 Actual causes can sometimes lower the probability of their effects in cases of preemption: Suppose that Billy and Suzy are aiming rocks at a bottle. Billy decides that he will give Suzy the opportunity to throw first; he will throw his rock just in case Suzy doesn’t throw hers. For mathematical convenience, we will assume that there is some small probability—0.1 say—that Billy does not faithfully execute his plan. Billy is a more accurate thrower than Suzy. If Billy throws his rock, there is a 90% chance that it will shatter the bottle; if Suzy throws, she has a 50% chance of success. Suzy throws her rock and Billy doesn’t; Suzy’s rock hits the bottle and smashes it. By throwing, Suzy lowered the probability of shattering from 81% (the probability that Billy would both throw and hit if Suzy hadn’t thrown) to 54.5% (accommodating the small probability that Billy will throw even if Suzy throws). Suzy’s throw preempts Billy’s throw: she prevents Billy from throwing, and substitutes her own, less reliable throw. Nonetheless, Suzy’s throw actually caused the bottle to shatter.