When I was at the screen to choose a faction to start a campaign, I clicked on the map, hoping for some interactivity, but the color changed to a light tan.

After using assassins a bunch, as a purely 'intuitive' observation, it seems that the best chance is actually around a displayed 30% w/ a new assassin. Also, when I get into 40-50%, they've failed me a few out of many tries. Anyway, the displayed % seems funky, and I wish that it would just display the real %.