Godplayers is an extremely energetic and engaging novel, one in which the author is obviously having fun, and just as obviously a work by a writer who knows and loves the SF field.
The main action of the novel follows a young man from Australia named August Seebeck. His parents disappeared, presumed dead, when he was a boy, and he was raised by relatives, in particular his Aunt Miriam and later his Great-Aunt Tansy. He comes home to Tansy's house after herding cattle in the outback, to find that she claims dead bodies have been showing up in her bathtub. She's a bit dotty, and works as a psychic, so he tends to discount this, and goes to wash up. And naturally a dead body shows up soon after, carried through the mirror by two women, one of whom, Lune, is sufficiently beautiful that August is drastically smitten despite the unfortunate circumstances of their meeting. Especially when he notices that she has the same curious metallic design in her foot that he has. But Lune and her companion inform him that they will have to wipe his memory, and out comes the "green ray"...
Mysteriously, the memory wipe doesn't stick. Quickly August is involved in some very strange doings indeed. He tries to follow the mysterious women through the mirror, and in very rapid order indeed he is jumping from universe to universe. It soon comes clear that August is part of a family he has not suspected (the other members have significant names like Maybelline, and Juni, and Marchmain... see the pattern?), and that the family is engaged in something called the Contest of Worlds.
And so the novel goes, recomplicating again and again, as August desperately tries to make sense of things, to find his Aunt Tansy, and to learn the secret behind his new family and his parents' disappearance. He's also trying to forge a relationship with the beautiful Lune (one that develops perhaps just a bit implausibly quickly). In the process we visit numerous parallel worlds, and several different "levels" of the universe -- mostly based on real (if perhaps not precisely mainstream) physical theories. It's all great fun, very fast moving, clever stuff.
The afterword mentions as influences Fritz Leiber and Roger Zelazny. "Destiny Times Three" is the Leiber story Broderick mentions, while the obvious Zelazny parallel is Amber. And indeed the novel recalls those writers a bit, as well as perhaps Charles Stross' new series that has also been compared to Amber, The Merchant Princes. But Broderick's work is not simply hommage, nor is it derivative -- it is original SF that happily nods to its precursors. And it is, put simply, purely fun, and at the same time intriguing speculative SF.