From the given excerpt, the reason why George Washington believed that the game was "pretty near up" was the short enlistment policy for continental troops.
When the American Revolutionary War broke out, George Washington at some point believed that the Americans had lost.
One reason for this was the short enlistment policy of the Continental army which meant that he didn't have access to enough troops.
The excerpt in question is:
"I think the game is pretty near up, owing, in a great measure, to the insidious arts of the Enemy…but principally to the accursed policy of short enlistments, and placing too great a dependence on the militia … "
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