In this case: Where is the issue? If the ship survived 10 jumps, it is probably safe to make another one—the same decision could be done on earth, which exists in both relevant cases.
With sufficient intelligence, the robot could calculate a probability of 1-eps that there are robots from earth, even if earth could have developed without a robot-building species. The robot can use its own existence to update probabilities in both cases.
Uh, yes, you would program the robot that way. That’s the point.
In this case: Where is the issue? If the ship survived 10 jumps, it is probably safe to make another one—the same decision could be done on earth, which exists in both relevant cases.
With sufficient intelligence, the robot could calculate a probability of 1-eps that there are robots from earth, even if earth could have developed without a robot-building species. The robot can use its own existence to update probabilities in both cases.