That first game experience was the only experience I had with No Thanks. It was one of the dullest games I have ever played. For such a simple game, it should be easy to understand what is a good play, but it really didn't seem to be. I haven't played it since because it went over so poorly. I'd be willing to give it another shot but my one and only experience was dreadful.
The basic gist is you're going to use your chips to pass on cards until it becomes a good enough deal for someone to take it, and then you use the cards you have to extort your opponents.
Let's say the 33 card is active (35 is the highest in the game). Say 16 people pass until you finally decide it's worth it to pick the card up along with the tokens. If you're in a 4 person game, 12 of those tokens were put down by others. Since each token subtracts one point from your score at the end of the game, you're only netting 21 points of the 33 card that you picked up.
Now, where the game gets fun is let's say the next card is the 35 card. No one wants to add 35 points to their score, but you might not mind picking it up if you think the 34 card is in the deck too and you can make a sequence which will add only the lowest sequenced card (33) to your score. So maybe you'll pick it up, but you want to make everyone else pay you to do it first. So you keep passing until there are 16 tokens on the card, then pick it up.
Then later the 34 comes out. And adding that card to your set will cost you nothing, but it would cost everyone else 34 points. So you start extorting them again, but when the tokens on it get to 16 you decide to go one more round, and someone else takes it and fucks you, because now you can't complete your sequence and your 33 and 35 both get added to your score.
The higher the card you pick up to try to start a sequence, the more it hurts your score up front, but the more you'll be able to get out of your opponents later on in the game.
The game is crazy fun, especially if you're having a few drinks.