Suppose we are the god-emperor of a massive space civilization fighting a war on 3000 different planets at once against a rebel army. The outcomes of the battles determining control of the various planets are independent and on each individual planet we have a 70% chance of ending the galactic year in control. We need to end the galactic year in control of 1160 more planets than the rebels in order to crush them into oblivion. Estimate the probability we can crush them into oblivion at the end of the galactic year.