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Go with Royal carribean as there is stacks for kids, with clubs and so much else, they cater for all children big time under 16 years, they even split age groups like 3-5 6-8 9-11 and 12-14 so all ages are around a range. Each range has it's own separateclub, IT, etc You may not see your kids all day, kids love it. Many kids pools and eating places for childen only, RCCL put a lot into the arrangements for the children.
Been 3 times over 3 years.
There is a good kids' club which we booked our 10-year-old son into on the first day but he made friends with some kids there and they did their own thing for the rest of the holiday. There are two swimming pools and a water slide, a games room, a pool table, a football/basketball court, chess, golf driving range, four jacuzzis and loads of space to play. There are TVs in all the rooms and the bars. Our son wasn't bored for a minute and there are bound to be other children there too.