US during the Great Game

During the decades of the Great Game, did official US policy favor Britain, favor Russia, or favor neither? What US interests, if any, were at stake during the Game?

And for that matter, how did the Game play out in North America between Russian Alaska and British Canada, and what did the US think of it?
 
For most of the 19th century, in Asia, the US would have had little interest in the Great Game in Central Asia or the Middle East. By the turn of the century it would have likely favoured the British in China as they both sought an open trade policy with China, while Russia wanted to carve out northern China for itself.

In North America, the US generally had good relations with Russia for most of the 19th century, and would have favoured Russia over Britain, until the turn of the century when relations with the UK improved.
 
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