He was visually terrified at the imagery of the emperors being unbeatable. "There is no way to beat them", "now you know why they've ruled the sea for so long", "you must have felt it in your biological instincts"... Does this sound like a "robot only doing logic choices"? No, it doesn't, which is why Killer explicitly confronts him on getting too emotional and fearing dying too much to oppose Kaido, even though he's regretting his decision of betraying the alliance.
Hawkins isn't a robot who only obeys the chances from his cards. He's a coward man completely terrified by the concept of "emperor"; in opposition, Kid challenges this legend this last chapter by assuring that nobody is invincible. Oda depicting a scenario in which Hawkins doesn't betray Kaido even if he has a 99% chance of dying would not only fit the character (the real character, not the facade you described) but would have been significantly more interesting than anything he chose to close his prediction subplot with.