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It would be hard for even an adult to fall over the side of a ship but there are always dangers, on land as well as on a ship and I would certainly be aware of what they were doing all the time. The best about RCI is that their children's clubs are some of the best afloat and your children would be well cared for whilst attending them. Neil.
I really don't think that RCI would be promoted as the child-friendly line that they are if the little cherubs keep falling over the side would they....it really takes some effort to fall over; ususally copious amounts of alcohol helps those that have.
If you have any worries or concerns then book inside cabins. On our last 2 cruises myself and my husband have an ouside cabin and our kids are opposite in an inside cabin. We always book early so we have a good choice available. This saves any worries.