In my experience playing this game (far, far too much) I have picked up a few tips. Perhaps, it's because I'm tired and have a final tomorrow, or that I'm zonked out on ambien and I'll forget that I wrote this in the morning, but here are a few tips for players who are in dire need of achieving a higher score.
My credentials in this are high score records at three places, an average score of 11k (when I play it all the way through) and a high of 18.4k
1. Accuracy of clicking- There really isn't a lot of explanation needed for this. Always be sure that you click the coin accurately rather than quickly. If you decide to go crazy when you see a pattern and just wildly start clicking in the general area of the coin, your time will diminish. Make sure the pointer of the mouse is over the coin, or very close, and click. That is a fundamental I adhered to when achieving my all time high, which I did today. Granted I had a lot of speed behind my clicks, which leads into the next part.
2. Practice- Not everybody is going to be quick at this right away. I remember when I first started playing, I was finishing levels at around 30 seconds and I considered 5000 to be a very good score (I can still get this on a laptop computer with a laptop mouse). This is a game that requires understanding and a good amount of practice.
Also, if you have rather quick hand/mind/eye coordination, that will speed the process up rapidly. After God knows how long of practice, not to mention a background in speed solitaire (don't ask, I'm insanely competitive) I can finish Level 1 in 10 seconds, Level 4 by minute 1, Level 7 by minute 2 and be at Level 10 usually with 2 minutes to spare. That's not a benchmark as I know there are far greater players on this page than me, but it's something to think about.
3. Scoping the puzzle- Your eyes have to be quick and see the board not just for the combination that you want initially, but for the ones after, and more importantly for the bonus coins. After my first move, and while I am making my first move, I like to look at other pieces on the board and figure out a good follow up move.
Important: Utilize the small window from when the coins disappear until they reappear to scout the board and look for your next move.
When the coins disappear, I usually like to take that time to scout my next two moves and plan. I will stick to that plan unless I see something that looks vastly better. Don't be afraid to change on the fly if you feel that it will help and save time.
4. The bonus debate- I've read that you shouldn't go after the bonus until you hit Level 5, through the first 3 Levels, and so on. I would have to agree more with the latter opinion than the former for the following reasons:
1. Level 2- A 5 bonus doesn't really help you if it holds back your time. Go with what is convenient and available, the quickest combination to get out of the level.
2. Level 3- A 10 bonus is pretty much the same, however I'm more inclined to take an extra second or two to go after it should it be within good clicking range. Again, go with convenience over trying to get under 200 points (The 10 bonus is 180 or 160, I don't remember which)
3. Level 4- Since a 15 bonus is 360 points, I'm somewhat iffy on whether or not to go after them if they are far away. I like to try to stick to a clock, and beat the level by a certain time, so if there is enough time available then I will go after a 15 bonus even if the individual coins are far away. However, they are not essential unless you are in a tight competitive race so you can avoid them without too much trouble.
4. Level 5- I absolutely go for any kind of bonus starting with this level. A 20 bonus is 600 points, and for those of you who are averaging medium four figure scores, adding 600 points to your arsenal is pretty good and something to consider. So my advice would ultimately conclude on Level 4 is where the buck stops in terms of passing on bonuses should they be available.
Those are all of the tips that I can currently think of at the moment. I'm getting a little sleepier. Hopefully this helps out those of you who need that extra kick to get your game to the next level. If not, well then I won't remember writing it 
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