Some of the ideas, such as the likelihood of two people in a group sharing a birthday, can be found in plenty of other places, but Havil goes into greater detail - for instance looking at the case of 3 or more people sharing a birthday. There are chapters on how to make two losing games into one winning one, on why the 13th of the month is more likely to be a Friday than any other day, on the hypervolume of hyperspheres, and plenty of other topics. (There does seem to be one mistake. Havil demonstrates a solid with infinite surface area and finite volume, and implies that one exists with the conditions reversed - but it doesn't. This is discussed in Learn from the Masters chapter 7).
There is are plenty of calculations in this book, but they don't require more than school level mathematics. Also I found that it was possible to follow the arguments without working through the mathematics - you can always go back later to fill in the detail. It would make an ideal gift for anyone who is keen on mathematics or who enjoys being puzzled by paradoxical ideas.