In a duel, both players start off with the same resources. 5 cards per hand, and one draw per turn. However, when one plays a card, often times, they lose that card in the process leaving them with one less card, or sometimes less than that. The concept that a player is in a good position when he/she has more cards on the field and in the hand is called card advantage. This theory is extremely important in becoming an advanced Yu-Gi-Oh player, and especially in becoming a successful deck builder.
1. Why is Card Advantage Important?
Basically, the average player will look at a duel scenario and pick out the person in the lead based on life point count and the attack points of the monsters that they have on the field. Although this can sometimes be used to gauge the leader of a given duel, a much better way to approach the matter is via card advantage. Generally, a player with more cards on the field and in the hand, even if they aren't necessarily leading in life points, is in a better position than someone with no cards in their hand and a monster or two on the field.
Having Card Advantage gives you options, and in a duel, that is vital. The ability to use your resources to produce many different effects is invaluable. I can't speak for all of us, but I know I've been in situations where I have exhausted most of my resources in a duel bringing out one or two big boss monsters, and am left with no cards in my hand. I ram my opponent for a few turns and they stall out a while, until the topdeck the card that they need in combination with the 4+ cards in their hand to make a game-winning play. This is a perfect example of Card Advantage.
2. What do all of those +'s and -'s mean?
The pluses and minuses are just shorthand notation of writing down what kind of advantage, or disadvantage, a given card generates. Its quite easy to calculate the card advantage potential of a card. A plus is given when you end up with more cards either on the field or in your hand than you started with. A plus can also be awarded if you take out more of your opponent's cards than your own. A minus is given when you have less cards on the field or in your hand than when you started, or for some reason, your opponent gained cards because of the card you played.
I think a good way of explaining this is by example. A card such as Upstart Goblin is a +0 because you gain a card with it, however you also lose a card as the Upstart Goblin you originally played goes to the graveyard. You end up with the same number of cards as when you started.
Another slightly more complex example is Gemini Spark. You tribute a monster to destroy an opponent's card, which is a +0 in it of itself as you lose a monster, but so does your opponent. The second part of its effect states that you draw a card, however you also lose the initial Gemini Spark, resulting in another +0. The card in its entirety is a +0.
A -1 type of card is something such as Dark World Dealings. You get to draw a card, but must also discard one, resulting in a +0. But then you must keep in mind that you had to play the Dark World Dealings in the first place, producing a -1 effect. This type of card is generally ok to have in a deck, but isn't perfect. The fact that you are losing a card must balance out with the purpose of why you are running it. A -1 search card like Dark World Dealings would excel only in a deck that needs speed desperately.
3. But hang on. I thought it was good to have stuff on your field?
Its not bad to have stuff on your field, but NOT if it compromises your hand! If your deck requires more than 2 cards to get out the win condition monster, than its simply not worth it. The ability to recover from a random spell card such as Dark Hole or Smashing Ground relies on your hand and your hand alone. Your hand is as important as your field if not more important.
An example could be, you are trying to get out an Earthbound Immortal monster card. You have the ability to special summon three monster from your hand to tribute for your Earthbound Immortal. You also have the ability to use Mausoleum of the Emperor. This might seem like a dumb example but really, most situations in a duel come down to something like this. Should I deplete my resources to do a cool play, or should I play it safe and take some damage to get the same play using fewer resources.
4. Ok. So why is this significant in deck building?
If you have a deck that seems to be able to get out the cards necessary for a win condition to take place, but just can't seem to maintain the game state for long, your problem is card advantage. This is most commonly associated with decks that tend to focus on summoning big monsters with big costs. The easiest way to fix this problem is to go through your deck and calculate the potential advantage of each card. Then think to yourself, is there a better way to accomplish this goal? Could I do the same thing, but end up with more cards in the end?
5. How can I apply this knowledge in a duel?
The most basic way to maintain card advantage in a duel is NOT TO OVEREXTEND. Overextending is basically doing too much, too fast in a duel, usually early game. Often times, overextending will deplete your hand extremely quickly just to get a few big beaters on the field. Although this might win you the duel, it more often than not loses you the duel early game. Playing conservatively until you are absolutely sure there is NOTHING that can get in your way is the safest way to maintain card advantage. A single Solemn Warning can put you at a -3 or more depending on how much you have overextended. Be aware of your opponent's backrow, possible hand traps, and graveyard effects before you even think about attempting a big play.