Tripeaks...the game many love and hate in the same time. For many, it's seen to be as the 'safe game' seeing how you cannot cheat at it. This along with the easygoing slow pace of the game also makes this a game to be well considered in the competitive area of Points2Shop. After a few months of playing, I've found a fairly solid method of play.
When you start, you'll find an assortment of various cards lined up behind a series of other cards that make up three triangles. Your goal is to eliminate every single card in those three triangles using the face-down cards found on the bottom of the screen, along with the help of your trusty Wild Card.
When you first go in, you may see a run just waiting to be made. The one thing to consider is that in the first tier of cards you are looking to open the most possibilities for the next tier.
If you find yourself having a 7+ or 8+ run in the first tier, try to plan out how events could turn out if you continued on with your run using your Wild Card. If you see a card that could help you with your run in the second tier of cards, rearrange the numerical path you are going so that it will lead to as many cards taken as possible.
If you happen to eliminate 4 or 5 more cards, you'll gain a run bonus. That means you'll gain 9 points on your next card, and it increases by one every card on. If you happen to take 4-5 cards, you could end up with an extra 43-55 points. If you waited to use it to get rid of a final card, you'll only get 31 bonus points. This means that you gained a greater amount of points using it here than you did for the final tier cards. (I'm not saying you should use your Wild Card by the first tier, but if you see a better run that could be combined with your first run, then you should definitely consider the option.)
As you come across the deeper tiers of cards, you may get lucky with the face cards, you may not. In the case if you run across a heap of bad cards, go 2-3 face down cards to the left and click that one. If that card does not work, repeat the process. A big mistake I see sometimes is people just clicking every single card from right to left without any variation in how they choose the cards. This method may not work all the time, but it's definitely worth a shot.
One final thing: Know when to quit. If you have a 150, and you see two cards in the final tier and you only have 5 face down cards left, then just Submit your score. If you use all 5 of your cards, you could wind up eliminating 15 points from your score. You might also get lucky and get those bonus points. In the end, it's up to whether you're willing to take the chance.
I follow this method and I normally get scores around 125-160, with the occasional 225. (Even though my record is 335, but I had insane luck with that game.)
In conclusion, always practice in the 0 point game area until you eventually end up with scores in the triple digits. Once you feel like you have a good feeling around this game, test your mettle at the 10 or 25 point games. Good luck and have fun!