It might have been pure ignorance paired with a certain amount of overconfidence that made the British general Jeffrey Amherst act like he had an army of 10.000 behind him when he triggered the Great Indian War, because, actually, Amherst had no army to speak of.
After the end of the Seven Years' War that brought Great Britain immense territorial gains but had cost a fortune, Lord Bute's Tory government had decided in 1762 to demote most of the large army still stationed in North America to cut expenses but to severe many officers' connections with the former Whig government as well. Bute had just survived a beginning political debacle due to a well aimed shot from the Secretary of Treasure Samuel Martin into the chest of the radical journalist John Wilkes during a duel and decided to root out any Whiggish tendencies wherever they might be found.
Besides the political hotbed, the cost of maintaining a large standing army overseas could probably not have been financed without additional taxation of the American colonies, such as a Stamp Act, in brief discussion in 1764 but finally dismissed for various reasons. However, the 2.000 soldiers Amherst had at his disposal were neither enough to much impress the French settlers in Canada who refused to swear their allegiance to King George to move places to their new settlements in Louisiana nor to lend weight or even credibility to the policy the British general pursued on the new Indian frontier.
When various Cherokee and Great Lakes people, mainly the Ottawa chief Pontiac, decided they'd had it with Amherst's arrogance and bullying and attacked settlements and undermanned British forts, a large portion of the continents English speaking population from Illinois to the Ohio and the Appalachians was fleeing for the East Coast. The war raged on for two years with almost genocidal dimensions on both sides, the Native's forces more or less openly supported with materiel by France until finally fresh British regiments arriving in Boston and New York were able to at least stop Pontiac from invading the East Coast.
In 1766 The following Treaty of Fort Ticonderoga drove a coach and six horses through the British gains of the Seven Years' War, in the former French territories of North America and Canada where the rebellion of the Franco-Canadians already had begun. The impotence of King George to protect his American subjects was one of the main reasons for the American Rebellion 10 years later.