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Subject: Lost Cities strategy ... a slightly different view rss

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Joe Grundy
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My missus started out winning all our Lost Cities games, but now I usually win. Some things that may or may not be obvious involve understanding some of the simple numbers before you start. So this "strategy" article contains some straight up play hints, but is mostly about wrapping your head around the numbers.

Here's the executive summary, with the detail and extra strategy points below:

You only have 22 cards to play. You can only make this less.
You need a minimum three numbered cards per suit. (You have 80% chance of doing it in three if you start with a 7-10 card, 45% chance if you don't.) Consider carefully your distribution of 22 plays less doublers before starting a fourth suit.
At the start, a suit is worth 22 points plus 60% of the numbered cards you have in your hand.
You scored minus 20 (or minus fourty) when you started the suit, not when you "didn't finish it". Other plays may be more valuable than bringing a suit to twenty.
Discarding is BAD... you'd better have a darn good reason. Consider abandoning options on an undoubled suit instead.
Every time you buy yourself time by picking up a worthless discard, you give time to your opponent too. So you are assuming your final plays are worth more than your opponents' final plays.


DISCUSSION IN EXCRUCIATING DETAIL:

How Many Cards?
You only get to play 22 cards into your suits. (More later about discards.)

This one's my main mantra at the start of each hand...
Unless your opponent discards more than you, you only get to play 22 cards. You only get to play 22 cards. You only get to play 22 cards.

At the end, there's 8 cards in each hand, and 44 cards on the table. There's two players. (You only get to play 22 cards.)

How Many Cards Per Suit?
You need at least three numbered cards in a suit to score positive. Basically to "do it in three cards" you need two cards out of 7 to 10. (Ok trivially you can also do 10+6+5.) If you haven't got any of 7 to 10 to start a suit it's about 45% chance that you'll "do it in three". If you've got one 7 to 10 card it's about 80% chance.

Think about how to distribute basically around 22 played cards between the number of suits you start, remembering you'll need three or four numbers in each suit you start.

Examples:
4 suits including 6 doublers: 22 plays minus six doublers, minimum three numbered cards per suit to "break even", leaves only four actual scoring cards leverage to distribute between suits including the sense of topping up the suits that didn't get to 20 in three cards.
4 suits, no doublers: 22 plays minus twelve numbered cards to "break even" leaves 10 scoring cards leeway. Better.
3 suits including 6 doublers: 22 plays minus six doublers minus nine numbered cards leaves seven scoring cards (well doubled) to top up your three suits.

So don't start four suits unless you don't have good doublers.

If you do start four suits with doublers, be prepared to deliberately abandon some low cards (2 to 4) even if you have them!. (This may be better than discarding.)


These days I often end the hand with my hand full of a "wasted" suit. But I'm winning!

Will I Get Card X?
At the start of the game, if it's not in your hand it's in the deck or in your opponent's hand. The last card you draw is usually not playable (because the game will end). You will draw 21 playable cards out of the 52 cards you don't start with.

You have roughly 40% chance of getting any one card you don't have at the start. Take off roughly 1% for each card drawn from the deck (by either you or your opponent).

Hoping for a single card is usually a mug's game, except maybe for the long suit bonus. Of course, you may be hoping for three single cards in different suits. This is better, at 4/5 chance you'll get one of them or 2/3 chance you'll get two. By the end of the hand.

What will this suit be worth?
When you look at your starting hand, a suit will average 22 points, plus 60% of whatever you already have. eg if you have just the ten you will on average see 22 + 60% x 10 = 28 points in this suit. BUT: You may not be able to play it all, if the low points come late.

Should I play an "unsupported" doubler?
Each doubler is worth ... the expected suit value minus twenty. Multiple doublers are only worth more because it gives you focus (eggs in one basket) and more chance of an eight card suit.

Each doubler for an otherwise empty suit would be worth an average 2 points, assuming you could expect to play all the cards you get in that suit. I consider it's a start, it keeps options open, it's better than discarding, but only if there's nothing else to play.

Should I Discard?
Remember the mantra? ("You only get to play 22 cards.")
I lied.

You get to play 22 cards, but minus a card every time you discard
You both get to play plus 1/2 a card every time either player picks up a discard.
Note: if your opponent never discards, you can only make the +1/2 for picking up a discard if you alread did -1 by discarding, so the net effect is minus half for you, plus half for your opponent.

Each time you discard you lose a card from your final layout. Is it worth it? What's an average card in your layout worth? This question really depends on if you have the discipline to maybe abandon some low point cards if you are shortening your layout. But assuming:
10 to 12 of your cards are just for "breaking even"
10 to 12 are for scoring
Usually, say, 20 to 80 points per hand final score
Then in really loose numbers one average card extra card is worth somewhere about four to six points. Or, to put it another way, one average discard is worth about minus five points.

But you don't discard just one, do you!?

