Assuming there are no other players in this scenario, the mother should say, "You will return him." Let us start by assuming that the croc plans to return the child. If the mother says "You will return him," then she guessed correctly and the croc will return the child. If the mother says, "You will eat him," then she guessed incorrectly, and consequently the croc will eat the child. However, this is exactly what the mother said the croc would do, so he is forced to return the child, but that leaves us back where we started, and on and on and on in a never-ending loop. Now let us assume that the croc plans to eat the child. If the mother says "You will return him," the croc will eat the child. If the mother says, "You will eat him," then she correctly predicts the croc's course of action and the croc is forced to return the child, but then again because the croc is returning the child and not eating him, the mother did not make the correct prediction, so the croc will eat the child; this is another endless loop. So, if the mother says you will return the child, she has a probability of getting the child back that is equal to the probability that the croc already decided to return the child. Of course 1 - (that probability) equals the probability of the child being eaten. However, if she tells the croc that he will eat the child, the result is a endless loop. Now at this stage the answer depends on other players in the scenario. If there are none, then as mentioned previously she should say, "You will return the child" because this is the best (only) chance for her to get the child back--saying "You will eat him" will result in the croc taking an infinite amount of time to come to a decision. However, if there are other players in the scenario, then the mother should say "You will eat him" to ensure the safety of the child while she runs for help--she can find a hunter to kill the croc while he is stuck in the endless loop, for instance.