I have been working through Thorp's paper, and with some guidance have got as far as page 20, but I am now stuck with Thorp's result in Ex 6.2 (on that page) where I cannot get the result for $Cor(X_1, X_2)$, so if anyone is able to show the derivation of this it would be much appreciated. Thanks
I have found the answer. And it is a very dull one:
There is a typo in the paper, the first $Cor(X_1, X_2)$ is actually meant to be $Cov(X_1, X_2)$. There is a lesson here, and that is to read ahead before trying to replicate the results in a paper.