
Drawing from the deck is vital. Obviously, if a good card is available among the discards, or you need to delay the endgame, take a discarded card. But otherwise, take from the deck, because either it's a card that may benefit you, a card you can discard to buy time, or the card your opponent is waiting for.
It's often more constructive to hold on to a suit your opponent is trying to complete than to try completing it yourself!
Do not be afraid to lose a small amount of points in a suit if it allows you to stall and continue drawing from the deck. Effective stalling (while you wait for the cards you really need) is the heart of this game.
Keep in mind that if you leave a large gap in a suit, this helps your opponent: if you play Blue 7 after Blue 3, this means that your opponent may safely ditch Blue 4, 5, 6. Forcing them to hang on to cards for a long duration is important.