The law of large numbers states that given a large enough sample size, the results average out.
It seems you are experiencing it's corollary though:
The law of truly large numbers states that given a large enough sample size, any outragious thing is likely to happen.

When I started playing risk I got the advice to always leave behind two armies on a country as garrison.

So I decided to do the math on how dearly a garrison in a country sells their hide when they get overrun by insurmountable odds.

Calculations:
Using m to calculate the odds of killing a ...