I just started playing FNV a few weeks ago, and I've been getting into Caravan a bit for money and kicks.

For those who haven't played it, the basic rules are here: http://fallout.wikia.com/wiki/Caravan_(game)

I've done some reading on deck construction, and I've seen a lot of people recommending using lots of 10, 9, and 7 cards. I think this is good for starting out, when you don't have access to a lot of cards, but I believe I can show that it's not "optimal" when you have access to all cards. I'm still wrangling with the precise combinatorics, but I'll describe the general ideas here.

First, I'm going to use the following terms:

Track: A set of cards determining your bid (number of points) for a specific caravan (this is the term that the game uses).

Turn: An opportunity to play a card.

Sell: A track whose bid is 21 - 26.

Bust: A track whose bid exceeds 26.

Overview

A key principle is that turns are the most important resource you have: You want to achieve 2 or 3 sells before your opponent does. A lot of people seem to focus on getting the highest sells - but with proper play, you shouldn't find yourself in situations where you and your opponent are actively competing on the same track (more on this later). Anytime you do, it's much better to bust his track than to try adding to your total, which would mean keeping low-number cards in your deck.

Additionally, any "offensive" card you play (J, Q, or K on an opponent's card) is essentially meant to "destroy" turns by your opponent: you make some of the turns he's already spent useless, and you potentially cause him to take excess turns.

Since you can only play one card per turn, and since it takes at least three cards to get a sell, an ideal deck is going to give you as many opportunities as possible to get a sell in exactly three cards ("triples"). In fact, any card that can only be part of a 4-card sell is strictly worse than a card that can also be part of a 3-card sell, and should not be in your deck. This is the general idea behind a small 10-9-7 deck, so it makes sense that this kind of deck is going to be very good.

However, there are problems with a 10-9-7 deck:

1. Order matters. If you're forced to start with a 9, you must have a 10 and 7 of the same suit, or a 7 and a K, to get a sell. If you're forced to play a 10 and 7, the only card that will get a sell is a suited 9. The list goes on.

2. More distinct numbers. Each additional distinct card you put in your deck means each one is less likely to be drawn, assuming you keep your deck small (which you should).

3. Limited selling combinations. This is the key point, and I'll go into it more below.

You can reduce problem 1 by keeping all 10-9-7s of the same suit, or at least by minimizing the number of suits (you should need no more than 2). But why deal with them in the first place? Instead, I propose the following deck:

Building a Better Deck

4-5 10s and 6s, suited

4-5 more 10s and 6s, suited

2-4 Js

8-12 Ks

I call this this T6 deck; it should also work reasonably well with 9s and 8s in place of 10s and 6s.

Brief Overview of the T6 (10s and 6s) Deck Compared to the TN7 (10s, 9s, and 7s) (WARNING: A little math)

The T6 deck has the following "sell" combinations:

10-6-K (26 pts): This is the most common three-card combination in the deck. For example, with 5 of each number card, eight Ks, and two Js, there are 800 three-card combinations of this type, meaning that out of any three randomly drawn cards, there's an 800/4060 = 19.7% chance that it will be this combination.

Contrast that with TN7, with eight of each card (which is actually "overloaded" in that it leaves you with room for only six non-number cards instead of ten); then there are only 512 combos of this type in a 30-card deck, for a corresponding chance of 12.6%.

With seven of each, it drops to only 8.4%, and it gets worse from there. In fact, this may not even be the most common "selling" triple in the deck, depending on how many Ks you have...and every other triple in this deck is worse than 10-9-7, since they all get less than 26 points.

Even if you did make those percentages equal, you'd still be worse off, because 10-9-7 depends on order (or suits), while 10-6-K depends on neither.

Let's look at other triples in the T6 deck:

10-6-10 (26 points): 400 (9.9%) or 500 (12.3%), depending on if the first 10 is the same suit as the second.

6-K-K (24 points): 280 (6.9%)

6-10-6 (22 points): Same as 10-6-10

Total % of possible triples that are sells: 46.3% - 51.2%

Expected points per triple: 11.5 - 12.7

Compare to the TN7 deck I described above (with no Js, nine Ks):

9-7-K (25 points): 343 (8.4%)

9-7-9 (25 points): 140 (3.4%) or 168 (4.1%), depending on suit breakdown (5-2 or 4-3)

10-7-K (24 points): 343 (8.4%)

7-9-7 (23 points): Same as 9-7-9

Total % of possible triples that are sells: 32.2% - 33.6%

Expected points per triple: 8.0 - 8.3

"Expected points" is a summary measure reflecting how a given triple in T6 will typically outscore a triple in TN7. On top of this, T6 (very strongly) "stochastically dominates" TN7. The basic idea is this: Rank each possible three-card combo by the number of points it produces. To start with, the first 1200 combos in the T6 deck (in the worst case) produce 26 points, while the first 343 in the TN7 deck produce 26 points. So for their "best" 343 triples, they both score 26 points.

