The objective of the game is is to move all cards from the three Peaks onto the Waste. You can only move open cards to the Waste, a card is considered open if there are no other cards covering it. At the beginning the whole bottom row is open. Once you move cards from the Peaks you open up other cards that you can then flip over and are then open to move to the Waste as well.
You can move a card onto the Waste if it ranks one higher, or one lower than the topmost card on the waste. E.g. if there's a 6 on the Waste you can move a 5 or a 7 there. Initially the Waste is empty and you can move any card there. You are allowed to "turn the corner", i.e. go K A 2 A K, you can put an Ace on a 2 or a King.
If you have no cards in the Peaks that can be moved to the Waste then you can get a card from the Stock and turn it over to the Waste. You can only go one time through the Stock, there are no resets allowed, so don't use the Stock unless you definitely can't move any cards from the Peaks.
TriPeaks was invented in 1989 by Robert Hogue. Hogue has performed computer statistical analysis on the original game, which shows over 90% of all the games dealt are completely solvable and, under the original scoring system, an average of 60 is theoretically possible, which indicates the scoring system is balanced in such a way that the cost of the stock is paid for from the creation of the appropriate streaks during game play. This leaves all the bonus points for the player if the player has played the hand perfectly. Of course, since only a portion of the cards are known at the time of deal, the possibility of playing a perfect hand becomes very difficult. The average score per hand for most people is around 12. Players with better strategies and tactics have averaged over 17.