Well, it's probably true that to show-off is one of the honest answers. But what about having incredibly fun while doing it?
When reading about the arsenal of more or less fantastic gadgets and toys on yachts like Octopus and Lady Lola Shadow it is clear that at least some billionaires know how to have fun.
I know that we have many times, under different topics, mentioned a lot of amazing stuff for big boys (and maybe some big girls as well) to play with. I have however not found any topic dedicated specifically to toys.
Please contribute with links, info and stories! Maybe you have even succeeded in finding out some new stuff that not even Paul Allen has?