For the next 511 triples, T6 scores 26 points and TN7 only scores 25 points. For the next 343 triples, T6 scores 26 and TN7 scores 24, and so on. Stochastic domination (first-order) means that if you rank all of the triples in the two decks and compare them, then T6 outscores TN7 in every comparison...often by a lot. In fact, in the worst case, there are 515 triples where T6 scores a "sell," and TN7 doesn't!

So don't let the fact that TN7 can produce 26, 25, 24, and 23 points fool you - the bottom line is that T6 will produce 26 points far more often - in fact, more often than TN7 produces 26, 25, or even 24 points.

The anolysis above is far from complete, but I didn't want to overload a first post. You also need to consider your initial hand, including the fact that you have to lay down three numbers at the start. Even here, T6 has a strong advantage (TN7 has a 15% chance of having less than three 10s or 7s, while T6 has a 0.3% chance of having less than three 10s or 6s). You also need to consider mid-game, when you have 1 or 2 cards in a track already and have to "wait" for the last one to complete the sell; T6 has a strong advantage here, too, since there are much fewer "bad" cards.

Kings and Jacks

Kings are awesome. You can use them to double (or quadruple) the value of your own card, or use them to "bust" an opposing player's track. Busts can be extremely damaging - to recover, at a minimum your opponent needs to play a Jack to remove the "busted" card, then replace it with at least one card. So it costs him two turns, while it only costs you one turn to play. In extreme cases, it can be devastating: if he has to replace his entire track, he has to burn a turn discarding the track, then play at least three more cards to get a sell - so you've wasted at least four of his turns, at the cost of only one of your turns!

One great thing about T6 is that it loves Kings. They're needed for your 26-point sell, and they can be used in other sells, as well. For TN7, Kings are only part of lower-point combinations. On top of that, more Kings means less 10s, 9s, and 7s, which hurts your chances of getting a 26-point combo. This synergy in T6 makes it very potent in practice.

A few words about Jacks: It's usually not worth it to play a J on a single opponent's card; it costs you one turn to play, and it costs him one turn to replace the lost card, which is a net gain of zero. However, I still recommend keeping a few Jacks in your deck. They come in useful "defensively" (you'll only ever need to replace one card if your opponent busts you), and they come in handy "offensively" in emergencies.

Queens are basically useless for T6, and not worth a slot in the deck. That's a good thing, too - it increases the chances that you'll be able to complete a selling triple.

Basic Strategy

It's important to keep in mind that, while all three tracks need to be "sold" for the game to end, you only need to win two of them. So the overall strategy is this:

- Lay down your initial three number cards (10s or 6s).

- Figure out which track your opponent is trying to win. In my experience, almost all opponents will pick a track to focus on (once they're done trying to mess with your cards using Jacks).

- AVOID that track. Instead, put an additional 10, 6, or K on the OTHER two tracks until each one is 1 card away from selling (to you).

- Try to complete your two tracks with a third card when your opponent has 21-26 (or close to it) on the track he/she chose.

A lot of the time, an opponent will mess with one of your "sold" tracks between the two turns it takes to win the game, either by playing a J or busting it with a K. In these cases, T6 makes it very easy to recover; there's a very high probability that you have another selling triple in your hand. This is also a reason to keep Jacks in your deck and save them in your hand: replace the busted card, and (because of the way T6 is constructed) you have a very high probability of having the "right" cards in your hand to complete the triple again.

Non-ideal situations may also arise. Any time your opponent is one potential turn away from winning, use a K to bust one of his sold tracks. With T6, you have a glut of Ks, so there's little worry that you'll run out; even if you do, there's no combination of two cards (10-6, 6-10, 10-K, 6-K) that can't be completed into a sell without a K, so even if you do run out, you should almost always be able to complete tracks into sells some other way.

Another tip: Once you have two sold tracks, it's perfectly fine to place a K on your opponent's third track to bump him above 20. In fact, this is the right thing to do, since it will instantly win the game for you! (I've also had games where I have two sold tracks, and my opponent stupidly sells the third track himself. Thanks for the money, bro!)

That's all I can think of for now. Comments/suggestions welcome!