Call it the ultimate spoiler: Richard Vale, a lecturer in the Statistics Department at the University of Canterbury, has developed a mathematical model to predict the fates of the characters in the next two Game of Thrones novels.
More specifically, Vale's goal is to determine the number of chapters that will be told from the point of view of each character. He's not predicting what the characters will do; rather he's inferring who will survive and become the main focus of the plot as the epic continues to unfold.
The approach that Vale has taken is to use the distribution of characters in chapters in the first five books to predict the distribution in the forthcoming novels.
As the Physics arXiv blog explains:
Vale begins with a single table of data which summarizes the number of chapters that each character has starred in so far. For example, the character Jon Snow starred in nine chapters in the first book, eight in the second, 12 in the third, none in the fourth and 13 in the fifth. The character Brienne starred in 8 chapters in the fourth book but in none of the others. And so on.
The question that Vale sets out to answer is what can be predicted about future books based only on this data from the existing ones. And his approach is entirely statistical so it does not include common sense assumptions such as the idea that a character killed off in the past is unlikely to star in the future.
Of course, Vale has to make a number of assumptions about the statistical nature of the data. For example, he assumes that the chapters in which a character stars follows Poisson distribution, which is one of the simplest to handle mathematically. It is based on the idea that events in a given time interval occur independently, like the number of decay events per second from a radioactive source, and are not related by some deeper connection.
Having created a model, Vale then runs a computer program to find the parameters in the model that best fit the data. And having found the best fits, he then uses the model to find the probability distributions of the number of chapters that each character will star in in book 6 and book 7. (He points out that book 7 is less interesting because the probabilities can be sharpened after the publication of book 6).
The results make clear predictions. For example, it shows that certain characters are unlikely to star in any chapters. It also makes predictions about whether one particular character is likely to be dead or not, following an ambiguous chapter in the fifth novel.
Vale readily acknowledges that there are several shortcomings in his model—it's based on a rather small set of data and it ignores the likelihood that other characters will be introduced. He is, however, able to make an educated guess as to how many new characters we'll see. If you're curious, you'll find that spoiler in the second to last paragraph in his paper.