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Why should the order that the games finish affect your final score?
It actually shouldn't make a big difference. The mathematical equation ensures a fair rating, however, you have to see it in perspecive of 10-20 games. If you just look at 2 games, it's hard for the system to find your actual skill level.
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When playing multiple games, should your tactic be to kill your king in your losing games as quickly as possible?
Nope. Try to stay alive to make as many points as possible.
By the way, the upcoming release will show how your rating changes: +/-Quote:
Similarly, when you are the clear winner, should you delay victory until after your losing games have finished?
Not necessary - I don't think it makes a difference. You are welcome to check out the rating equation

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Is it possible to "game" the system by losing a few novice games -- dropping your expected rank to last in every game you play -- then winning every game from then on? It seems that this tactic would net you more points than simply winning every game from the outset.
No.