Let's paint a scenario by way of example.
You have three suits each waiting for a "nice" card. One of them is possibly going to make the 20 point bonus so you're waiting for the very next card in sequence. The other two suits, either of the next couple of cards will do. So you're hoping for any one of about six cards. It's early in the game, only about ten cards drawn so far, 34 still in the deck.

Hmmm. 34 in the deck, 8 in your opponent's hand, 6 that you want out of 42 you don't have. You've got about 1 chance in 7 of drawing a "nice" card... so you're going to make an average of 7 discards to get it, or about minus 35 points!

A more favourable scenario example...
You've played two doublers, you're hoping for a doubler in any of three suits, or the two or three in either of two suits. That's still only about eleven cards. Maybe 40 cards left in the deck and 8 in your opponent's hand, it's 11/48 or about 1/4.5 ... lose 23 points to discard "waiting for the right card".

A most favourable scenario example...
Near the end game. Ten cards left in the draw pile. You want any of six cards, the average value of those six cards to you is over fifteen points. Here, at last, there's a chance it's worth batting for 6/(10+8) or 1/3 chance of getting a fifteen point card. (Of course if you give up on one of your gaps you've still got four cards you might get. And this late in the game you're counting out the plays for the last five-to-ten turns. So it's not straightforward.)

Discarding is rarely worth it! (Even worse if you discard something your opponent can play later.)

As an alternative to discarding, you can play out a suit with three or four cards for a couple of positive points. eg you're less likely to score big in a suit your opponent has started, so when you need to buy some time to pick up cards, consider playing what you've got in your opponent's suit (if you have several cards there to play) and let it be, even if it's slightly negative.

So, Really, Should I Discard?
Now that I've poured ice all over the discarding idea, I'll thaw it slightly.

Remember: 3 suits if you are playing good doublers, 4 suits if you are playing none? You can consider one of those suits can be the "discard" suit, which will be worth zero at game end. So if your 3rd/4th suit is looking really unlikely, ok, start discards and plan to start one suit less.

Still, of course, only discard sparingly... but now you're using that discard of three to five cards in order to buy time to maybe draw one or two better cards for your other suits. (Don't kid yourself... if you get one extra good card you've done well.) So the time to discard the first three may be as soon as you made the decision to discard one. But (a) don't give cards to your opponent and (b) play any obvious plays available to you on your existing suits first. Earlier discards means you can see and plan any new options better.

At The Wire... the final plays
Don't get hung up on making each suit hit 20+. You scored minus 20 or minus fourty when you started the suit, not when you didn't make it up to 20.

A tripled five is worth more than an undoubled ten regardless if the suits are +ve or -ve, so in general play to fill gaps in the suits that are well doubled, eg in the early game by playing out what you've got in an undoubled suit to buy time, and in the late game by simply abandoning the undoubled suit to be negative if you are running out of turns.

If you have too many plays left, count your turns and skip the low scoring cards... which might be an undoubled eight or ten!

You can bluff (which of course can backfire)... at the wire if your opponent has obvious plays they want to make and your remaining plays are more subtle, you can push your opponent to draw the useless discards while you get the remaining deck if they believe you are ready to draw down to the end of the game. Which may stop them getting that last ten they were waiting for.

You don't need to play every possible card. Especially if your opponent's last plays are worth more than yours, count out your plays, abandon the low ones, and run out the hand as quickly as possible.
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Daniel Corban
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Reading this makes me want to play Lost Cities again. It's been a while. Interesting post. Thanks!
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Joe Grundy
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Glad to have touched a nerve. (Thanks for letting me know.)
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Lauren Neeff
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This is great. Thank you.
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Art Clausen
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Joe, I was about 24 games of play into my Lost Cities career, and I was getting a little frustrated. I originally thought of the game as being like cribbage, you get the cards and win 1/3 of the time, your opponent does another 1/3 of the time and you see who the better player is by winning the other 1/3 of the games that could go either way. I was searching for a strategy and losing more than my fair share. At first I thought it might just be an outlier of bad luck, but I was losing pretty soundly and steadily to my boss everyday at lunch. Many times it wasn't apparent that it was bad luck.

So, I resigned myself to the fact that I was just playing poorly and I had to figure out why. I read another rather lengthy and solid strategy guide on here, and it was like I wrote it. So, I'm thinking either it really is bad luck or I'm just not executing my own strategy correctly.

Then I read your little guide here. Wow! What an eye opener. I played my boss at lunch today and beat him soundly both games. I discarded once each game. On top of that, I only drew 4 multipliers each game, and three of them were worthless to me. He had to deal with a time crunch each game. I actually ended up playing 5 suits one game and four the other. Only one -2. The strategy just made sense to me and the results were not luck generated. It worked. I can't wait to see how it works if I actually manage to get a run of one suit or a few early multipliers. Of course, my boss will adjust to the time crunch eventually, but your guide is a very useful tool to have in one's arsenal. Great job and thanks. This game is going to be even more enjoyable now!
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