Cards may be turned up from the stock, one at a time, and placed face up on the wastepile. Both the top card of the stock and the top card of the wastepile are available for play, as are all cards in the pyramid which are not overlapped by other cards. Pairs of available cards whose ranks add to 13 (e.g. Ace + Queen, or 5 + 8) may be picked up and discarded. Kings may be discarded singly. The goal is to discard all cards.
There are three piles of cards in pyramid-shaped tableau. The piles are the stock, which starts out filled with all cards not in the tableau; the wastepile, where cards from the stock are dealt; and the discard pile, where matched pairs of cards are removed from play. The rules allow cards to move from the stock to the wastepile and back a couple of times during the game, these two piles can sometimes be thought of as a single source of cards. We will occasionally say "stock" for brevity when we really mean "stock and/or wastepile."
You can pick cards up from both the stock and the wastepile, so this move makes more cards available to you, and increases your choices and chances.
In fact, make a habit of moving the stock card to the wastepile before playing it. It can't hurt to see the next card under it before making your final decision about how to play it.
It's hard to discard from the stock. Occasionally, you'll get lucky and find a matched pair next to each other in the stock. But most of the cards in the stock can't be matched with other cards in the stock; they have to be matched with cards in the pyramid. This means you should not be too eager to match pairs of cards from the pyramid, because you might need one or both of them to match cards in the stock.
Remember what you've played
Don't trap half a pair under the other half
Be patient about matches in the stock
Remember that there are times when you must match stock cards with pyramid cards, to avoid burying half a match under the other half.
Match cards from the middle, not the edge of the pyramid. Sometimes the card at the edge is one you really need or want to move. But if you have no pressing reason not to, you should favor discarding from the middle of the pyramid.
On your first move, play a stock card onto the wastepile. It gives you one more card to look at, and therefore gives you more information and more choices. In fact, you should usually not play a card from the stock until you've first moved it to the wastepile to see what's under it.
Match pyramid cards with stock or wastepile cards. Sometimes matching two pyramid cards is okay, even necessary. But in general, you should prefer to match a pyramid card with a card from the stock or wastepile. You can have at most two cards available in the stock and wastepile, while you can have up to seven available in the pyramid. This means it's harder to get rid of stock cards, so you shouldn't miss any opportunities to do so.
Remember what you've played
Don't trap half a pair under the other half. Cards at the base of the pyramid can be blocking most of the cards nearer the tip, and can't be matched with any of those cards. Make sure that such "blockers" can be matched with cards from the stock or from elsewhere in the pyramid.
Be patient about matches in the stock You can sometimes match a pair of cards that are both from the stock or wastepile. But don't be in a hurry to do so. If they're next to each other now, they'll be next to each other later, so you'll have another chance to discard them. Put such matches off until late in the game, when you're sure you won't need to use the cards in some other fashion.
Match cards from the middle, not the edge of the pyramid. Cards at the two edges of the pyramid directly overlap only one other card. Cards from the middle overlap two other cards. You should usually discard those middle cards first, making more new cards available than if you discarded from an edge.