What are good strategies for deciding which expeditions to start in Lost Cities?

Question

I've been enjoying playing Lost Cities a great deal, but find it very difficult to decide what to do over the first few turns — in particular deciding things like:

1. How long is it worth waiting to see if an investment card comes up, if you have some good high cards for an expedition?
2. What are enough points in a city to make it worth starting? I've been typically waiting until I have about 15 points, and I'm guessing this is too cautious.
3. Is it worth starting an expedition if you just have three low cards, say?
4. How do you deal with having a hand of high cards (which you don't want to discard) but nothing lower to start off an expedition with?

Of course, part of the fun has been in taking a big risk because you don't have any better options, but I wondered if people had any tried-and-tested rules of thumb to help beginners deal with the opening of the game?

Answer 1

1) You want to wait, but you can't wait all that long. Sitting there with half your hand made up of cards that you don't want to play is normally a huge problem in Lost Cities, and you risk giving up a huge amount of tempo to your opponent, in the very small hope of drawing one specific card. Sometimes you just have to quit hoping and start playing - after all, your opponent may have those investment cards in HIS hand! (Of course, holding out can result in the dream scenario - your opponent laying down multiple investment cards for a colour in which you hold a balance of points...)

2) With multiple investment cards? 15 sounds a safe-ish bet. But let's not forget that you can embark on expeditions without investment. I'm perfectly happy to start off expeditions with barely any cards sometimes - just because putting pressure on and psyching out your opponent can easily be worth the potential loss of 10+ points.

3) As above. I certainly would, but I almost certainly wouldn't risk multiplying my losses by 3 or 4 by playing investment cards first!

4) Possibly the most difficult scenario - you don't want to discard high cards and you don't want to play high cards, so what do you do? It can be quite good to bait your opponent by discarding medium-value cards, while holding the higher values so when they snap your discard up, you know they're on a hiding to nothing. But I agree, it's a hard situation to deal with comfortably. (Then again, it's difficult for me to feel much sympathy for someone whose "problem" is being dealt a hand of strong cards! Just play out an 8-9-10 for +7 points, and see what you draw in the meantime: a few investment cards would obviously have been nice to have, but it's not like you've really lost anything, is it?)

Answer 2

If you're looking for an advanced strategy, the game comes down to basically one question: "Will I get card X before the game ends?"

These answer to this is based on two things, first, is the odds of you getting any particular card you want, and second, the likelihood of getting it 'in time'.

Getting a card you want is fairly simple, it's the odds it's still in the draw pile times 50%. When the game starts you have the best chance of it being in the draw pile, as opposed to already in your opponent's hand. You need to read your opponent to get at the first part of this, but for any strategy for early game, it's probably safe to assume slightly less than 50% chance of getting any card.

For the second bit, namely playing things 'in time' the rules allow counting the remaining cards. This needs to be combined with the likelihood that either you or your opponent will draw from the discard piles instead of the draw pile, thus slowing the game down. You control your draw choices, so, in effect can slow the game ending by up to twice as many turns as the remaining number of cards.

As for rules of thumb, which there aren't many because the game is quite tactical, I'd say that calculating the expected value of remaining probabilities for cards undrawn, and assuming that your opponent's hand is 75% full of the cards you need is the safe way to go. Also, don't reveal your intentions (start expeditions) until you absolutely have to, as this increases the chance that your opponent will start/discard cards you need before you do. In this way it's not about what cards to have before starting, it's about your opponent's reveal.

So, specific answers:

1. Draw until odds are less than 50%. If you have 3 cards, and 10 remain in the deck, assume your opponent has four of them, so there are 3 remaining. With proper math probabilities, you need to draw 3 times to have a better than 50% chance of getting one of the those 3 cards.
2. This depends on when in the game you are. 15 points is probably too high early on, but I wouldn't start an expedition with 15 until I know if my opponent is or isn't competing in it (and they don't have hand room to block me on it)
3. Probably not. Even early game.
4. Depends on when in the game it is. Early on you can try for cornering the market early on it, before it's revealed. However, it's probably the first expedition you start, getting those cards out early so you can keep the next one secret (where there will be more competition).