This is where the game gets messy. Random chance gives us a 60% win chance, but the likelihood of the group accepting a random team is very low as certain individuals are sure in their accusations of others (myself included). I don't have any good strategy for this one but, sorry Thief, I still think you're a spy. Don't pick yourself.
60% at random? I'm horrible at math, but that doesn't sound right at all.
The first person you randomly choose out of a pool of 10 has a 60% chance of being Resistance. The second person has either a 55.56% or 66.67% chance depending on whether the first was a spy or not. But we can ignore that since even 1 spy being chosen is too much. So the chance or randomly picking the correct people is 60%, 55.56%, 50%, 42.86%, and 33.33% for each successive pick. The chance of picking a spy is the inverse, or 40%, 45%, 50%, 57%, and 67%. In other words, a random team is a BAD idea. It actually gives the SPIES a 67%+ chance of winning.