The Buddhist doctrine of Anatman - no-self - is certainly true. The self you perceive is a conflux of influences, none of which have permanence.
There is every reason to believe you will be "reincarnated" into different iterations of your neurobiological brain throughout eternity. There is also good reason to suspect that not all of these neurobiologies will be tied to the same fate - again, assuming a bounded universe to which the Poincare theorem applies, it's plausible the universe will eventually reproduce a brain arbitrarily similar enough that your stream of perception would emerge into it (a clone would not suffice, nor would a computer simulation; it would have to be an exact replica of your brain developing as a fetus under the precise conditions of your moment of conception) which then "takes on a life of its own". And there is no reason to assume this brain wouldn't be subject to probability also - literal reincarnation, as your own stream of perception in your own body, with endless possibilities, infinitely good, infinitely bad, without end. But very early on into this process, "you" would cease being "you". Your perception endures, in a body genetically near-identical to yours, but its history should diverge fairly quickly in most iterations, most of the time subtly, sometimes radically. There should also be many near-you iterations which are too divergent from you for your perception to recur in it. "You", then, are simply a discontinuous stream of perception thrown into history.
There may be some kind of probabilistic distribution involved where the "yous" nearest "you" temporally are the most nearly identical to "you", shading off into entirely different existences gradually. Though a miscarriage would probably interrupt this process...
Also, Boltzmann brains. Lots and lots of Boltzmann brains.
Anyway, Buddhism is correct, except karma can only manifest once, but it might be a good idea to live well just in case probability comes into the equation.