You're right that both the in-manual and in-game introductions to Caravan are not very effective. This is what I figured out via a combination of trial-and-error and the instructions.
(Also, I keep the Caravan rules card from the deck that comes with the special edition out when I play New Vegas. Very handy quick-ref for the face cards once you get used to the rest.)
2 players play the game. You can use any cards you want, as long as (a) you have at least 30 cards in your deck and (b) no two identical cards (EG, 2 of clubs) come from the same casino. (In real life, if you wanted to play, they couldn't be the same deck/brand. Unless you frequent casinos enough to have a collection. :)
The game combines elements of blackjack, war, double-solitaire (that is, two player head-to-head solitaire) and even Uno.
Each player is initially dealt 8 cards. Your first three plays to the board must set up your initial caravans -- you have three to set up. Give them each a numbered (ace through 10) card. During these plays, you can discard any cards from your hand that you like, drawing a replacement card from your deck. Cards you discard are gone from play -- so don't discard your good ones. Discarding at this stage is required if you are dealt eight face cards and/or jokers.
Each of those caravans has a suit and a direction. The suit is the suit of the last numbered card dropped on the pile. The direction is either up or down from your starting point. An important thing to note (and I had to lose about a dozen hands before I learned this) is that the direction does not have to be sequential -- you do not, for example, have to follow a 10 with a 9, or a 5 with a 6. You can have the following sequence (which adds to 26): 10, 9, 7.
To play a numbered card on one of your caravans, it must either be going in the appropriate direction, or it must be of the same suit as the last numbered card. However, under no circumstances can you play the same number twice in a row, no matter what suit they are.
You're targeting a range of between 21 and 26 (inclusive) for each your three piles.
During the first three moves, when setting up your caravans, you do not draw replacement cards for those you lay out. Thus, when those turns are complete, you will have five cards in your hand.
Players take turns playing one card each. If you cannot or do not wish to play, you can discard a card from your hand. In any event, once a card is played or discarded, you draw a replacement from your deck. If desired, instead of playing or discarding a card, you can discard an entire caravan.
Play continues until "End game," below.
Cards and Their Effects
- Ace: Always a value of 1. Consider a number card except when a Joker is involved.
- 2 - 10: Face value.
- Jack: Removes the target card and all face cards attached to it from the board. Typically played offensively against the other player.
- Queen: Reverses the direction of the caravan. Can be used offensively and defensively.
- Offensive example: reversing a descending caravan to ascending when the opponent is near enough the target (and at a high enough last number) that the direction switch prevents him from landing within the range. Rare, but very effective when you can pull it off.
- Defensive example: You've been ascending or descending and either can't go farther (at a ten or an ace), or you need to reverse direction in order to land in the target range.
- King: Doubles the value of the target card. Again, can be used both offensively and defensively.
- Offensive example: Double the value of a high-value card in your opponent's caravan when he's at the high end of the target range. Boom, now he's overloaded.
- Defensive example: Double your own card (typically effective early-game) to get a leg up on the competition.
- Joker: This one has different impacts depending on the card you play it against. Often ends up doing "collateral" damage -- that is, damage to you as well as your opponent. Use them wisely.
- Against an ace, removes all non-face cards of the same suit as the ace from the table, except the ace on which it's played.
- Against numbered cards, removes all cards of that value from the table, except the card against which it's played.
The game is over when all three Caravans are successfully sold. When a caravan is between 21 and 26 (inclusive), it is considered sold. However, you can continue to pile weight on a sold caravan, and your opponent can continue to outbid you. Whichever player has the highest bid (without going over) on two out of the three Caravans wins. Ultimately, the goal is to get two out of three caravans as high as possible (preferably 26) before the opponent does, and to prevent the opponent from outbidding you by using offensive maneuvers against him.
Note that the comments refer to bugs regarding this behavior. I've not personally observed any bugs here; I've never personally seen the game end without three caravans being sold. However, not all three must be sold by the same player. For example, if we numbered our caravans 1 - 3, a game could end with one player having sold #s 1 and 2, and the other having sold #3. Whoever has sold at least two at the end of the game has won.
But wait — there's more
In case this wasn't quite clear/useful enough, there's an excellent explanation here.
Building a Deck
I'm not going to give many strategies on this, but just the basics. First off, as of the (what I assume are final) patches, cards you purchase or find seem to go in your deck straightaway. You will need to modify the deck you have in play before the game begins. (This is the part where you see all your cards in two rows on the screen.)
For your deck, you want to think about the odds of getting the card you need when you need it. Really large decks allow you to survive even the most aggressive AI, but often don't provide the attack cards you need to keep the opponent from winning while you build out your plan. Really small decks often provide a card you need, but have no longevity against an opponent who relentlessly hits you with jacks and kings.
Personally, I build what I call a Deck of Black Death:
- Exactly one of each Ace (heart, club, spade, diamond)
- At least 4 of the following (all clubs or spades): 2, 3, 7, 8
- At least 3 of the following (all clubs or spades): 9, 10
- At least 5 of the following (all clubs or spades): 4, 5, 6
- At least 4 of the following (I try for all black, but can be any color): King, Jack, Joker
- Exactly 3 Queens (again, I try for all black, but can be any color)
Why the emphasis on black? Because of Joker-on-Ace. In all my playings, I've never seen the AI play a Joker. Never. But I will use them very aggressively. And by keeping most of my deck contained in two suits, I know that I can always play a Joker on a red Ace, hurt the AI, and probably not hurt myself at all. (YMMV if you're playing with actual cards and actual people.)
The other reason I emphasize black is to increase the odds that I can switch direction without playing a Queen. All of my value cards are either spades or clubs, making it more likely that I will get a matching suit when I draw, or already have one in-hand.
Note that this is pretty flexible: "at least." The main thing is the general proportions -- don't go for too many high cards, because they reduce flexibility. By the same token, don't get too many low cards, because they delay your advancement. You need a lot of face cards, but you need them to be well-outnumbered by your value cards. The only inflexible bits are the Aces and Queens -- Aces because you only need one of each, Queens because they have very limited use, especially with limited suits.