What gamble does washington take to save his men from smallpox?

Inoculation. Washington tried this new therapy called inoculation. Basically, you'd infect your soldiers with a less virulent strain of the disease (in this case, Variola or Smallpox) so that they'd be immune to harsher diseases later. The Redcoats were already inoculated, giving them the advantage over the ragtag colonists, 1/4 of whom were already infected.

Inoculation which is when you infect your soldiers with small diseases so make them immune to big ones.